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Stiff light composite panels for duct noise reduction
Applied Acoustics 64 (2003) 511–524 www.elsevier.com/locate/apacoust
Stiff light composite panels for duct noise reduction Wing Cheong Tang*, Wei Zheng Lin Institute of Acoustics, Tongji University, 1239 Siping Road, Shanghai, China Received 25 March 2002; received in revised form 18 September 2002; accepted 7 October 2002
Abstract Low-frequency duct noise reduction using stiff light composite panels is developed and tested. Since these composite panels are made of lightweight and stiff materials, this actuation strategy will enable the creation of composite panels for duct noise control without using traditional heavy structural mass. The results suggest that the mass-spring resonance absorption in the case of a comparatively stiff thick panel with a thin flexible plate is more efficient with minimum weight, verifying that when subjected to low-frequency (< 500 Hz). The efficiency of the panel absorber depends on the mass of the thin flexible plate and the stiffness of the panel. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Stiff composite panels; Duct; Noise reduction
1. Introduction A very simple formula [1] is frequently used in the acoustic design of ventilation ducts. Allen’s formula is, however, not so applicable at low frequency where only single mode acoustical transmission occurred in the duct. Guthrie [2] carried out an experimental study on low-frequency internal/external sound transmission through the walls of rectangular ducts. He found that noise reduction could be achieved by slightly raising the dips in the sound transmission loss (STL) curve. However, Cummings [3–7] carried out a series of investigations into the transmission of an internally-propagated sound wave through single-layer ventilation ducts. He showed that the special characteristics of low frequency breakout was a series of dips in the * Corresponding author. E-mail address: [email protected] (T.W. Cheong). 0003-682X/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(02)00109-3
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curve of the STL as a function of frequency, and these dips were attributed to transverse structural resonances in the duct walls. It is the acoustic resonance which is the most troublesome aspect of breakout through the duct walls. Porous or fibrous materials have been used in a great variety of applications to absorb acoustic energy at medium and high frequencies above approximately 200 Hz (e.g. in a ventilation duct). However, there are many cases where their openings and rough surface entails certain disadvantages with respect to hygiene and cleaning requirements. It is not difficult to eliminate high-frequency noise based on the properties of sound transmission, but, with traditional materials, it is not easy to completely shield off environmental noise, especially low-frequency noise (because of the mass-density law) where huge soundproof structures are needed. For medium and low frequencies, which would require a relatively large absorber thickness and weight, there is a need for an alternative absorber. Great demands are made on airhandling devices, for examples, in ‘‘clean rooms’’ for the production of semi-conductor elements, in kitchens for large-scale catering, and in supplying packing appliances in the food industry with sterile air. Consequently, it is desirable not to use porous materials in ventilation ducts. An alternative method to tackle this problem is to use the sandwich panel (i.e. panel absorber). Panel absorbers dissipate acoustic energy by different modes of vibration excitable in a complex system of rather thin, though comparatively stiff thick metals or plastic membranes. An air gap in-between a stiff panel and a thin flexible plate will prove to be an efficient way of noise reduction in the low-frequency range, especially the ‘‘mass–air–mass’’ resonance. The absorption of the vibrational energy is the resonant ‘‘mass–spring–mass’’ behavior of the system. The sound absorption characteristics are increased by filling the air gap behind the absorber with sound absorbing material. When the stiffness of the panel or the depth of the air gap between the panels is suitably adjusted, the resonant frequency can be adjusted at a particular noise spectrum. These combined vibrational and damping mechanisms enable the construction of a new generation of sound absorber which no longer requires additional porous materials to be incorporated in order to make it effective in a broadband of low frequency. Although much works [8–12] has been done on developing such panel absorbers, many researchers focus on panel applications as sound absorbers in a room and the results cannot be readily used in duct design. However, Astley et al. [13] found that this effect was caused by ‘‘gas pumping’’through the absorbent and was driven by the resonance motion of the flexible wall. Then, Cummings [14] used a flexible-wall design to describe acoustic attenuation in the duct (i.e. having neither internal acoustic treatment nor external lagging). This method has an influence on noise attenuation design for a ventilation duct system. Duct wall vibration can actually enhance the noise attenuation in a narrow-frequency band around the fundamental transverse wall resonance frequency band. Up to now, Kiyama et al. [11] found that panel absorbers provided good absorption at low-frequency range. Under conventional mass density law, the thickness of insulating materials needs to be in inverse proportion to the frequency of sound. The stiff light composite panel has many advantages, it is of lower profile, lower mass, and requires only a simple modification of materials already installed on the duct. In this study, the resonant
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mass–spring behavior of the panel absorber is studied and its applicability as an alternative means of noise reduction is investigated. Through extensive experiments on the noise attenuation performances of various panels with different geometrical orientation in the duct, a very interesting phenomenon was observed.
2. Construction and preliminary testing This section outlines the design, construction, and preliminary testing of the panel absorbers. A particular emphasis is placed on identifying duct noise reduction at low frequency. 2.1. Definition of the problems A sound pressure level outside the duct walls is generated when vibrations in the walls excite a sound field outside the duct. The radiated sound is sometimes called duct-breakout noise. Breakout noise is predominantly a low frequency problem, since fans produce most of their sound power at low frequencies, and it is also in this region where the almost universally used dissipative type of attenuator is less effective. Hence one’s breakout calculations have to be valid at low frequencies; high frequency accuracy is less important. The key problems of the ventilation duct system are as follows: 1. the low modal density inside the duct and different transmission properties of different modes implies that the noise source’s relative excitation of modes is a key problem; 2. the ventilation noise often is a low frequency problem, the low modal density in the room outside the duct causes another prediction problem; 3. the acoustic nearfield inside the duct excite free bending waves in the duct wall. The waves radiate sound and destroy the high transmission loss of circular ducts at low frequencies.
