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Reception plate method for characterisation of structure-borne sound sources in buildings: Installed power and sound pressure from laboratory data
Applied Acoustics 70 (2009) 1431–1439
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Reception plate method for characterisation of structure-borne sound sources in buildings: Installed power and sound pressure from laboratory data M.M. Späh a,1, B.M. Gibbs b,* a b
Hochschule für Technik – University of Applied Sciences, Department of Civil Engineering, Building Physics and Economy, Schellingstrasse 24, 70174 Stuttgart, Germany Acoustics Research Unit, School of Architecture, University of Liverpool, Liverpool L69 3BX, United Kingdom
a r t i c l e
i n f o
Article history: Received 17 July 2007 Received in revised form 5 January 2009 Accepted 23 April 2009 Available online 28 May 2009 Keywords: Structure-borne sound Source characterisation Reception plate method
a b s t r a c t In a companion paper, a laboratory method is described to obtain the structure-borne sound power of machines before they are installed in heavy-weight buildings. The laboratory method is based on the concept of the reception plate. In this paper, the method is shown to provide appropriate input data for the prediction of the installed structure-borne power, and thence the resultant sound pressure level in rooms removed from the room containing the machine. Case studies of two common sources are described: a whirlpool bath and a water cistern. It is shown that the method can be incorporated into recently proposed standard prediction models and that sound pressure levels in buildings can be predicted. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In sound propagation in buildings, the structure-borne transmission often is the dominant contribution. In a companion paper, it is shown that the structure-borne sound power of a source can be simply evaluated in a laboratory by a reception plate method [1]. In this paper, a procedure is described for transforming the laboratory data in order to predict the structure-borne power into supporting floors and walls, when the machine is installed in a building (the installed power). In order to then predict the resultant sound pressure level in adjacent rooms, reference is made to calculation procedures for European standardisation. These procedures were developed for the prediction of sound transmission to adjoining rooms in heavyweight buildings, using laboratory measurements of the airborne sound insulation of walls and floors [2] and the impact sound insulation of floors [3] as input data. The prediction of sound pressure in heavy-weight buildings, from airborne, duct-borne and structure-borne sound sources, is now being addressed [4]. As input data, a measure of the ‘‘source strength” is required. For the case of structure-borne sound sources, the source strength is expressed as a power obtained in a laboratory by the reception plate method [1]. It is shown that the laboratory data obtained can be transformed into the installed power and thence the resultant sound pressure level in the far
* Corresponding author. Tel.: +44 1517944937; fax: +44 1517944944. E-mail address: [email protected] (B.M. Gibbs). 1 Present address: Fraunhofer Institut Bauphysik, Nobelstr. 12, 70569 Stuttgart, Germany. 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.04.011
field. The prediction model is described, along with two case studies. 2. Structure-borne sound power The structure-borne sound power P from a source, such as a machine in a building, into a connected receiver structure, such as a floor, is the real part of the complex power W, which can be described in terms of source activity and mobility (ratio of response velocity to applied force) and receiver mobility. The activity can be in the form of velocity of the free (uncoupled) source or the blocked force, i.e. when the source is attached to an inert receiving structure. For a single contact and single component of excitation [5],
P ¼ Re½W ¼
jv Sf j2 jY S þ Y R j2
Re½Y R
ð1Þ
where v Sf is the root mean square free velocity of the source, and Y S and Y R are the complex source and receiver mobility, respectively. Previous work has shown that the main mechanism of vibration energy transfer, from sources into buildings, is mainly through excitation of bending vibration fields on the attached structure, which is generally a structural plate [6,7]. In a companion paper, the reception plate method is proposed as a laboratory test [1]. The method is based on the principle of steady-state energy balance between connected systems. The total emission of a source, through multiple contacts and components of excitation, equals the bending energy loss in the supporting plate, e.g. a reception plate. The reception plate power Prec. is given as,
Prec: ¼ gxmv~ 2
ð2Þ
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where m is the mass of the plate and v~ 2 is the mean square velocity averaged over the plate surface. The plate losses (at the edges of the attached walls/floors, internal losses and due to acoustic radiation) sum to the total loss factor g. The prototype reception plate considered was a free 100 mm concrete plate, of dimensions 2.8 m 2.0 m, where the plate losses were adjusted by supporting the plate edges with resilient pads of high internal damping [1]. This gave a dynamic behaviour where the lower vibration modes of the plate are significantly damped. The infinite plate power is proposed in order to correct the properties of the finite reception plate, in particular for its modal behaviour. It, therefore, is suitable for comparison of source data, measured on different reception plates of the same thickness and material, in different laboratories. The infinite plate power is given by,
Pinfinite ¼ P rec:
Re Y infinite Re Y rec:
ð3Þ
rec: is the spatial average of the point mobility for forces where Y perpendicular to the reception plate. Yinfinite is usually termed the characteristic mobility and corresponds to the plate of same thickness and material as that of the reception plate but is of infinite extent [8],
1 ffi Y infinite ¼ pffiffiffiffiffiffiffiffiffiffi 8 B0 m00
ð4Þ
where the plate bending stiffness is 3
B0 ¼
E h 1 l2 12
ð5Þ
and m00 is the mass per unit area, E, the modulus of elasticity, l, the Poisson’s ratio and h, the plate thickness. Yinfinite is frequency invariant and real-valued and therefore is the same as the desired quantity Re(Yinfinite). The term ‘characteristic’ will not be used in this paper, in order to avoid confusion concerning the separate term ‘characteristic power’, proposed by Moorhouse [9]. The spatial average of the point mobility, for forces perpendicular to the reception plate, represents the mean receiver mobility. The infinite plate power is transformed into the installed power Pinst. for the source when in a building, as follows:
Pinst: ¼ Pinfinite
ReðY build: Þ ReðY infinite Þ
ð6Þ
where ReðY build: Þ is the real part of the mobility of the building element. The simplest estimate of the real part of the building element mobility again is the infinite plate mobility and this often is sufficient to describe mid- and high-frequency plate behaviour. At low frequencies, floors and walls display modal behaviour with spatial and spectral variations in point mobility. The modal behaviour is sensitive to the edge conditions, which seldom are known precisely in buildings. However, an upper and lower limit to the point mobility is obtainable and thence for the installed power. The maximum mobility is given by [10]
Y max ¼ ReðY infiniite Þ coth
1 b
ð7Þ
where
b¼
4 mxB ReðY infinite Þ
ð8Þ
and xB = xg is the modal spacing. The minimum mobility is given by,
Y min ¼ ReðY infinite Þ= coth
1 b
ð9Þ
For these estimates, only the dimensions of the building plate and the loss factor are required. The latter can be approximated from empirical data [11–13]. The maximum and minimum installed power then yields the maximum and minimum sound pressure level, respectively, in rooms removed from the source.
