Vibration isolation on floating floors

AppliedAcoustics15 (1982) 97 109

VIBRATION ISOLATION ON F L O A T I N G FLOORS

P. A. NELSON

Sound Attenuators Ltd, Eastgates, Colchester, Essex (Great Britain) (Received: 7 April, 1981)

SUMMARY

An analysis is presented of the noise problem produced when the application of standard acoustic treatment to a roof-mounted diesel generator Jailed to meet the design criterion. The problem was diagnosed as excessive vibration reaching the building due to the excitation of a resonance of the supporting structure. The resonance responsible was identified as a flexural mode of the partial floating floor installed below the generator set in order to provide a high transmission loss acoustic barrier. A solution to the problem was provided by converting the existing vibration isolation into a compound system. The reasons for the Jailure of the existing system are analysed. A simple theory is developed which illustrates that the ratio of machine mass to floating floor mass is the important parameter determining the severity o[ excitation of )qoating floor resonance. It is concluded that machines can be safely mounted via vibration isolators onto continuous floating floors provided the)' have a low mass compared with the floatingfloor mass and are provided with a low mounted resonant frequeno, compared with the floating floor resonant J?equency.

INTRODUCTION

Floating floors are increasingly being used in buildings to provide a substantial degree of acoustic isolation of machinery. A typical installation consists of a plantroom in which an additional 100 mm thick concrete slab is supported off the basic structural slab by a series of resilient pads. Such an arrangement is usually designed to have a resonant frequency of around 20 Hz. The floating slab/structural slab combination can produce a net Sound Reduction Index (SRI) of as much as 50 dB at 100 Hz. The introduction of such a resonant system onto a plantroom floor does, however, introduce a problem with regard to the vibration isolation of the 97

Applied Acoustics 0003-682X/82/0015-0097/$02.75 ~" Applied Science Publishers Ltd, England, 1982 Printed in Great Britain

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P . A . NELSON

machinery. It has to be ensured that the floating floor is not excited into resonance by machinery vibrations. There are two possible approaches to this. First, concrete plinths or 'upstands' can be built onto the main slab to protrude through the floated floor, onto which the machinery can be mounted via conventionally selected vibration isolators. This system has the disadvantage of producing an 'acoustic weak link' and may lead to the deterioration of the net SRI of the floor. Secondly, a continuous floated slab can be used with machinery mounted directly onto the slab via high deflection coil spring isolators to ensure a mounted resonant frequency well below the floor resonance. Although such a continuous floor has to be provided with high load bearing resilient pads at specific machinery locations, it does not suffer from any acoustic weak links and is, in general, more straightforward to install. The more desirable continuous floating floor system has been successfully installed on literally thousands of occasions in the United States and in several hundred buildings in the UK. There has been little evidence of the excitation of floating floor resonance by machinery vibration. To the author's knowledge, there has only been one floating floor installation which has proved problematic. This paper presents a case history of that noise problem and the lessons learnt from providing its solution. The particular installation considered was somewhat unusual in that it made use of a partial floating floor covering a specific area of a roof slab which was surrounded by an acoustic enclosure. This type of installation is finding increasing use in the acoustic treatment of individual items of machinery installed in buildings. A severe vibration problem was produced in this particular case, as the enclosed machinery excited the floating floor into resonance. The diagnosis of this problem in itself proved an interesting process and a brief account is presented here of the techniques used to establish the exact cause of the problem. The effectiveness of the solution implemented provides some important practical data, which is also presented. Finally, the measurements made give a useful starting point for producing a design guide for the selection of vibration isolation equipment used on partial foating floor installations. A theory is outlined which identifies the ratio of machine mass to floating floor mass as a vital parameter determining the possibility of the serious excitation of floor resonance. This analysis provides a firm basis for ensuring that problems with partial floating floors can be avoided in future installations.

THE PROBLEM INSTALLATION

Figure 1 shows a schematic layout of the acoustic enclosure and partial floating floor used to reduce the transmission of noise from a 400 kW diesel generator set. The set was mounted on the roof top of a multi-storey building and was installed to provide standby power generation. The acoustic enclosure was constructed from modular 16 swg galvanised mild steel panels lined internally with 100 mm thick glass fibre, and