2.2. Panel absorber design Tests were carried out between two reverberant rooms. The rooms were isolated from each other and a 1.8 m long square duct opening with dimensions of 0.330.33 m was the only means to transfer airborne sound between the two rooms. The duct was constructed with four galvanized steel panels of the same physical and geometric properties. The duct wall has an effective Young’s modulus of 19.51010 Pa, density of 7700 kg/m3 and thickness of 1 mm. The Poisson’s ratio was not measured, but the published data suggested that it should be around 0.28. The coordinates and the internal dimensions of the cavity are shown in Fig. 1. The inside surfaces of the cavity were smooth and had been left unpainted. All the joints between the duct walls were sealed with plastic-bond to prevent air leaks. The flanking transmission was reduced with a massive concrete block (Plate 1). To give anechoic termination
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Fig. 1. Coordinate system of the duct: panel-cavity model.
Plate 1. Front view of the duct between two test rooms.
condition at the end of the duct, a 0.5 mm long wedge made of glass wool was placed at the end of the duct to give a gradual change in impedance, thereby minimizing the reflection from the end of the duct. A test on the anechoic performance termination showed the experimental error due to the flanking path and reflection was measured to be less than 0.5 dB. To compare the noise breakout through the wall in different panel absorber configurations, nine specimens were built. They were constructed with either a single
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layer plate and fibreglass, or fibreglass and air gap. Once the duct is fixed, there are three geometrical variables. They are the thickness of air-gap, the fiberglass and the duct wall. The detailed structural parameters of the panel absorbers and cross-sectional view of the square duct are given in Table 1 and Fig. 2.
3. Experimental configuration 3.1. Acoustic measurement The measurement equipment consisted of a random noise generator (Bruel & Kjaer type 1027), connected via a power amplifier to a loudspeaker placed in the Table 1 Detail structural parameters of panel absorbers Thickness (mm) No.
G.S. face sheet
Fibreglass
Cavity depth
Symbol
1 2 3 4 5 6 7 8 9
0.3 0.3 0.3 0.3 0.1 0.1 0.1 0.1 Nil
60 60 30 30 60 60 30 30 50
40 0 70 25 40 0 70 25 0
G.S. (0.3,60,40) G.S. (0.3,60,0) G.S. (0.3,30,70) G.S. (0.3,30,25) G.S. (0.1,60,40) G.S. (0.l,60,0) G.S. (0.1,30,70) G.S. (0.l,30,25) N (0,50,0)
G.S.—galvanized steel. N—no face sheet.
Fig. 2. Cross-sectional view of the square duct (A–A0 ).
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corner of the source room. Random sound field was produced inside the source room. Two half-inch microphones (Bruel & Kjaer type 4155) were fed to a digital frequency analyzer (Bruel & Kjaer type 2144), or a real-time frequency analyzer (HP type 3569A). One microphone inside the duct was used to measure the internal induct sound pressure level (SPL) along the center axis. The second microphone was placed at a fixed position 300 mm distance from the duct wall surface to measure the breakout noise. They were calibrated with a sound level calibrator (Bruel & Kjaer type 4230) before and after the test. Guthrie [2] found that low frequency acoustic waves in a section of the duct varied very little across the duct’s cross-section. The front view of the duct is shown in Plate 1. The measurement of the previous experiment has confirmed that the sound pressure level in the cross-section is uniform. Consequently, the radiation was nearly symmetric. An acoustic measurement set-up and an anechoic treatment of the receiving room are shown in Fig. 3. 3.2. Vibration measurement The vibratory displacement, velocity and acceleration measurement of the test duct wall specimens were conducted at two points over the external duct wall to investigate the dependence of the sound transmission through the structures upon their structural performances. A light-weight (4 g) accelerometer, the lightest available, was selected to minimize the damping on the panel vibration. The basic vibration system consisted of a small accelerometer (Rion type 2125) and a charge amplifier (Rion type VM-27). The accelerometer was calibrated with a calibration exciter (Bruel & Kjaer type 4291) before and after the test. With a random pink noise input to the loudspeaker, an accelerometer mounted on the duct wall centerline at two points was used to measure the acceleration level spectrum. The output of the charge amplifier was fed to a real-time frequency analyzer (Hewlett Packard type 3569A). With a random sinusoidal input, the accelerometer was used to measure the transverse acceleration profile. Signals picked up by the accelerometers passed through the charge amplifiers with proper setting and then through the frequency filters to remove the disturbance of high frequency. When signals were observed to be stable on the oscilloscope, the vibratory velocity and acceleration of the duct wall was recorded in the real-time frequency analyzer. The experiment setup for the duct wall vibration response measurement is indicated in Fig. 4 and the appearance of the test system is shown in Plate 2. With reference to the experimental errors, the flanking transmission was reduced by massive concrete block. The joints between the duct walls were sealed with plastibonded to prevent air leakage. When measurements are one-third octave, the levels should be at least 10 dB below the source noise in every band of interest.