3. Experimental validation A reference floor of 180 mm concrete, in a transmission suite, was selected for experimental validation. It was part of a laboratory transmission suite assembly of six rooms (Fig. 1). The transmission suite assembly included an opening for lightweight timber elements, and the reference floor had one edge effectively free, without connection to other heavy-weight building elements. However, a lightweight removable wall was installed at the free edge to form an enclosed room on the upper level. Opposite to it, a masonry wall formed a cross-junction with the floor, see Fig. 2. The walls were of 115 mm autoclaved aerated concrete, plastered on both surfaces. The mass per unit area was 90 kg/m2. Both walls were erected on strips of 10 mm polystyrene, also placed between the walls and the transmission suite walls. The top of both walls was sealed with mortar. The reference floor allowed the measurement of a vertical–diagonal transmission from the floor plate across the cross-junction. As the acoustical behaviour of the reference floor is somewhat different to that of the elements in buildings, its main characteristics are described below. 3.1. Loss factor The loss factor of building elements in several countries has been measured in situ and reported in [11–14]. The measurement surveys were of homogeneous heavy-weight building constructions such as masonry walls and concrete floors. Empirical values, obtained in France [11] and Germany [12], are similar. The values obtained in Spain are slightly higher [13], with values in the United Kingdom the highest [14]. The loss factor of the reference floor was obtained by a decay method, over 5 to 25 dB (T20), using an impulse response method with Multiple Length Sequence (MLS). The reverberation time was recorded at three excitation positions and at least four registration positions in one-third octave bands. The floor loss factors are shown in Fig. 3, along with empirical values from [12]. The low value is thought to be due to the low losses within the whole transmission suite assembly, which is resiliently supported to reduce background sound and vibration levels. The test assembly basically consists of two rooms, one above the other, without connections to the walls and floors that transmit energy to the far field. 3.2. Floor mobility The mobility of finite plates can be calculated by assuming ideal boundary conditions [15]. For the prediction of the point mobility of the reference floor, a simply supported condition was assumed for the three edges with attached heavy-weight elements and a free condition for the edge with the lightweight partition wall. For the damping, a regression of the measured loss factor of the floor plate was utilised (see Fig. 3). The mobility was measured by an electro-dynamic shaker and accelerometer pair. Results are shown in Fig. 4, along with the infinite plate mobility and maximum point mobility according to [10]. The measured mobility has much less-pronounced peaks and dips, and the overall value is higher than predicted. The lowest resonance frequency of the real plate is lower than predicted, and there are more resonance peaks than predicted. This behaviour is thought to be due to global
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Fig. 1. Vertical section of transmission suite with reference floor.
Reference floor
Aereated autoclaved concrete Polystyrene interlayer
Aereated autoclaved concrete
Fig. 2. Detail of the cross-junction in the transmission suite.
Fig. 4. Measured and predicted point mobility of the reference floor. Also shown is the infinite plate and maximum mobility.
Fig. 3. Measured loss factor of reference floor with regression curve. Also shown is the value according to [12]. Fig. 5. Velocity measurement traverse on reference floor.
resonances, i.e. due to resonances of connected building elements, which return energy to the floor plate. This behaviour has also been observed by Craik [14]. At frequencies above 800 Hz, the measured mobility increases due to local stiffness effects. The abrupt phase change above 1000 Hz at the shaker measurement is thought to be due to the resonance frequency of the stringer connection between the shaker and the force transducer. The dynamic characteristics of the measured floor can be assumed to lie between two asymptotic conditions. First, the floor is heavily damped and the mobility tends to that of an infinite plate. Second, the behaviour is that of a finite plate with high mod-
al density, giving a diffuse sound field on the plate. In the second case, the average response again would be that of an infinite plate [16]. To evaluate which assumption is the most appropriate, a study of the spatial variation in floor velocity was conducted. 3.3. Spatial variation of floor velocity The spatial variation in floor velocity was measured. A traverse was selected with locations marked at 250 mm intervals away from the source as shown in Fig. 5. At each accelerometer position,
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the velocity of the plate was recorded. Simultaneously, the contact velocity from the shaker was recorded. In Fig. 6, the velocity level differences are shown in one-third octave bands as a function of distance from the source. The predicted difference, for a pure direct field, is also shown. Results indicate strong modal behaviour at frequencies below 160 Hz. For the 100 Hz third-octave band, the path length is within one bending wavelength. For frequencies of 160 Hz and above, there is some agreement with the predicted decrease up to a distance of 2 m. Diffuse field behaviour is generally not observed. The influence of the direct field on the sound transmission across the junction was considered by moving a shaker along the same traverse line on the floor, shown in Fig. 5. At each position, the direct power was recorded, along with the resultant sound pressure level in the room diagonally below the floor, at two microphone positions and as an average (see Fig. 1). For a plate behaviour dominated by a direct field, it would be expected that the resultant sound pressure level would rise as the shaker approached the cross-junction. The measured sound pressure levels, normalised with respect to the input power from the shaker, are shown in Fig. 7, in third octave bands from 63 Hz to 1 kHz. A systematic rise of sound pressure level is not observed. This suggests that the sound transmission does not occur across one junction only, but that the whole transmission suite assembly, including the side walls, is involved in the process. The transmission is insen-
sitive to the excitation location, despite direct-field behaviour on the excited floor plate. 3.4. Case study A whirlpool bath was selected for this study, shown in Fig. 8. The bath was of acrylic resin, supported by a frame of 50 mm box steel sections. The frame contained a water pump, fan and associated pipe-work. The bath was supported on 8 mounts. Each mount consisted of a threaded rod, with a rigid connection, giving the worst-case condition in terms of noise emission. It ensured a well-defined situation with good reproducibility. The whirlpool bath was first attached to the 100 mm reception plate and activated, and the power obtained according to Eq. (2). Results are shown in Fig. 9 for the operation of the water pump at full speed. Also shown is the infinite plate power from Eq. (3). For this transformation, the average point mobility of the reception plate was obtained from the measured values at all eight contact points, using a calibrated impulse hammer. Results show that the deviations are greatest (3 dB) at 50 Hz. The generally small difference, between the infinite plate power and the reception plate power, is because of the ‘rain-on-the-roof’ effect of the distributed contacts. In addition, the transformation of narrow band into third octave band values reduces the influence of spatial variation in mobility.
Fig. 6. Level difference between velocity at excitation position and at distance from the source, and the theoretical difference for a direct field.
M.M. Späh, B.M. Gibbs / Applied Acoustics 70 (2009) 1431–1439
Fig. 7. Normalised sound pressure level in room diagonally below reference floor for a shaker source traverse.
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Fig. 10. Predicted installed power for whirlpool bath on reference floor, with maximum and minimum values.
maximum and minimum mobility of the floor (Eqs. (7) and (9)) gave the predicted maximum and minimum installed power, shown in Fig. 10. The maximum and minimum values are about 10 dB from the mean value at 50 Hz and about 3 dB at 1 kHz, respectively. 4. Sound pressure level from installed power
Fig. 8. Whirlpool bath.