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faced with perforated metal sheet. The enclosure was provided with inlet and outlet splitter attenuators to allow the passage of cooling air. The floating floor consisted of a 100mm thick concrete slab supported off the roof slab by precompressed moulded glassfibre pads. The roof slab itself was provided with additional support from structural steel beams built into the steel frame of the building. The generator set weighed 7-4 tonnes and was mounted on a concrete inertia base weighing 8.4 tonnes. This inertia base was mounted off the floating floor via eight coil spring isolators. The static deflection of each isolator was 31 mm. This provided the inertia base/generator set combination with a mounted natural frequency of 2.8 Hz. The set ran at a constant 1500 rpm, producing a basic rotational frequency excitation of 25 Hz. All pipework and electrical cables connected to the set were flexible to ensure no short-circuiting of the vibration isolators. The exhaust pipe was ducted into primary and secondary reactive attenuators mounted offthe roof slab external to the enclosure via resilient pads. The exhaust pipe in the enclosure was suspended from the enclosure roof via spring hangers. This type of installation has been used very successfully on numerous occasions in order to acoustically insulate roof-mounted diesel generator sets. In this instance, the subjective impression gained by a listener on the roof top adjacent to the set was that the enclosure proved remarkably effective. In the offices on the floor below the installation, however, the characteristic ~thud' of a diesel engine was clearly and unacceptably audible. In a collection of offices immediately beneath the set, a substantial level of vibration was perceptible on the building structure. The target design criterion of NC35 was exceeded by 15 dB in the 63 Hz octave band. A series of experiments was thus undertaken in order to establish the precise cause of failure of this particular installation.

THE DIAGNOSIS OF THE PROBLEM

The first series of experiments undertaken was to measure the one-third octave band SPL in three specific locations. Figure 2(a) shows the SPL measured at a fixed location inside the acoustic enclosure, Fig. 2(b) shows the spectrum measured at 1 m from the exhaust pipe exit and Fig. 2(c) shows the spectrum measured in an office immediately below the set. At each of these three measurement positions the SPL was measured with the set operating with an electrical load of 170 kW and also with the set 'running light'. First note that the measured office noise spectrum is dominated by a peak in the 80 Hz third octave band. The exhaust noise spectrum is similarly dominated by a peak at 80 Hz. This can be related to the firing frequency of the engine. The V12 deisel engine produced three combustion strokes for every revolution of the crank-shaft, resulting in a firing frequency of 75 Hz. The peak level in the spectrum measured inside the enclosure was also 80 Hz, but was not nearly so pronounced. Also note that both the exhaust exit noise and the noise level in the

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enclosure increased slightly (between 3 and 5 dB) with increasing load, whilst the office noise level decreased. Further to this, the office noise spectrum contains a peak in the 25 Hz one-third octave band (the rotational frequency) whilst the exhaust noise has a peak in the 40 Hz one-third octave band (half the firing frequency). All these aspects of the measured spectra tend to rule out airborne noise transmission, either from the enclosure or the exhaust pipe exit. The evidence provided by these fairly subtle features of the measurements is a little tenuous. Further experiments were undertaken in order to positively eliminate airborne sound transmission. A loudspeaker source was used to generate airborne noise inside the enclosure without the set running. A modulated pure tone was used

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to generate a broad-band spectrum over the 63 Hz octave. The average SPL was measured in both the enclosure and the office. The results showed clearly that 25 dB more noise was generated in the office with the engine running than would be expected from the transmission of airborne sound through the floating floor. The SR! of the floor estimated from this approximate measurement was also in accordance with the expected value for this installation. A similar procedure was repeated in order to simulate exhaust exit noise. It was again concluded that the levels generated in the office would not be as the result of airborne sound from the exhaust, even though the office noise was subjectively almost identical to the exhaust noise. Attention was thus focused on a possible vibration source associated with either the engine or the exhaust system. Figure 3 shows a 3 per cent bandwidth analysis of

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the acceleration level measured on the inertia base and at the exhaust pipe exit. The inertia base vibration spectrum clearly contains peaks at the engine rotational frequency (25 Hz) and firing frequency (75 Hz) and their various harmonics. The exhaust vibration spectrum only clearly shows a peak at the engine firing frequency.

VIBRATION ISOLATION ON FLOATING FLOORS

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Figure 4 shows the acceleration spectra measured on the floating floor (at the foot of a spring isolator) and on the wall of the office below the generator set. The office wall vibration spectrum was dominated by a peak at the engine firing frequency, although other multiples (at 50 Hz and 62.5 Hz) of the engine rotation were also evident. This suggested that it was, indeed, engine vibrations that were being transmitted into the building structure, since the exhaust vibration spectrum did not contain the 50 Hz and 62.5 Hz peaks.