4. Effects of panel absorber parameters In this section, the effects of panel absorber geometric parameters on panel absorber performance are discussed and guidelines for panel absorber parameter
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Fig. 3. Acoustic measurement set-up for the STL test (not to scale).
selection are presented. These guidelines are obtained from laboratory measurements. They should not be used as quantitative guidelines in duct design because the quantitative effects of one parameter may be influenced by changes in other parameters. The proper way to examine the effect of a single parameter for a particular panel absorber is to calculate the duct noise attenuation using the baseline panel absorber parameters, then change the subject parameter and recalculate the attenuation. 4.1. Effect of flexible thin plates The results of a conventional duct with a panel absorber are plotted in Fig. 5, which shows an improvement in effectiveness on the Sound Transmission Loss
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Fig. 4. Vibration response measurement of duct wall.
Plate 2. Appearance of duct wall.
(STL) of the conventional G.S. duct over all frequencies above 50 Hz. Below the fundamental resonance frequency, the wall impedance’s captive is ‘‘stiffness controlled’’. The panel absorber G.S. (0.3,30,70) provides good sound absorption at low frequency. It provides a maximum of 5 dB noise reduction in the frequency region of 100–160 Hz. The primary effect of fibreglass on the STL is the reduction in the amplitude of lateral standing waves in the cavity, therefore improving the STL above minor dip frequency. The panel absorber with an air gap between the flexible thin plate and thick stiff panel provides low-frequency sound absorption. This is because the mass-spring system amplifies certain vibrations in the system. This
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Fig. 5. The effectiveness of panel absorber used inside the duct.
operates a damping system which changes the mechanical energy to heat and removes it from the whole system. 4.2. Effect of depth of cavity behind panel The comparison of the sound transmission loss of panel absorbers with different cavity inside the duct is shown in Fig. 6. Between 100 and 160 Hz, the sound transmission loss of G.S. (0.3,60,40) is higher than that of G.S. (0.3,60,0). It is because the greater is the cavity depth, the higher is the sound transmission loss (STL). The panel-controlled resonance of the G.S. plate is caused by the (1,3) panel mode at 98.6 Hz. However, the maximum sound absorption of the G.S. panel absorber is achieved at the resonance frequency of 152 Hz. As the air gap increases, the noise reduction improvement of sandwich duct construction can be greater. It shows that there is no significant effect on the STL by varying the cavity depth except the resonance frequency of the panel absorber. 4.3. Effect of the internal plate’s thickness The comparison of the sound transmission loss of the conventional duct with different thickness of internal plates inside the duct is shown in Fig. 7. The width of the fiberglass and the depth of the cavity are kept constant. The STL of 0.1 mm G.S. plate is higher than that of 0.3 mm G.S. plate at low frequencies except 98.6 Hz, which is caused by the (1,3) panel mode at 98.6 Hz. Out of the stiffness-controlled frequency range, the smaller the thickness of the G.S. plate, the higher the sound transmission loss at low frequency. An increase
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Fig. 6. Comparison the STL of panel absorbers with different cavity depth inside the duct.
Fig. 7. Comparison the STL of the conventional duct with different thickness of internal plates inside the duct.
in the stiffness ratio of the duct wall and the thin plate provides good noise attenuation at low frequency. 4.4. Effect of fiberglass Fig. 8 indicates the sound transmission loss of panel absorbers in different configurations inside the duct. G.S. (0.3,30,25) provides the best acoustic performance
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Fig. 8. The STL of panel absorbers in different configurations inside the duct.
in the frequency region of 50–100 Hz. Between 200 and 400 Hz, G.S. (0.3,60,0) attains the highest sound transmission loss. However, G.S. (0.3,30,70) is better than the other two in the frequency range of 100–200 Hz. It shows that the 30 mm fibreglass with 70 mm cavity depth at 0.3 mm G.S. plate is the best panel absorber configuration in this frequency range. In other words, the noise reduction performance at specific frequency can be upgraded by tuning through different panel configurations. 4.5. In-duct sound characteristics Some typical axial sound pressure patterns are measured inside the duct as shown in Fig. 9. At a pure tone of 100 Hz, the standing wave ratio of G.S. (0.3,30,70) is only 3 dB. Comparing with the conventional galvanized steel duct, 0.3 mm G.S. metal plate with 30 mm fibreglass and 70 mm air gap which has a 4 dB in-duct noise attenuation at the end of the duct. 4.6. Anechoic termination The CIBSE Design Guide [15] gives the noise attenuation values of unlined duct (in dB/m) for various sizes of duct, expressed as a mean duct dimension, and for three frequency bands of 125, 250 and 500 Hz and above. The ASHRAE Handbook [16] uses a different method, based on the ratio of duct section perimeter to cross sectional area, and frequency bands of 63, 125 and 250 Hz and above. However, two methods give very similar results (0.3 dB/m) for a wide range of duct sizes, from 300 to 900 mm mean duct diameter, but there are differences at low frequencies for large
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Fig. 9. In-duct sound pressure level (SPL) inside the duct at 100 Hz.