The prediction of the resultant sound pressure level from the installed structure-borne power is possible through the recent draft of EN 12354 Part 5 [4]. At present, the method is restricted to heavy-weight homogeneous building constructions. The approach is to calculate the sound transmission for all paths, direct and first order, where one junction lies between the excited and the radiating building element in an adjacent room. The contributions of all paths sum to the total sound transmission. The paths are regarded as independent, and the sound transmission of each path can be calculated separately. An equivalent incident airborne sound power is obtained for each path, which gives the same input power into the excited building element as the structure-borne sound source. In the following, airborne excitation variables are denoted by index a and structure-borne excitation variables by index s. The relation between airborne and structure-borne power is given by Gerretsen [17] 2 P2struc;n;ij W inc;i;a W rad;j Pstruc;n;ij ¼ W inj;i;s q0 c0 W inj;i;s W inc;i;a q0 c0 W rad;j
ð10Þ
where Pstruc,n,ij is the normalised sound pressure in the receiving room, caused by the structure-borne sound transmission via the elements i and j; Winj,i,s is the structure-borne sound power into the ith building element; and Winc,i,a is the airborne sound power incident on the same building element. The normalised sound pressure level for the transmission path i and j is given by,
Lp;n;:ij ¼ LW;i;s þ 10 lg
W inc;i;a 4 Rij þ 10 lg Aref W inj;i;s
ð11Þ
where Ri,j is given by [2]:
Ri;situ Rj;situ lij SS þ DRi;situ þ þ K ij 10 lg pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 10 lg pffiffiffiffiffiffiffiffi 2 2 ai;situ aj;situ Si Sj
Fig. 9. Reception plate power and the infinite plate power of the whirlpool bath, located centrally on the plate.
Ri;j ¼
The installed power was predicted according to Eq. (6), using the mobility of a 180 mm concrete plate of infinite extent. The
where Ri,j,situ is the sound reduction index of the elements i and j in situ and Kij is the vibration reduction index of the building
ð12Þ
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elements at the junction. Si,j is the surface area of the flanking building elements and SS the surface area of the separating element. The ratio of the powers in (10) gives rise to the adjustment term, given in [4]:
Ds;a;i ¼ 10 lg
2pm00i 2:2si q0 c0 T s;i ri
ð13Þ
with m00 the mass of unit area, si the airborne sound transmission factor for resonant transmission, Ts,i the structural reverberation time and ri the radiation efficiency of element i. The normalised sound pressure level for the transmission path ij can now be written as,
Lp;n;ij ¼ LW;i;s Ds;a;i Rij 10 lg
Aref Si 10 lg Sc 4
ð14Þ
The structure-borne sound power LW,i,s is obtained from the transformed reception plate power. The total normalised sound pressure level Lp,n,s from all paths is obtained from logarithmic summation. The diagonal transmission considered consists of two paths (see Fig. 1). The model of EN 12354 is essentially based on Statistical Energy Analysis (SEA), and each building element should exhibit the properties of an ideal SEA subsystem [14]. Each should support resonant modes of vibration in the frequency range of interest; there should be a uniform energy density (by virtue of a reasonably diffuse field); the subsystems should be weakly coupled and the system should be moderately damped. In buildings, most subsystems only approximate these conditions, and the accuracy of the SEA prediction is usually determined by the approximations. Nevertheless, SEA has been shown to be suitable for homogeneous isotropic building element in masonry buildings [14]. Unlike the prediction model of EN 12354, SEA is not restricted to the first-order flanking transmission and more than one junction on each path can be considered, and therefore, the transmission to remote rooms can be predicted.
Fig. 11. Cistern frame without ceramic.
4.1. Case studies The first case considered was the whirlpool bath described earlier (Fig. 8). The bath has a set of six venturi-valves at the side of the tub, where water is forced in by the water pump. The pressure of the water could be regulated and air added at the valves. Additionally, there was a second system with 16 air valves operated by a fan. The two systems operated separately or simultaneously. The bath weight was 85 kg and was filled with 198 l of water for all measurements. Preliminary measurements of whirlpool baths in domestic situations confirmed that the frequencies of interest are below 2 kHz [7]. Additionally, a preliminary investigation confirmed that the excitation of the supporting floor was predominantly by forces perpendicular to the floor, although moment excitation can assume importance in a few frequency bands [7]. When attached to the reception plate, the bath constitutes a high mobility source with point mobility 10 dB or more than the point mobility of the receiving element [1]. Therefore, the data transformation described in this paper is applicable. The second case was a cistern frame. The system consists of a frame, with cistern, valves, pipe work and ceramic (Fig. 11). This source has a time-dependent excitation; the strongest excitation occurs at the beginning of the flushing cycle. For installations on heavy homogeneous walls and lightweight double-leaf walls the frequencies of interest are again below 2 kHz. The point mobility of the cistern frame was measured prior to installation, and the results are shown in Fig. 12. Also shown is the measured mobility of the reception plate. The source mobility is between one and two orders of magnitude greater than the receiver mobility. Below
Fig. 12. Point mobility at one contact of cistern frame, along with the reception plate mobility at one contact; also shown is the infinite plate mobility.
80 Hz, the source mobility displays mass-like behaviour. Between 80 Hz and 1000 Hz, the source mobility displays stiffness-controlled behaviour. At the minimum at 80 Hz, it is still 10 dB above the receiver mobility, indicating a high mobility source condition over the whole frequency range. The sources were attached in turn to the reception plate, and the average plate velocity was recorded. In both cases, a rigid connection between source and plate was obtained using super glue, giving a reliable contact with good reproducibility. For the whirlpool bath, results are shown for the operation of the water pump at full speed with no added air at the venturi-valves. With the source in operation, the velocity at 12 accelerometer positions was measured and the spatial average obtained to give the reception plate power from Eq. (1). For the cistern frame, the spatial average plate velocity was measured at several stages during the cycle of operation. Equivalent plate velocity levels Leq over 125 ms were recorded in third octave
M.M. Späh, B.M. Gibbs / Applied Acoustics 70 (2009) 1431–1439
bands. As the flushing cycles showed a relative poor repeatability, 10 cycles of operation were recorded and averaged. A typical time signal is shown in Fig. 13 for the 400 Hz third octave band. The initial flushing was defined as for the time between 0 and 5 s, giving a maximum power. The installed power was calculated from Eq. (3) and is shown in Figs. 10 and 14 for the whirlpool bath and cistern, respectively. Diagonal transmission, from the floor plate across the junction, was considered. In addition to the installed power, further data are required. Initially, the sound reduction index was calculated according to EN 12354 Part 1 [2], based on theoretical considerations. The structural reverberation times and vibration reduction indices Kij were obtained from measured data. As the latter were gained by steady-state vibration measurements, relevant transmission via other paths in the transmission suite, besides the first-order junction, was included. For the whirlpool bath, the predicted sound pressure levels in the receiving room are shown in Fig. 15, for the two transmission paths and the sum. At mid and high frequencies, both paths are equally important. At low frequencies, the heavier floor plate is the dominant path, due to a lower critical frequency. The critical
Fig. 13. Velocity–time signal at 400 Hz on reception plate.
Fig. 14. Predicted installed power from cistern frame on reference floor, with maximum and minimum values, for the flushing cycle.