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An attempt was then made to measure the insertion loss of the coil spring isolators. Steel wedges were driven between the inertia base and the floating floor, in order to short-circuit the coil springs. Figure 4 shows the effect of this short-circuit on the office wall. The results are, at first sight, confusing. The measurements made at the isolator foot show that this particular coil spring has an insertion loss of the normally anticipated value of 20 30 dB. The office wall measurements, however, imply that the coil spring isolators have an insertion loss approaching zero in the region of 75 Hz, but provide adequate isolation at frequencies well above and below

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this. The isolator insertion loss deduced from the office wall measurements is plotted in Fig. 5. This measurement gives a clear indication that the isolator performance is reduced in a specific frequency range by a resonance of the structure. The reduction of isolator insertion loss in a specific frequency range by foundation resonance is illustrated by Snowdon.1 The observation of an apparently effective isolator may be explained by the form of the foundation resonance excited. A systematic series of measurements made along the floating floor surface below one edge of the inertia base resulted in a well defined spatial pattern of acceleration level in the 3 per cent band centred on 75 Hz. 20 o

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Coil spring isolator insertion loss measured from short-circuit test.

This is illustrated in Fig. 6. The results measured have been extrapolated to show the probable vibrational mode shape of the foundation. Although it was not possible to make vibration measurements at each end of the floating floor slab, due to the presence of the inlet and outlet attenuators, the measurements made imply that the floating floor was vibrating in the first flexural mode of a plate with the free boundary conditions. The mode appears to be driven by the two centre coil spring isolators down each side of the inertia base. The isolators at the ends of the inertia base are closer to the nodes of the mode shape. The apparently high insertion loss measured for one of these isolators could, perhaps, have been caused by a slight shift in the mode shape when the isolators were short-circuited and the excitation modified. It is interesting to calculate the natural frequency of this mode to be expected from theory. Since the floating floor measured 8.76 m × 2.88 m - - t h u s having an aspect ratio of about 3:1 the natural frequency can be estimated by treating the floor as a beam (Leissa2). The resonant frequency, (~r, is given by: ~or = A

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where A is a constant depending on the mode number and boundary conditions, L is the beam length, E 1 is the beam stiffness and p the mass per unit length. The value of A for a free free beam in its first flexural mode is 22.4 (Harris and Crede3). Taking.

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E for concrete as 13.9 × 109 N/m 2 and the density of concrete as 2240 kg/m 3 results in a value of the resonant frequency of 66 Hz. This confirms the view that the resonance responsible for the problem was produced by a flexural vibration of the partial floating floor. The extent to which this was made more severe by the supporting steelwork in the building structure is not easy to determine. It is almost certain, however, to have made the situation worse, rather than better.

THE SOLUTION

The solution to this problem was to provide a compound isolation system for the generator set. It was evident that providing a low mounted natural frequency compared with the floor resonance was not sufficient to avoid the strong excitation of the resonance by the engine firing frequency. The mechanics of the compound isolation system has been thoroughly dealt with by many authors (for a detailed treatment see Snowdon 1 or Unga~ and Dietrich4). The system is produced by providing two sets of resilience separated by an additional 'blocking mass' between the mounted mass and the foundation. This system produces two mounted resonant frequencies, but a considerably improved high frequency performance. The high

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P. A. N E L S O N

frequency insertion loss of such a system, mounted on a hypothetical rigid foundation, increases at 24 dB/octave compared with the 12 dB/octave for a simple mass spring system. The existing inertia base was used to provide the intermediate mass, being almost ideally suited to the task since it was of a similar mass to that of the generator set. The remedial work involved was thus simply to insert additional resilience between the generator set and the inertia base. It was necessary to design the stiffness of the additional resilience to ensure that the natural frequencies of the compound system were both well below the basic rotational frequency of the engine. These natural frequencies, 0)~ and 0)2, are given by (Snowdont): (1 + ~ 0)~22--- 0)°2\ 2 ~ - J / ( l

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Here M~ is the mass of the generator set, M z the mass of the inertia base, K 2 the stiffness of the coil springs and K~ the stiffness of the additional resilience. This was provided by a series ofglassfibre pads inserted between the skids of the generator set and the inertia base. This was accomplished by lifting the entire set on hydraulic jacks and extending the vertical height of the exhaust pipe inside the enclosure. The two natural frequencies produced by this system were 2.9 Hz and 12.6 Hz. The basic natural frequency of the system was thus only marginally changed. The change in acceleration level produced on the office wall below the generator set is shown in Fig. 7(a) and the reduction in the office sound pressure level in Fig. 7(b). The use of the compound system reduced the peak response of the floating floor resonance by 15 dB. The reduction in noise level produced was sufficient to exactly meet the NC35 design criterion in the 63 Hz octave band and was below NC35 in all other octave bands. Subjectively, the engine noise was no longer perceptible.