ducts and at the higher frequencies for small ducts. The two methods also give very similar predictions, within 1 dB in most situation, for the attenuation of unlined rectangular bands. Both methods give very similar results, usually within 1 or 2 dB, for the correction to be applied for reflection at the end of a duct. However, the ASHRAE method gives more guidance about conditions under which this correction should be applied. The full end correction should not be applied unless the duct termination is proceeded by a straight section of ductwork of at least three to five meters diameters long, and is without any diffuser or griller. Waves propagating in modes are reflected at discontinuities in the long uniform duct if the end is a discontinuities. Standing waves in the axial direction may then appear for a steady state condition. Hence, anechoic termination is necessary to prevent the standing wave reflection. The anechoic termination in the square duct was also effective. Fig. 10 shows the axial sound pressure pattern measured inside the square duct at different frequency. Even at 63 Hz, the standing-wave ratio is only 7 dB (representing an energy reflection coefficient of approximately 0.15), and this falls to 1 dB or less at higher frequencies. As long as the effectiveness of the anechoic termination in terms of structural waves is concerned, the situation appears complicated. Axial, structural, ‘‘standing-wave’’ patterns were detected, but interpretation proved difficult. The separation of the displacement nodes was generally considerably smaller than that in the coupled wave system, and was not very regular. Whether these displacement patterns can be attributed to structural reflection from the anechoic termination or to any effect caused by reflections at the joints in the duct is a moot point, but in all events, the reflections were of small magnitude.
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Fig. 10. Axial sound pressure pattern inside the square duct at different frequency.
5. Conclusions As the basis of model solution for sandwich panels used for duct noise reduction at low frequency, sound absorption characteristics of panel absorbers with different configurations have been studied. Compared with the sound absorption performance of panel absorbers carried out by other researchers (Astley et al. [13] and Kiyama et al. [11]), the noise reduction properties of panel absorbers are similar. In this study, it was found that the noise reduction of a combination of a flexible thin plate and a duct wall, with air cavities and porous material in-between, was more effective than that of the conventional duct at low frequency. Panel absorbers dissipate acoustic energy by different modes of vibration excitable in a complex system of rather thin, though comparatively stiff thick metals or plastic membranes. The absorption of the vibrational energy is the resonant ‘‘mass–spring– mass’’ behavior of the system. The sound absorption characteristics are increased by filling the air gap behind the absorber with sound absorbing material. When the stiffness of the panel or the depth of the air gap between the panels is suitably adjusted, the resonant frequency can be adjusted at a particular noise spectrum. These combined vibrational and damping mechanisms enable the construction of a new generation of sound absorber which no longer requires additional porous materials to be incorporated in order to make it effective in a broadband of low frequency. Two advantages of this design over traditional external lagging are its smaller mass and lower profile. Additionally, the installation of panel absorbers requires only a slight modification to existing materials on the ventilation duct system. The key findings include: 1. low frequency sound transmission through finite ducts depends upon not only the physical parameter characteristic of the panel itself, but also the sound
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field performance, especially the acoustic resonant modes, inside the cavity; 2. in a narrow frequency range, excellent acoustic performance is achieved with 30 mm fibreglass and a 70 mm air-gap in a 0.3 mm G.S. plate, especially for reduction in cavity resonance. However, no significant improvement is achieved by increasing the thickness of the fiberglass filled in-between the thin metal plate and the duct wall; 3. an air gap between a comparatively stiff panel (duct wall) and a flexible thin plate is efficient in achieving low-frequency sound absorption in the duct ventilation system.
References [1] Allen CH. Noise reduction. Beranek LL, editor. New York: McGraw-Hill; 1960. [2] Guthrie A. Low frequency acoustic transmission through the walls of various types of ducts. MSc dissertation, Polytechnic of South Bank, UK; 1979. [3] Cummings A. Low frequency acoustic transmission through the walls of rectangular ducts. Journal of Sound and Vibration 1978;61:327–45. [4] Cummings A. Low frequency sound transmission through the walls of rectangular ducts: further comments. Journal of Sound and Vibration 1979;63:463–5. [5] Cummings A. Low frequency acoustic radiation from duct walls. Journal of Sound and Vibration 1980;71:201–26. [6] Cummings A. Stiffness control of low frequency acoustic transmission through the walls of rectangular ducts. Journal of Sound and Vibration 1981;74:351–80. [7] Cummings A. Design charts for low frequency acoustic transmission through the walls of rectangular ducts. Journal of Sound and Vibration 1981;78:269–89. [8] Bolton JS, Shiau NM, Kang YJ. Sound transmission through multi-panel structures lined with elastic porous materials. Journal of Sound and Vibration 1996;191:317–47. [9] Frommhold W, Fuchs HV, Sheng S. Acoustic performance of membrane absorbers. Journal of Sound and Vibration 1994;170:621–36. [10] Kang YJ, Bolton JS. A finite element model for sound transmission through foam-lined doublepanel structures. Journal of the Acoustical Society of America 1996;99(5):2755–65. [11] Kiyama M, Sakagami K, Tanigawa M. A basic study on acoustic properties of double-leaf membranes. Applied Acoustics 1998;54:239–54. [12] Takahashi D, Sakagami K, Morimoto M. Acoustic properties of permeable membrane. Journal of the Acoustical Society of America 1996;99(5):3003–9. [13] Astley RJ, Cummings A, Sormaz N. A finite element scheme for acoustic propagation in flexiblewalled duct with bulk-reacting liners, and comparison with experiment. Journal of Sound and Vibration 1991;56:119–38. [14] Cummings A. The attenuation of sound in unlined ducts with flexible wall. Journal of Sound and Vibration 1994;174:433–50. [15] CIBSE Design Guide. Sound control, Section B.12. Chartered Institute of Building Services Engineers; 1986. [16] ASHRAE Handbook. Sound and vibration control, chapter 32. Atlanta (GA): American Society of Heating. Refrigeration and Air Conditioning Engineers; 1987.