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frequency of the wall is approximately 200 Hz, above which path 1 assumes importance. In order to measure the resultant sound pressure level, the whirlpool bath was installed on the floor away from the transmission junction, with no contact to the surrounding walls. Undersampling of the sound pressure at low frequencies was partly compensated for by considering the energy density at the wall boundaries of a room relative to the central positions, according to Waterhouse [18]. The corrected measured values were compared with the predicted values. The predicted and measured sound pressure levels in the room diagonally below the excited floor are shown in Fig. 16. Also shown are the maximum and minimum predicted values. The predicted levels overestimate the measured levels by about 5 dB. This is possibly due to the conservative prediction of the transmission loss of the building elements. The discrepancy at low frequencies is thought to be caused additionally by weak coupling of wall and floor bending modes with room modes in the receiving room. This is generally the reason for large deviations in sound reduction index of building elements at low frequencies. In the given case, the radiation efficiency of the building elements, which is implicitly incorporated into the sound
Fig. 15. Predicted normalised sound pressure levels by the two transmission paths.
Fig. 16. Measured (corrected) and predicted normalised sound pressure levels due to whirlpool bath.
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5. Conclusions
Fig. 17. Measured (corrected) and predicted normalised sound pressure levels of cistern.
A laboratory reception plate test method has been developed to determine the structure-borne sound power of mechanical sources when installed in heavy-weight buildings. The installed power can be given as a mean, maximum and minimum value. These values form input data for predicting the resulting sound pressure levels in rooms removed from the source. Recent research seeks to extend the approach to lightweight building constructions [19]. A study of the behaviour of a floor, with three fixed edges and one edge effectively free, shows that the sound transmission does not occur across one junction only, but through the whole transmission suite assembly, and the resultant sound pressure level is insensitive to source location. Two sources have been considered: a whirlpool bath representative of complex sources with powerful active components; a cistern representative of time-variant sources. For the whirlpool bath, predicted levels overestimated measured levels by about 5 dB at low frequencies. In this case, the measurement tracked the prediction of the minimum value. The overestimation is possibly due to the conservative prediction of the sound reduction index of EN 12354 Part 1 Appendix B. For the cistern, there was agreement between the predicted and measured values at mid- and high frequencies. At frequencies below 125 Hz, again the predicted values were greater than the measured values, but there is agreement with the minimum predicted values. The generally better agreement, for the cistern, could be the result of the close proximity of the source to the transmitting junction, which might lead to additionally near-field excitation and transmission. The method is applicable to mechanical installations which connect to more than one building element. A machine in a corner location could have contact with up to three surfaces. A prototype three-plate laboratory reception system has been constructed where the mutually perpendicular plates are structurally isolated [20]. Each plate acts as an independent reception plate and three reception plate powers can be obtained. The process of predicting the installed powers and then the resultant sound pressure levels is as before, but three sound pressure levels are summed up to give the total.
Acknowledgements
Fig. 18. Measured (corrected) and predicted normalised sound pressure levels for the maximum output of cistern.
reduction index, is influenced by modal coupling. As a single-value comparison, the A-weighted sound pressure level was calculated for the frequency range from 50 to 1600 Hz. The predicted value is 41.8 dB(A), and the measured value is 35.9 dB(A). The same transmission path was considered for the cistern frame source, which was installed on the same floor, this time close to the separating wall. All other connections to the building elements were avoided, including the normally necessary pipes. The predicted normalised sound pressure level is shown in Fig. 17, along with the corrected measured values. Again, the maximum and minimum predicted values are also shown. The predicted and measured values, at mid and high frequencies, are within 3 dB. At low frequencies, the measured values are below the predicted values, again because of weak coupling of the wall/floor modes to room modes. The minimum predicted levels are in agreement with the measured levels at low frequencies. The predicted A-weighted sound pressure level is 31.8 dB(A); the measured value is 30.0 dB(A). Similar behaviour was observed at the maximum power of the cistern, shown in Fig. 18.
The authors gratefully acknowledge the contributions of HeinzMartin Fischer of Stuttgart University of Applied Science, Werner Scholl of Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Michel Villot of CSTB, Grenoble, and Qi Ning and Gary Seiffert of the Acoustics Research Unit of Liverpool University. References [1] Späh MM, Gibbs BM. Reception plate method for characterisation of structureborne sound sources in buildings: assumptions and application. Appl Acoust 2009;70:361–8. [2] EN 12354-1. Building acoustics – estimation of acoustic performance of buildings from the performance of elements. Part 1: airborne sound insulation between rooms; 2000. [3] EN 12354-2. Building acoustics – estimation of acoustic performance of buildings from the performance of elements. Part 2: impact sound insulation between rooms; 2000. [4] prEN 12354-5. Building acoustics – estimation of acoustic performance of building elements from the performance of elements – Part 5: sound levels due to service equipment; 2004. [5] Mondot JM, Petersson BAT. Characterisation of structure-borne sound sources: the source descriptor and the coupling function. J Sound Vib 1987;114(3):507–18. [6] Moorhouse AT, Gibbs BM. Measurement of structure-borne sound emission from resilient mounted machines in situ. J Sound Vib 1995;180(1):143–61. [7] Späh MM. Characterisation of structure-borne sound sources in buildings, Ph.D. Thesis, University of Liverpool; 2006.
M.M. Späh, B.M. Gibbs / Applied Acoustics 70 (2009) 1431–1439 [8] Cremer L, Heckl M. Körperschall (structure-borne sound). Springer-Verlag; 1996. [9] Moorhouse AT. On the characteristic power of structure-borne sound sources. J Sound Vib 2001;248(3):441–59. [10] Moorhouse AT, Gibbs BM. Calculation of the mean and maximum mobility for concrete floors. Appl Acoust 1995;45:227–45. [11] Acoubat: Manuel Technique du Logiciel Acoubat V2.1, CSTB Grenoble, technical documentation; 1997. [12] Späh MM, Blessing S, Fischer H-M. Verification of the calculation model for airborne sound insulation according to EN 12354-1 for homogenous heavyweight buildings, Part 1: influence of the input data. In: Proc. DAGA 2001, Hamburg (in German); 2001. [13] Esteban A, Cortés A, Arribillaga O. In situ loss factor in Spanish hollow constructions: improving EN 12354‘s accuracy. In: Proc. Inter Noise 2004, Prague; 2004. [14] Craik RJM. Sound transmission through buildings using statistical energy analysis. England: Gower Publishing Limited; 1996.
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[15] Fahy F, Walker J. Advanced applications in acoustics, noise and vibration, chapter 9: mobility and impedance methods in structural dynamics. London: E&FN Spon; 2004. [16] Skudrzyk E. The mean value method of predicting the dynamic response of complex vibrators. J Acoust Soc Am 1981;67:347–59. [17] Gerretsen E. Additional information on structure-borne sound transmission: related to CEN/TC126/WG2 N265 – final draft prEN 12354-5, Document CEN/ TC126/WG2 N266. Delft; 2005. [18] Waterhouse RV. Interference patterns in reverberant sound fields. J Acoust Soc Am 1955;27(2):247–58. [19] Gibbs BM, Cookson R, Qi N. Vibration activity and mobility of structure-borne sound sources by a reception plate method. J Acoust Soc Am 2008;123(6):4199–209. [20] Späh MM, Fischer H-M, Gibbs BM. New laboratory for the measurement of structure-borne sound power of sanitary installations. In: Proc. Forum Acusticum, Budapest; 2005.