THE A V O I D A N C E OF F U T U R E PROBLEMS

Attention will now be focused on the reasons for the failure of this particular installation. Certainly it was unfortunate that the engine firing frequency coincided with a natural frequency of the floating floor. However, there are many other installations which have proved successful, even when a machine firing frequency is close to the nominal floor resonant frequency. The provision of a low mounted

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natural frequency usually reduces the extent of resonance excitation. The failure of this installation is due to the unusually high mass of the mounted equipment relative to the mass of the floating floor. The influence of this parameter on the insertion loss of isolator systems mounted on resonant foundations is evident in the work of Snowdon.1 This effect is made more explicit by the following simple analysis. The insertion loss of a massless isolator of mobility, M I, between a vibration source of mobility, Ms, and a receiver of mobility, MR, is given by (Ungar and Dietrich 4): IL=2Ologlo

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P . A . NELSON

It will now be assumed that the source mobility is that of a rigid mass, M, and the isolator mobility is that of a massless spring of stiffness K. The receiver will be assumed to be a floating floor in resonance at a frequency, cot. The floor mobility will be assumed to be damping controlled (at resonance) and thus consist of only a real part given by the inverse of the damping coefficient. This can be expressed in terms of the resonant frequency, tot, the quality factor, Q, of the resonance and the "reduced mass', m, of the simple system representing the floating floor resonance. The expression for the isolator insertion loss at the frequency % is thus:

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where to,, = x / K / M is the mounted natural frequency of the equivalent system on a rigid foundation. Thus, for this somewhat idealised model, the isolator insertion loss is shown to be a function of the frequency ratio (to/to,,), mass ratio (M/m) and damping ratio (which is given by (I/2Q)). This analysis illustrates clearly that the extent to which isolator insertion loss is reduced by floating floor resonance is crucially dependent on the ratio of the machine mass to the floating floor mass. Thus, in general, relatively lightweight machinery (M << m) will not suffer from deterioration in isolator insertion loss due to floor resonance and sufficient insertion loss is ensured by a large value of tot/tom' This is entirely consistent with experience. Relatively light machines provided with a low mounted natural frequency do not produce severe excitation of floating floor resonances, even when the excitation j?equency is close to floor resonant J?equeney. The particular problem considered here represented the complete reverse of that situation. The total floating floor mass was 5-7 tonnes. The reduced mass, m, for practical floors is typically between 0.1 and 0.3 times the total mass (see the discussion by Breeuwer and TukkerS). The total mounted mass, M, was 15.8 tonnes. The value of M/m was thus of the order of 25. In addition, the value of Q was of the order of 10. This value of damping is estimated from the bandwidth of the resonance in the acceleration spectrum measured on the office wall. It is also consistent with the damping of conventional floor resonances assumed by Melzig-Thiel and Meltzer* and those measured by Fahy and Westcott. 7 Thus, even with a frequency ratio of the order of 25, the isolator insertion loss to be expected at the floating floor resonant frequency is only of the order of 8 dB. This is reasonably close to the value measured using the isolator short-circuit test.

VIBRATION ISOLATION ON FLOATING FLOORS

109

CONCLUSIONS

(1)

(2)

It is possible to mount vibrating machinery directly onto continuous floating floors provided a given machine is relatively light compared with the floor mass and has a relatively low mounted natural frequency compared with the floor resonant frequency. Experience has shown that most installations involving mechanical services plant mounted on a complete plantroom floating floor fall into this category. Mounting particularly heavy machinery on relatively light partial floating floor installations results in the possibility of the excitation of floor resonance, even when the machine is provided with a mounted natural frequency much less than the floating floor resonant frequency. In these instances, a compound system can be used to provide adequate vibration isolation. This avoids the use of plinths or upstands, which may short-circuit the floating floor and reduce the net Sound Reduction Index.

REFERENCES 1. J. C. SNOWDON,Vibration and shock in damped mechanical systems, John Wiley & Sons Inc., New York, London, Sydney, 1968. 2. A. W. LEISSA, The free vibration of rectangular plates, Journal of Sound and Vibration, 31(3)(1973), pp. 257-93. 3. C. M. HARRIS and C. E. CREDE, Shock and vibration handbook, Volume 1; Basic theory and measurements, McGraw-Hill Book Co., New York, 1961. 4. E. E. UNGAR and C. W. DIETRICH, High frequency vibration isolation, Journal of Sound and Vibration, 4(2) (1966), pp. 224~41. 5. R. BREEUWERand J. C. TUKKER, Resilient mounting systems in buildings, Applied Acoustics, 9(2) (1976), pp. 77-101. 6. R. MELZIG-THIEL and G. MELTZER, Messung und Berechnung der Eingangsadmittanzen yon Gebaudedecken, 7th ICA Congress, 20 V3, Budapest, 1971. 7. F.J. FAHY and M. E. WESXCOTT,Measurement of floor mobility at low frequencies in some buildings with long floor spans, Journal of Sound and Vibration, 57(1) (1978), pp. 101 29.