Stiff light composite panels for duct noise reduction Wing Cheong Tang*, Wei Zheng Lin Institute of Acoustics, Tongji University, 1239 Siping Road, Shanghai, China Received 25 March 2002; received in revised form 18 September 2002; accepted 7 October 2002
Abstract Low-frequency duct noise reduction using stiff light composite panels is developed and tested. Since these composite panels are made of lightweight and stiff materials, this actuation strategy will enable the creation of composite panels for duct noise control without using traditional heavy structural mass. The results suggest that the mass-spring resonance absorption in the case of a comparatively stiff thick panel with a thin flexible plate is more efficient with minimum weight, verifying that when subjected to low-frequency (< 500 Hz). The efficiency of the panel absorber depends on the mass of the thin flexible plate and the stiffness of the panel. # 2003 Elsevier Science Ltd. All rights reserved. Keywords: Stiff composite panels; Duct; Noise reduction
1. Introduction A very simple formula [1] is frequently used in the acoustic design of ventilation ducts. Allen’s formula is, however, not so applicable at low frequency where only single mode acoustical transmission occurred in the duct. Guthrie [2] carried out an experimental study on low-frequency internal/external sound transmission through the walls of rectangular ducts. He found that noise reduction could be achieved by slightly raising the dips in the sound transmission loss (STL) curve. However, Cummings [3–7] carried out a series of investigations into the transmission of an internally-propagated sound wave through single-layer ventilation ducts. He showed that the special characteristics of low frequency breakout was a series of dips in the * Corresponding author. E-mail address: [email protected] (T.W. Cheong). 0003-682X/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. PII: S0003-682X(02)00109-3
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curve of the STL as a function of frequency, and these dips were attributed to transverse structural resonances in the duct walls. It is the acoustic resonance which is the most troublesome aspect of breakout through the duct walls. Porous or fibrous materials have been used in a great variety of applications to absorb acoustic energy at medium and high frequencies above approximately 200 Hz (e.g. in a ventilation duct). However, there are many cases where their openings and rough surface entails certain disadvantages with respect to hygiene and cleaning requirements. It is not difficult to eliminate high-frequency noise based on the properties of sound transmission, but, with traditional materials, it is not easy to completely shield off environmental noise, especially low-frequency noise (because of the mass-density law) where huge soundproof structures are needed. For medium and low frequencies, which would require a relatively large absorber thickness and weight, there is a need for an alternative absorber. Great demands are made on airhandling devices, for examples, in ‘‘clean rooms’’ for the production of semi-conductor elements, in kitchens for large-scale catering, and in supplying packing appliances in the food industry with sterile air. Consequently, it is desirable not to use porous materials in ventilation ducts. An alternative method to tackle this problem is to use the sandwich panel (i.e. panel absorber). Panel absorbers dissipate acoustic energy by different modes of vibration excitable in a complex system of rather thin, though comparatively stiff thick metals or plastic membranes. An air gap in-between a stiff panel and a thin flexible plate will prove to be an efficient way of noise reduction in the low-frequency range, especially the ‘‘mass–air–mass’’ resonance. The absorption of the vibrational energy is the resonant ‘‘mass–spring–mass’’ behavior of the system. The sound absorption characteristics are increased by filling the air gap behind the absorber with sound absorbing material. When the stiffness of the panel or the depth of the air gap between the panels is suitably adjusted, the resonant frequency can be adjusted at a particular noise spectrum. These combined vibrational and damping mechanisms enable the construction of a new generation of sound absorber which no longer requires additional porous materials to be incorporated in order to make it effective in a broadband of low frequency. Although much works [8–12] has been done on developing such panel absorbers, many researchers focus on panel applications as sound absorbers in a room and the results cannot be readily used in duct design. However, Astley et al. [13] found that this effect was caused by ‘‘gas pumping’’through the absorbent and was driven by the resonance motion of the flexible wall. Then, Cummings [14] used a flexible-wall design to describe acoustic attenuation in the duct (i.e. having neither internal acoustic treatment nor external lagging). This method has an influence on noise attenuation design for a ventilation duct system. Duct wall vibration can actually enhance the noise attenuation in a narrow-frequency band around the fundamental transverse wall resonance frequency band. Up to now, Kiyama et al. [11] found that panel absorbers provided good absorption at low-frequency range. Under conventional mass density law, the thickness of insulating materials needs to be in inverse proportion to the frequency of sound. The stiff light composite panel has many advantages, it is of lower profile, lower mass, and requires only a simple modification of materials already installed on the duct. In this study, the resonant
W.C. Tang, W.Z. Lin / Applied Acoustics 64 (2003) 511–524
513
mass–spring behavior of the panel absorber is studied and its applicability as an alternative means of noise reduction is investigated. Through extensive experiments on the noise attenuation performances of various panels with different geometrical orientation in the duct, a very interesting phenomenon was observed.
2. Construction and preliminary testing This section outlines the design, construction, and preliminary testing of the panel absorbers. A particular emphasis is placed on identifying duct noise reduction at low frequency. 2.1. Definition of the problems A sound pressure level outside the duct walls is generated when vibrations in the walls excite a sound field outside the duct. The radiated sound is sometimes called duct-breakout noise. Breakout noise is predominantly a low frequency problem, since fans produce most of their sound power at low frequencies, and it is also in this region where the almost universally used dissipative type of attenuator is less effective. Hence one’s breakout calculations have to be valid at low frequencies; high frequency accuracy is less important. The key problems of the ventilation duct system are as follows: 1. the low modal density inside the duct and different transmission properties of different modes implies that the noise source’s relative excitation of modes is a key problem; 2. the ventilation noise often is a low frequency problem, the low modal density in the room outside the duct causes another prediction problem; 3. the acoustic nearfield inside the duct excite free bending waves in the duct wall. The waves radiate sound and destroy the high transmission loss of circular ducts at low frequencies.