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Reception plate method for characterisation of structure-borne sound sources in buildings: Installed power and sound pressure from laboratory data M.M. Späh a,1, B.M. Gibbs b,* a b
Hochschule für Technik – University of Applied Sciences, Department of Civil Engineering, Building Physics and Economy, Schellingstrasse 24, 70174 Stuttgart, Germany Acoustics Research Unit, School of Architecture, University of Liverpool, Liverpool L69 3BX, United Kingdom
a r t i c l e
i n f o
Article history: Received 17 July 2007 Received in revised form 5 January 2009 Accepted 23 April 2009 Available online 28 May 2009 Keywords: Structure-borne sound Source characterisation Reception plate method
a b s t r a c t In a companion paper, a laboratory method is described to obtain the structure-borne sound power of machines before they are installed in heavy-weight buildings. The laboratory method is based on the concept of the reception plate. In this paper, the method is shown to provide appropriate input data for the prediction of the installed structure-borne power, and thence the resultant sound pressure level in rooms removed from the room containing the machine. Case studies of two common sources are described: a whirlpool bath and a water cistern. It is shown that the method can be incorporated into recently proposed standard prediction models and that sound pressure levels in buildings can be predicted. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In sound propagation in buildings, the structure-borne transmission often is the dominant contribution. In a companion paper, it is shown that the structure-borne sound power of a source can be simply evaluated in a laboratory by a reception plate method [1]. In this paper, a procedure is described for transforming the laboratory data in order to predict the structure-borne power into supporting floors and walls, when the machine is installed in a building (the installed power). In order to then predict the resultant sound pressure level in adjacent rooms, reference is made to calculation procedures for European standardisation. These procedures were developed for the prediction of sound transmission to adjoining rooms in heavyweight buildings, using laboratory measurements of the airborne sound insulation of walls and floors [2] and the impact sound insulation of floors [3] as input data. The prediction of sound pressure in heavy-weight buildings, from airborne, duct-borne and structure-borne sound sources, is now being addressed [4]. As input data, a measure of the ‘‘source strength” is required. For the case of structure-borne sound sources, the source strength is expressed as a power obtained in a laboratory by the reception plate method [1]. It is shown that the laboratory data obtained can be transformed into the installed power and thence the resultant sound pressure level in the far
* Corresponding author. Tel.: +44 1517944937; fax: +44 1517944944. E-mail address: [email protected] (B.M. Gibbs). 1 Present address: Fraunhofer Institut Bauphysik, Nobelstr. 12, 70569 Stuttgart, Germany. 0003-682X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2009.04.011
field. The prediction model is described, along with two case studies. 2. Structure-borne sound power The structure-borne sound power P from a source, such as a machine in a building, into a connected receiver structure, such as a floor, is the real part of the complex power W, which can be described in terms of source activity and mobility (ratio of response velocity to applied force) and receiver mobility. The activity can be in the form of velocity of the free (uncoupled) source or the blocked force, i.e. when the source is attached to an inert receiving structure. For a single contact and single component of excitation [5],
P ¼ Re½W ¼
jv Sf j2 jY S þ Y R j2
Re½Y R
ð1Þ
where v Sf is the root mean square free velocity of the source, and Y S and Y R are the complex source and receiver mobility, respectively. Previous work has shown that the main mechanism of vibration energy transfer, from sources into buildings, is mainly through excitation of bending vibration fields on the attached structure, which is generally a structural plate [6,7]. In a companion paper, the reception plate method is proposed as a laboratory test [1]. The method is based on the principle of steady-state energy balance between connected systems. The total emission of a source, through multiple contacts and components of excitation, equals the bending energy loss in the supporting plate, e.g. a reception plate. The reception plate power Prec. is given as,
Prec: ¼ gxmv~ 2
ð2Þ
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where m is the mass of the plate and v~ 2 is the mean square velocity averaged over the plate surface. The plate losses (at the edges of the attached walls/floors, internal losses and due to acoustic radiation) sum to the total loss factor g. The prototype reception plate considered was a free 100 mm concrete plate, of dimensions 2.8 m 2.0 m, where the plate losses were adjusted by supporting the plate edges with resilient pads of high internal damping [1]. This gave a dynamic behaviour where the lower vibration modes of the plate are significantly damped. The infinite plate power is proposed in order to correct the properties of the finite reception plate, in particular for its modal behaviour. It, therefore, is suitable for comparison of source data, measured on different reception plates of the same thickness and material, in different laboratories. The infinite plate power is given by,
Pinfinite ¼ P rec:
Re Y infinite Re Y rec:
ð3Þ
rec: is the spatial average of the point mobility for forces where Y perpendicular to the reception plate. Yinfinite is usually termed the characteristic mobility and corresponds to the plate of same thickness and material as that of the reception plate but is of infinite extent [8],
1 ffi Y infinite ¼ pffiffiffiffiffiffiffiffiffiffi 8 B0 m00
ð4Þ
where the plate bending stiffness is 3
B0 ¼
E h 1 l2 12
ð5Þ
and m00 is the mass per unit area, E, the modulus of elasticity, l, the Poisson’s ratio and h, the plate thickness. Yinfinite is frequency invariant and real-valued and therefore is the same as the desired quantity Re(Yinfinite). The term ‘characteristic’ will not be used in this paper, in order to avoid confusion concerning the separate term ‘characteristic power’, proposed by Moorhouse [9]. The spatial average of the point mobility, for forces perpendicular to the reception plate, represents the mean receiver mobility. The infinite plate power is transformed into the installed power Pinst. for the source when in a building, as follows:
Pinst: ¼ Pinfinite
ReðY build: Þ ReðY infinite Þ
ð6Þ
where ReðY build: Þ is the real part of the mobility of the building element. The simplest estimate of the real part of the building element mobility again is the infinite plate mobility and this often is sufficient to describe mid- and high-frequency plate behaviour. At low frequencies, floors and walls display modal behaviour with spatial and spectral variations in point mobility. The modal behaviour is sensitive to the edge conditions, which seldom are known precisely in buildings. However, an upper and lower limit to the point mobility is obtainable and thence for the installed power. The maximum mobility is given by [10]
Y max ¼ ReðY infiniite Þ coth
1 b
ð7Þ
where
b¼
4 mxB ReðY infinite Þ
ð8Þ
and xB = xg is the modal spacing. The minimum mobility is given by,
Y min ¼ ReðY infinite Þ= coth
1 b
ð9Þ
For these estimates, only the dimensions of the building plate and the loss factor are required. The latter can be approximated from empirical data [11–13]. The maximum and minimum installed power then yields the maximum and minimum sound pressure level, respectively, in rooms removed from the source.