2.2. Panel absorber design Tests were carried out between two reverberant rooms. The rooms were isolated from each other and a 1.8 m long square duct opening with dimensions of 0.330.33 m was the only means to transfer airborne sound between the two rooms. The duct was constructed with four galvanized steel panels of the same physical and geometric properties. The duct wall has an effective Young’s modulus of 19.51010 Pa, density of 7700 kg/m3 and thickness of 1 mm. The Poisson’s ratio was not measured, but the published data suggested that it should be around 0.28. The coordinates and the internal dimensions of the cavity are shown in Fig. 1. The inside surfaces of the cavity were smooth and had been left unpainted. All the joints between the duct walls were sealed with plastic-bond to prevent air leaks. The flanking transmission was reduced with a massive concrete block (Plate 1). To give anechoic termination
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Fig. 1. Coordinate system of the duct: panel-cavity model.
Plate 1. Front view of the duct between two test rooms.
condition at the end of the duct, a 0.5 mm long wedge made of glass wool was placed at the end of the duct to give a gradual change in impedance, thereby minimizing the reflection from the end of the duct. A test on the anechoic performance termination showed the experimental error due to the flanking path and reflection was measured to be less than 0.5 dB. To compare the noise breakout through the wall in different panel absorber configurations, nine specimens were built. They were constructed with either a single
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layer plate and fibreglass, or fibreglass and air gap. Once the duct is fixed, there are three geometrical variables. They are the thickness of air-gap, the fiberglass and the duct wall. The detailed structural parameters of the panel absorbers and cross-sectional view of the square duct are given in Table 1 and Fig. 2.
3. Experimental configuration 3.1. Acoustic measurement The measurement equipment consisted of a random noise generator (Bruel & Kjaer type 1027), connected via a power amplifier to a loudspeaker placed in the Table 1 Detail structural parameters of panel absorbers Thickness (mm) No.
G.S. face sheet
Fibreglass
Cavity depth
Symbol
1 2 3 4 5 6 7 8 9
0.3 0.3 0.3 0.3 0.1 0.1 0.1 0.1 Nil
60 60 30 30 60 60 30 30 50
40 0 70 25 40 0 70 25 0
G.S. (0.3,60,40) G.S. (0.3,60,0) G.S. (0.3,30,70) G.S. (0.3,30,25) G.S. (0.1,60,40) G.S. (0.l,60,0) G.S. (0.1,30,70) G.S. (0.l,30,25) N (0,50,0)
G.S.—galvanized steel. N—no face sheet.
Fig. 2. Cross-sectional view of the square duct (A–A0 ).
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corner of the source room. Random sound field was produced inside the source room. Two half-inch microphones (Bruel & Kjaer type 4155) were fed to a digital frequency analyzer (Bruel & Kjaer type 2144), or a real-time frequency analyzer (HP type 3569A). One microphone inside the duct was used to measure the internal induct sound pressure level (SPL) along the center axis. The second microphone was placed at a fixed position 300 mm distance from the duct wall surface to measure the breakout noise. They were calibrated with a sound level calibrator (Bruel & Kjaer type 4230) before and after the test. Guthrie [2] found that low frequency acoustic waves in a section of the duct varied very little across the duct’s cross-section. The front view of the duct is shown in Plate 1. The measurement of the previous experiment has confirmed that the sound pressure level in the cross-section is uniform. Consequently, the radiation was nearly symmetric. An acoustic measurement set-up and an anechoic treatment of the receiving room are shown in Fig. 3. 3.2. Vibration measurement The vibratory displacement, velocity and acceleration measurement of the test duct wall specimens were conducted at two points over the external duct wall to investigate the dependence of the sound transmission through the structures upon their structural performances. A light-weight (4 g) accelerometer, the lightest available, was selected to minimize the damping on the panel vibration. The basic vibration system consisted of a small accelerometer (Rion type 2125) and a charge amplifier (Rion type VM-27). The accelerometer was calibrated with a calibration exciter (Bruel & Kjaer type 4291) before and after the test. With a random pink noise input to the loudspeaker, an accelerometer mounted on the duct wall centerline at two points was used to measure the acceleration level spectrum. The output of the charge amplifier was fed to a real-time frequency analyzer (Hewlett Packard type 3569A). With a random sinusoidal input, the accelerometer was used to measure the transverse acceleration profile. Signals picked up by the accelerometers passed through the charge amplifiers with proper setting and then through the frequency filters to remove the disturbance of high frequency. When signals were observed to be stable on the oscilloscope, the vibratory velocity and acceleration of the duct wall was recorded in the real-time frequency analyzer. The experiment setup for the duct wall vibration response measurement is indicated in Fig. 4 and the appearance of the test system is shown in Plate 2. With reference to the experimental errors, the flanking transmission was reduced by massive concrete block. The joints between the duct walls were sealed with plastibonded to prevent air leakage. When measurements are one-third octave, the levels should be at least 10 dB below the source noise in every band of interest.
4. Effects of panel absorber parameters In this section, the effects of panel absorber geometric parameters on panel absorber performance are discussed and guidelines for panel absorber parameter
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Fig. 3. Acoustic measurement set-up for the STL test (not to scale).
selection are presented. These guidelines are obtained from laboratory measurements. They should not be used as quantitative guidelines in duct design because the quantitative effects of one parameter may be influenced by changes in other parameters. The proper way to examine the effect of a single parameter for a particular panel absorber is to calculate the duct noise attenuation using the baseline panel absorber parameters, then change the subject parameter and recalculate the attenuation. 4.1. Effect of flexible thin plates The results of a conventional duct with a panel absorber are plotted in Fig. 5, which shows an improvement in effectiveness on the Sound Transmission Loss
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Fig. 4. Vibration response measurement of duct wall.
Plate 2. Appearance of duct wall.
(STL) of the conventional G.S. duct over all frequencies above 50 Hz. Below the fundamental resonance frequency, the wall impedance’s captive is ‘‘stiffness controlled’’. The panel absorber G.S. (0.3,30,70) provides good sound absorption at low frequency. It provides a maximum of 5 dB noise reduction in the frequency region of 100–160 Hz. The primary effect of fibreglass on the STL is the reduction in the amplitude of lateral standing waves in the cavity, therefore improving the STL above minor dip frequency. The panel absorber with an air gap between the flexible thin plate and thick stiff panel provides low-frequency sound absorption. This is because the mass-spring system amplifies certain vibrations in the system. This
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Fig. 5. The effectiveness of panel absorber used inside the duct.
operates a damping system which changes the mechanical energy to heat and removes it from the whole system. 4.2. Effect of depth of cavity behind panel The comparison of the sound transmission loss of panel absorbers with different cavity inside the duct is shown in Fig. 6. Between 100 and 160 Hz, the sound transmission loss of G.S. (0.3,60,40) is higher than that of G.S. (0.3,60,0). It is because the greater is the cavity depth, the higher is the sound transmission loss (STL). The panel-controlled resonance of the G.S. plate is caused by the (1,3) panel mode at 98.6 Hz. However, the maximum sound absorption of the G.S. panel absorber is achieved at the resonance frequency of 152 Hz. As the air gap increases, the noise reduction improvement of sandwich duct construction can be greater. It shows that there is no significant effect on the STL by varying the cavity depth except the resonance frequency of the panel absorber. 4.3. Effect of the internal plate’s thickness The comparison of the sound transmission loss of the conventional duct with different thickness of internal plates inside the duct is shown in Fig. 7. The width of the fiberglass and the depth of the cavity are kept constant. The STL of 0.1 mm G.S. plate is higher than that of 0.3 mm G.S. plate at low frequencies except 98.6 Hz, which is caused by the (1,3) panel mode at 98.6 Hz. Out of the stiffness-controlled frequency range, the smaller the thickness of the G.S. plate, the higher the sound transmission loss at low frequency. An increase
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Fig. 6. Comparison the STL of panel absorbers with different cavity depth inside the duct.
Fig. 7. Comparison the STL of the conventional duct with different thickness of internal plates inside the duct.
in the stiffness ratio of the duct wall and the thin plate provides good noise attenuation at low frequency. 4.4. Effect of fiberglass Fig. 8 indicates the sound transmission loss of panel absorbers in different configurations inside the duct. G.S. (0.3,30,25) provides the best acoustic performance
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Fig. 8. The STL of panel absorbers in different configurations inside the duct.
in the frequency region of 50–100 Hz. Between 200 and 400 Hz, G.S. (0.3,60,0) attains the highest sound transmission loss. However, G.S. (0.3,30,70) is better than the other two in the frequency range of 100–200 Hz. It shows that the 30 mm fibreglass with 70 mm cavity depth at 0.3 mm G.S. plate is the best panel absorber configuration in this frequency range. In other words, the noise reduction performance at specific frequency can be upgraded by tuning through different panel configurations. 4.5. In-duct sound characteristics Some typical axial sound pressure patterns are measured inside the duct as shown in Fig. 9. At a pure tone of 100 Hz, the standing wave ratio of G.S. (0.3,30,70) is only 3 dB. Comparing with the conventional galvanized steel duct, 0.3 mm G.S. metal plate with 30 mm fibreglass and 70 mm air gap which has a 4 dB in-duct noise attenuation at the end of the duct. 4.6. Anechoic termination The CIBSE Design Guide [15] gives the noise attenuation values of unlined duct (in dB/m) for various sizes of duct, expressed as a mean duct dimension, and for three frequency bands of 125, 250 and 500 Hz and above. The ASHRAE Handbook [16] uses a different method, based on the ratio of duct section perimeter to cross sectional area, and frequency bands of 63, 125 and 250 Hz and above. However, two methods give very similar results (0.3 dB/m) for a wide range of duct sizes, from 300 to 900 mm mean duct diameter, but there are differences at low frequencies for large
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Fig. 9. In-duct sound pressure level (SPL) inside the duct at 100 Hz.