3. Experimental validation A reference floor of 180 mm concrete, in a transmission suite, was selected for experimental validation. It was part of a laboratory transmission suite assembly of six rooms (Fig. 1). The transmission suite assembly included an opening for lightweight timber elements, and the reference floor had one edge effectively free, without connection to other heavy-weight building elements. However, a lightweight removable wall was installed at the free edge to form an enclosed room on the upper level. Opposite to it, a masonry wall formed a cross-junction with the floor, see Fig. 2. The walls were of 115 mm autoclaved aerated concrete, plastered on both surfaces. The mass per unit area was 90 kg/m2. Both walls were erected on strips of 10 mm polystyrene, also placed between the walls and the transmission suite walls. The top of both walls was sealed with mortar. The reference floor allowed the measurement of a vertical–diagonal transmission from the floor plate across the cross-junction. As the acoustical behaviour of the reference floor is somewhat different to that of the elements in buildings, its main characteristics are described below. 3.1. Loss factor The loss factor of building elements in several countries has been measured in situ and reported in [11–14]. The measurement surveys were of homogeneous heavy-weight building constructions such as masonry walls and concrete floors. Empirical values, obtained in France [11] and Germany [12], are similar. The values obtained in Spain are slightly higher [13], with values in the United Kingdom the highest [14]. The loss factor of the reference floor was obtained by a decay method, over 5 to 25 dB (T20), using an impulse response method with Multiple Length Sequence (MLS). The reverberation time was recorded at three excitation positions and at least four registration positions in one-third octave bands. The floor loss factors are shown in Fig. 3, along with empirical values from [12]. The low value is thought to be due to the low losses within the whole transmission suite assembly, which is resiliently supported to reduce background sound and vibration levels. The test assembly basically consists of two rooms, one above the other, without connections to the walls and floors that transmit energy to the far field. 3.2. Floor mobility The mobility of finite plates can be calculated by assuming ideal boundary conditions [15]. For the prediction of the point mobility of the reference floor, a simply supported condition was assumed for the three edges with attached heavy-weight elements and a free condition for the edge with the lightweight partition wall. For the damping, a regression of the measured loss factor of the floor plate was utilised (see Fig. 3). The mobility was measured by an electro-dynamic shaker and accelerometer pair. Results are shown in Fig. 4, along with the infinite plate mobility and maximum point mobility according to [10]. The measured mobility has much less-pronounced peaks and dips, and the overall value is higher than predicted. The lowest resonance frequency of the real plate is lower than predicted, and there are more resonance peaks than predicted. This behaviour is thought to be due to global
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Fig. 1. Vertical section of transmission suite with reference floor.
Reference floor
Aereated autoclaved concrete Polystyrene interlayer
Aereated autoclaved concrete
Fig. 2. Detail of the cross-junction in the transmission suite.
Fig. 4. Measured and predicted point mobility of the reference floor. Also shown is the infinite plate and maximum mobility.
Fig. 3. Measured loss factor of reference floor with regression curve. Also shown is the value according to [12]. Fig. 5. Velocity measurement traverse on reference floor.
resonances, i.e. due to resonances of connected building elements, which return energy to the floor plate. This behaviour has also been observed by Craik [14]. At frequencies above 800 Hz, the measured mobility increases due to local stiffness effects. The abrupt phase change above 1000 Hz at the shaker measurement is thought to be due to the resonance frequency of the stringer connection between the shaker and the force transducer. The dynamic characteristics of the measured floor can be assumed to lie between two asymptotic conditions. First, the floor is heavily damped and the mobility tends to that of an infinite plate. Second, the behaviour is that of a finite plate with high mod-
al density, giving a diffuse sound field on the plate. In the second case, the average response again would be that of an infinite plate [16]. To evaluate which assumption is the most appropriate, a study of the spatial variation in floor velocity was conducted. 3.3. Spatial variation of floor velocity The spatial variation in floor velocity was measured. A traverse was selected with locations marked at 250 mm intervals away from the source as shown in Fig. 5. At each accelerometer position,
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the velocity of the plate was recorded. Simultaneously, the contact velocity from the shaker was recorded. In Fig. 6, the velocity level differences are shown in one-third octave bands as a function of distance from the source. The predicted difference, for a pure direct field, is also shown. Results indicate strong modal behaviour at frequencies below 160 Hz. For the 100 Hz third-octave band, the path length is within one bending wavelength. For frequencies of 160 Hz and above, there is some agreement with the predicted decrease up to a distance of 2 m. Diffuse field behaviour is generally not observed. The influence of the direct field on the sound transmission across the junction was considered by moving a shaker along the same traverse line on the floor, shown in Fig. 5. At each position, the direct power was recorded, along with the resultant sound pressure level in the room diagonally below the floor, at two microphone positions and as an average (see Fig. 1). For a plate behaviour dominated by a direct field, it would be expected that the resultant sound pressure level would rise as the shaker approached the cross-junction. The measured sound pressure levels, normalised with respect to the input power from the shaker, are shown in Fig. 7, in third octave bands from 63 Hz to 1 kHz. A systematic rise of sound pressure level is not observed. This suggests that the sound transmission does not occur across one junction only, but that the whole transmission suite assembly, including the side walls, is involved in the process. The transmission is insen-
sitive to the excitation location, despite direct-field behaviour on the excited floor plate. 3.4. Case study A whirlpool bath was selected for this study, shown in Fig. 8. The bath was of acrylic resin, supported by a frame of 50 mm box steel sections. The frame contained a water pump, fan and associated pipe-work. The bath was supported on 8 mounts. Each mount consisted of a threaded rod, with a rigid connection, giving the worst-case condition in terms of noise emission. It ensured a well-defined situation with good reproducibility. The whirlpool bath was first attached to the 100 mm reception plate and activated, and the power obtained according to Eq. (2). Results are shown in Fig. 9 for the operation of the water pump at full speed. Also shown is the infinite plate power from Eq. (3). For this transformation, the average point mobility of the reception plate was obtained from the measured values at all eight contact points, using a calibrated impulse hammer. Results show that the deviations are greatest (3 dB) at 50 Hz. The generally small difference, between the infinite plate power and the reception plate power, is because of the ‘rain-on-the-roof’ effect of the distributed contacts. In addition, the transformation of narrow band into third octave band values reduces the influence of spatial variation in mobility.
Fig. 6. Level difference between velocity at excitation position and at distance from the source, and the theoretical difference for a direct field.
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Fig. 7. Normalised sound pressure level in room diagonally below reference floor for a shaker source traverse.
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Fig. 10. Predicted installed power for whirlpool bath on reference floor, with maximum and minimum values.
maximum and minimum mobility of the floor (Eqs. (7) and (9)) gave the predicted maximum and minimum installed power, shown in Fig. 10. The maximum and minimum values are about 10 dB from the mean value at 50 Hz and about 3 dB at 1 kHz, respectively. 4. Sound pressure level from installed power
Fig. 8. Whirlpool bath.
The prediction of the resultant sound pressure level from the installed structure-borne power is possible through the recent draft of EN 12354 Part 5 [4]. At present, the method is restricted to heavy-weight homogeneous building constructions. The approach is to calculate the sound transmission for all paths, direct and first order, where one junction lies between the excited and the radiating building element in an adjacent room. The contributions of all paths sum to the total sound transmission. The paths are regarded as independent, and the sound transmission of each path can be calculated separately. An equivalent incident airborne sound power is obtained for each path, which gives the same input power into the excited building element as the structure-borne sound source. In the following, airborne excitation variables are denoted by index a and structure-borne excitation variables by index s. The relation between airborne and structure-borne power is given by Gerretsen [17] 2 P2struc;n;ij W inc;i;a W rad;j Pstruc;n;ij ¼ W inj;i;s q0 c0 W inj;i;s W inc;i;a q0 c0 W rad;j
ð10Þ
where Pstruc,n,ij is the normalised sound pressure in the receiving room, caused by the structure-borne sound transmission via the elements i and j; Winj,i,s is the structure-borne sound power into the ith building element; and Winc,i,a is the airborne sound power incident on the same building element. The normalised sound pressure level for the transmission path i and j is given by,
Lp;n;:ij ¼ LW;i;s þ 10 lg
W inc;i;a 4 Rij þ 10 lg Aref W inj;i;s
ð11Þ
where Ri,j is given by [2]:
Ri;situ Rj;situ lij SS þ DRi;situ þ þ K ij 10 lg pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 10 lg pffiffiffiffiffiffiffiffi 2 2 ai;situ aj;situ Si Sj
Fig. 9. Reception plate power and the infinite plate power of the whirlpool bath, located centrally on the plate.
Ri;j ¼
The installed power was predicted according to Eq. (6), using the mobility of a 180 mm concrete plate of infinite extent. The
where Ri,j,situ is the sound reduction index of the elements i and j in situ and Kij is the vibration reduction index of the building
ð12Þ
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elements at the junction. Si,j is the surface area of the flanking building elements and SS the surface area of the separating element. The ratio of the powers in (10) gives rise to the adjustment term, given in [4]:
Ds;a;i ¼ 10 lg
2pm00i 2:2si q0 c0 T s;i ri
ð13Þ
with m00 the mass of unit area, si the airborne sound transmission factor for resonant transmission, Ts,i the structural reverberation time and ri the radiation efficiency of element i. The normalised sound pressure level for the transmission path ij can now be written as,
Lp;n;ij ¼ LW;i;s Ds;a;i Rij 10 lg
Aref Si 10 lg Sc 4
ð14Þ
The structure-borne sound power LW,i,s is obtained from the transformed reception plate power. The total normalised sound pressure level Lp,n,s from all paths is obtained from logarithmic summation. The diagonal transmission considered consists of two paths (see Fig. 1). The model of EN 12354 is essentially based on Statistical Energy Analysis (SEA), and each building element should exhibit the properties of an ideal SEA subsystem [14]. Each should support resonant modes of vibration in the frequency range of interest; there should be a uniform energy density (by virtue of a reasonably diffuse field); the subsystems should be weakly coupled and the system should be moderately damped. In buildings, most subsystems only approximate these conditions, and the accuracy of the SEA prediction is usually determined by the approximations. Nevertheless, SEA has been shown to be suitable for homogeneous isotropic building element in masonry buildings [14]. Unlike the prediction model of EN 12354, SEA is not restricted to the first-order flanking transmission and more than one junction on each path can be considered, and therefore, the transmission to remote rooms can be predicted.
Fig. 11. Cistern frame without ceramic.
4.1. Case studies The first case considered was the whirlpool bath described earlier (Fig. 8). The bath has a set of six venturi-valves at the side of the tub, where water is forced in by the water pump. The pressure of the water could be regulated and air added at the valves. Additionally, there was a second system with 16 air valves operated by a fan. The two systems operated separately or simultaneously. The bath weight was 85 kg and was filled with 198 l of water for all measurements. Preliminary measurements of whirlpool baths in domestic situations confirmed that the frequencies of interest are below 2 kHz [7]. Additionally, a preliminary investigation confirmed that the excitation of the supporting floor was predominantly by forces perpendicular to the floor, although moment excitation can assume importance in a few frequency bands [7]. When attached to the reception plate, the bath constitutes a high mobility source with point mobility 10 dB or more than the point mobility of the receiving element [1]. Therefore, the data transformation described in this paper is applicable. The second case was a cistern frame. The system consists of a frame, with cistern, valves, pipe work and ceramic (Fig. 11). This source has a time-dependent excitation; the strongest excitation occurs at the beginning of the flushing cycle. For installations on heavy homogeneous walls and lightweight double-leaf walls the frequencies of interest are again below 2 kHz. The point mobility of the cistern frame was measured prior to installation, and the results are shown in Fig. 12. Also shown is the measured mobility of the reception plate. The source mobility is between one and two orders of magnitude greater than the receiver mobility. Below
Fig. 12. Point mobility at one contact of cistern frame, along with the reception plate mobility at one contact; also shown is the infinite plate mobility.
80 Hz, the source mobility displays mass-like behaviour. Between 80 Hz and 1000 Hz, the source mobility displays stiffness-controlled behaviour. At the minimum at 80 Hz, it is still 10 dB above the receiver mobility, indicating a high mobility source condition over the whole frequency range. The sources were attached in turn to the reception plate, and the average plate velocity was recorded. In both cases, a rigid connection between source and plate was obtained using super glue, giving a reliable contact with good reproducibility. For the whirlpool bath, results are shown for the operation of the water pump at full speed with no added air at the venturi-valves. With the source in operation, the velocity at 12 accelerometer positions was measured and the spatial average obtained to give the reception plate power from Eq. (1). For the cistern frame, the spatial average plate velocity was measured at several stages during the cycle of operation. Equivalent plate velocity levels Leq over 125 ms were recorded in third octave
M.M. Späh, B.M. Gibbs / Applied Acoustics 70 (2009) 1431–1439
bands. As the flushing cycles showed a relative poor repeatability, 10 cycles of operation were recorded and averaged. A typical time signal is shown in Fig. 13 for the 400 Hz third octave band. The initial flushing was defined as for the time between 0 and 5 s, giving a maximum power. The installed power was calculated from Eq. (3) and is shown in Figs. 10 and 14 for the whirlpool bath and cistern, respectively. Diagonal transmission, from the floor plate across the junction, was considered. In addition to the installed power, further data are required. Initially, the sound reduction index was calculated according to EN 12354 Part 1 [2], based on theoretical considerations. The structural reverberation times and vibration reduction indices Kij were obtained from measured data. As the latter were gained by steady-state vibration measurements, relevant transmission via other paths in the transmission suite, besides the first-order junction, was included. For the whirlpool bath, the predicted sound pressure levels in the receiving room are shown in Fig. 15, for the two transmission paths and the sum. At mid and high frequencies, both paths are equally important. At low frequencies, the heavier floor plate is the dominant path, due to a lower critical frequency. The critical
Fig. 13. Velocity–time signal at 400 Hz on reception plate.
Fig. 14. Predicted installed power from cistern frame on reference floor, with maximum and minimum values, for the flushing cycle.