ducts and at the higher frequencies for small ducts. The two methods also give very similar predictions, within 1 dB in most situation, for the attenuation of unlined rectangular bands. Both methods give very similar results, usually within 1 or 2 dB, for the correction to be applied for reflection at the end of a duct. However, the ASHRAE method gives more guidance about conditions under which this correction should be applied. The full end correction should not be applied unless the duct termination is proceeded by a straight section of ductwork of at least three to five meters diameters long, and is without any diffuser or griller. Waves propagating in modes are reflected at discontinuities in the long uniform duct if the end is a discontinuities. Standing waves in the axial direction may then appear for a steady state condition. Hence, anechoic termination is necessary to prevent the standing wave reflection. The anechoic termination in the square duct was also effective. Fig. 10 shows the axial sound pressure pattern measured inside the square duct at different frequency. Even at 63 Hz, the standing-wave ratio is only 7 dB (representing an energy reflection coefficient of approximately 0.15), and this falls to 1 dB or less at higher frequencies. As long as the effectiveness of the anechoic termination in terms of structural waves is concerned, the situation appears complicated. Axial, structural, ‘‘standing-wave’’ patterns were detected, but interpretation proved difficult. The separation of the displacement nodes was generally considerably smaller than that in the coupled wave system, and was not very regular. Whether these displacement patterns can be attributed to structural reflection from the anechoic termination or to any effect caused by reflections at the joints in the duct is a moot point, but in all events, the reflections were of small magnitude.
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Fig. 10. Axial sound pressure pattern inside the square duct at different frequency.
5. Conclusions As the basis of model solution for sandwich panels used for duct noise reduction at low frequency, sound absorption characteristics of panel absorbers with different configurations have been studied. Compared with the sound absorption performance of panel absorbers carried out by other researchers (Astley et al. [13] and Kiyama et al. [11]), the noise reduction properties of panel absorbers are similar. In this study, it was found that the noise reduction of a combination of a flexible thin plate and a duct wall, with air cavities and porous material in-between, was more effective than that of the conventional duct at low frequency. Panel absorbers dissipate acoustic energy by different modes of vibration excitable in a complex system of rather thin, though comparatively stiff thick metals or plastic membranes. The absorption of the vibrational energy is the resonant ‘‘mass–spring– mass’’ behavior of the system. The sound absorption characteristics are increased by filling the air gap behind the absorber with sound absorbing material. When the stiffness of the panel or the depth of the air gap between the panels is suitably adjusted, the resonant frequency can be adjusted at a particular noise spectrum. These combined vibrational and damping mechanisms enable the construction of a new generation of sound absorber which no longer requires additional porous materials to be incorporated in order to make it effective in a broadband of low frequency. Two advantages of this design over traditional external lagging are its smaller mass and lower profile. Additionally, the installation of panel absorbers requires only a slight modification to existing materials on the ventilation duct system. The key findings include: 1. low frequency sound transmission through finite ducts depends upon not only the physical parameter characteristic of the panel itself, but also the sound
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field performance, especially the acoustic resonant modes, inside the cavity; 2. in a narrow frequency range, excellent acoustic performance is achieved with 30 mm fibreglass and a 70 mm air-gap in a 0.3 mm G.S. plate, especially for reduction in cavity resonance. However, no significant improvement is achieved by increasing the thickness of the fiberglass filled in-between the thin metal plate and the duct wall; 3. an air gap between a comparatively stiff panel (duct wall) and a flexible thin plate is efficient in achieving low-frequency sound absorption in the duct ventilation system.
References [1] Allen CH. Noise reduction. Beranek LL, editor. New York: McGraw-Hill; 1960. [2] Guthrie A. Low frequency acoustic transmission through the walls of various types of ducts. MSc dissertation, Polytechnic of South Bank, UK; 1979. [3] Cummings A. Low frequency acoustic transmission through the walls of rectangular ducts. Journal of Sound and Vibration 1978;61:327–45. [4] Cummings A. Low frequency sound transmission through the walls of rectangular ducts: further comments. Journal of Sound and Vibration 1979;63:463–5. [5] Cummings A. Low frequency acoustic radiation from duct walls. Journal of Sound and Vibration 1980;71:201–26. [6] Cummings A. Stiffness control of low frequency acoustic transmission through the walls of rectangular ducts. Journal of Sound and Vibration 1981;74:351–80. [7] Cummings A. Design charts for low frequency acoustic transmission through the walls of rectangular ducts. Journal of Sound and Vibration 1981;78:269–89. [8] Bolton JS, Shiau NM, Kang YJ. Sound transmission through multi-panel structures lined with elastic porous materials. Journal of Sound and Vibration 1996;191:317–47. [9] Frommhold W, Fuchs HV, Sheng S. Acoustic performance of membrane absorbers. Journal of Sound and Vibration 1994;170:621–36. [10] Kang YJ, Bolton JS. A finite element model for sound transmission through foam-lined doublepanel structures. Journal of the Acoustical Society of America 1996;99(5):2755–65. [11] Kiyama M, Sakagami K, Tanigawa M. A basic study on acoustic properties of double-leaf membranes. Applied Acoustics 1998;54:239–54. [12] Takahashi D, Sakagami K, Morimoto M. Acoustic properties of permeable membrane. Journal of the Acoustical Society of America 1996;99(5):3003–9. [13] Astley RJ, Cummings A, Sormaz N. A finite element scheme for acoustic propagation in flexiblewalled duct with bulk-reacting liners, and comparison with experiment. Journal of Sound and Vibration 1991;56:119–38. [14] Cummings A. The attenuation of sound in unlined ducts with flexible wall. Journal of Sound and Vibration 1994;174:433–50. [15] CIBSE Design Guide. Sound control, Section B.12. Chartered Institute of Building Services Engineers; 1986. [16] ASHRAE Handbook. Sound and vibration control, chapter 32. Atlanta (GA): American Society of Heating. Refrigeration and Air Conditioning Engineers; 1987.