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frequency of the wall is approximately 200 Hz, above which path 1 assumes importance. In order to measure the resultant sound pressure level, the whirlpool bath was installed on the floor away from the transmission junction, with no contact to the surrounding walls. Undersampling of the sound pressure at low frequencies was partly compensated for by considering the energy density at the wall boundaries of a room relative to the central positions, according to Waterhouse [18]. The corrected measured values were compared with the predicted values. The predicted and measured sound pressure levels in the room diagonally below the excited floor are shown in Fig. 16. Also shown are the maximum and minimum predicted values. The predicted levels overestimate the measured levels by about 5 dB. This is possibly due to the conservative prediction of the transmission loss of the building elements. The discrepancy at low frequencies is thought to be caused additionally by weak coupling of wall and floor bending modes with room modes in the receiving room. This is generally the reason for large deviations in sound reduction index of building elements at low frequencies. In the given case, the radiation efficiency of the building elements, which is implicitly incorporated into the sound
Fig. 15. Predicted normalised sound pressure levels by the two transmission paths.
Fig. 16. Measured (corrected) and predicted normalised sound pressure levels due to whirlpool bath.
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5. Conclusions
Fig. 17. Measured (corrected) and predicted normalised sound pressure levels of cistern.
A laboratory reception plate test method has been developed to determine the structure-borne sound power of mechanical sources when installed in heavy-weight buildings. The installed power can be given as a mean, maximum and minimum value. These values form input data for predicting the resulting sound pressure levels in rooms removed from the source. Recent research seeks to extend the approach to lightweight building constructions [19]. A study of the behaviour of a floor, with three fixed edges and one edge effectively free, shows that the sound transmission does not occur across one junction only, but through the whole transmission suite assembly, and the resultant sound pressure level is insensitive to source location. Two sources have been considered: a whirlpool bath representative of complex sources with powerful active components; a cistern representative of time-variant sources. For the whirlpool bath, predicted levels overestimated measured levels by about 5 dB at low frequencies. In this case, the measurement tracked the prediction of the minimum value. The overestimation is possibly due to the conservative prediction of the sound reduction index of EN 12354 Part 1 Appendix B. For the cistern, there was agreement between the predicted and measured values at mid- and high frequencies. At frequencies below 125 Hz, again the predicted values were greater than the measured values, but there is agreement with the minimum predicted values. The generally better agreement, for the cistern, could be the result of the close proximity of the source to the transmitting junction, which might lead to additionally near-field excitation and transmission. The method is applicable to mechanical installations which connect to more than one building element. A machine in a corner location could have contact with up to three surfaces. A prototype three-plate laboratory reception system has been constructed where the mutually perpendicular plates are structurally isolated [20]. Each plate acts as an independent reception plate and three reception plate powers can be obtained. The process of predicting the installed powers and then the resultant sound pressure levels is as before, but three sound pressure levels are summed up to give the total.
Acknowledgements
Fig. 18. Measured (corrected) and predicted normalised sound pressure levels for the maximum output of cistern.
reduction index, is influenced by modal coupling. As a single-value comparison, the A-weighted sound pressure level was calculated for the frequency range from 50 to 1600 Hz. The predicted value is 41.8 dB(A), and the measured value is 35.9 dB(A). The same transmission path was considered for the cistern frame source, which was installed on the same floor, this time close to the separating wall. All other connections to the building elements were avoided, including the normally necessary pipes. The predicted normalised sound pressure level is shown in Fig. 17, along with the corrected measured values. Again, the maximum and minimum predicted values are also shown. The predicted and measured values, at mid and high frequencies, are within 3 dB. At low frequencies, the measured values are below the predicted values, again because of weak coupling of the wall/floor modes to room modes. The minimum predicted levels are in agreement with the measured levels at low frequencies. The predicted A-weighted sound pressure level is 31.8 dB(A); the measured value is 30.0 dB(A). Similar behaviour was observed at the maximum power of the cistern, shown in Fig. 18.
The authors gratefully acknowledge the contributions of HeinzMartin Fischer of Stuttgart University of Applied Science, Werner Scholl of Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Michel Villot of CSTB, Grenoble, and Qi Ning and Gary Seiffert of the Acoustics Research Unit of Liverpool University. References [1] Späh MM, Gibbs BM. Reception plate method for characterisation of structureborne sound sources in buildings: assumptions and application. Appl Acoust 2009;70:361–8. [2] EN 12354-1. Building acoustics – estimation of acoustic performance of buildings from the performance of elements. Part 1: airborne sound insulation between rooms; 2000. [3] EN 12354-2. Building acoustics – estimation of acoustic performance of buildings from the performance of elements. Part 2: impact sound insulation between rooms; 2000. [4] prEN 12354-5. Building acoustics – estimation of acoustic performance of building elements from the performance of elements – Part 5: sound levels due to service equipment; 2004. [5] Mondot JM, Petersson BAT. Characterisation of structure-borne sound sources: the source descriptor and the coupling function. J Sound Vib 1987;114(3):507–18. [6] Moorhouse AT, Gibbs BM. Measurement of structure-borne sound emission from resilient mounted machines in situ. J Sound Vib 1995;180(1):143–61. [7] Späh MM. Characterisation of structure-borne sound sources in buildings, Ph.D. Thesis, University of Liverpool; 2006.
M.M. Späh, B.M. Gibbs / Applied Acoustics 70 (2009) 1431–1439 [8] Cremer L, Heckl M. Körperschall (structure-borne sound). Springer-Verlag; 1996. [9] Moorhouse AT. On the characteristic power of structure-borne sound sources. J Sound Vib 2001;248(3):441–59. [10] Moorhouse AT, Gibbs BM. Calculation of the mean and maximum mobility for concrete floors. Appl Acoust 1995;45:227–45. [11] Acoubat: Manuel Technique du Logiciel Acoubat V2.1, CSTB Grenoble, technical documentation; 1997. [12] Späh MM, Blessing S, Fischer H-M. Verification of the calculation model for airborne sound insulation according to EN 12354-1 for homogenous heavyweight buildings, Part 1: influence of the input data. In: Proc. DAGA 2001, Hamburg (in German); 2001. [13] Esteban A, Cortés A, Arribillaga O. In situ loss factor in Spanish hollow constructions: improving EN 12354‘s accuracy. In: Proc. Inter Noise 2004, Prague; 2004. [14] Craik RJM. Sound transmission through buildings using statistical energy analysis. England: Gower Publishing Limited; 1996.
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[15] Fahy F, Walker J. Advanced applications in acoustics, noise and vibration, chapter 9: mobility and impedance methods in structural dynamics. London: E&FN Spon; 2004. [16] Skudrzyk E. The mean value method of predicting the dynamic response of complex vibrators. J Acoust Soc Am 1981;67:347–59. [17] Gerretsen E. Additional information on structure-borne sound transmission: related to CEN/TC126/WG2 N265 – final draft prEN 12354-5, Document CEN/ TC126/WG2 N266. Delft; 2005. [18] Waterhouse RV. Interference patterns in reverberant sound fields. J Acoust Soc Am 1955;27(2):247–58. [19] Gibbs BM, Cookson R, Qi N. Vibration activity and mobility of structure-borne sound sources by a reception plate method. J Acoust Soc Am 2008;123(6):4199–209. [20] Späh MM, Fischer H-M, Gibbs BM. New laboratory for the measurement of structure-borne sound power of sanitary installations. In: Proc. Forum Acusticum, Budapest; 2005.