INTER-NOISE AUGUST 2007 ISTANBUL, TURKEY

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1 INTER-NOISE AUGUST 7 ISTANBU, TURKEY A comparison between the structure-borne sound generated by a low-frequency vibrating plate mounted on a light-weight structure and on a heavy-weight structure Pieter Schevenels a, Nathalie Geebelen, Gerrit Vermeir Katholieke Universiteit euven aboratory of Acoustics and aboratory of Building Physics Celestijnenlaan d, bus 2416 B-31 euven BEGIUM ieven De Geetere, Bart Ingelaere Belgian Building Research Institute ombardstraat 42 B- Brussel BEGIUM ABSTRACT Vibrating therapy appliances in medical institutions and fitness centers are gaining interest, because of their curative effect on the human body. As the demand of appliances rises, so does the problem of their noise production. A lot of the vibrational energy is passed to the supporting structure, after which it is radiated as audible sound in other rooms of the building (structure-borne sound). This paper describes how a vibrating plate will behave installed on a light-weight wooden structure, on a heavy-weight concrete structure and on a heavy-weight floating floor structure. All supporting structures are part of a floor between two vertically separated transmission rooms. Sound levels of both rooms, as well as acceleration levels of the floors, are measured. The total sound transmission consists of airborne sound transmission and structure-borne sound transmission. The measured sound pressure level is then compared with the predicted sound pressure level achieved by the draft standards pren and pren (the reception plate method). It appears that the low-mobility nature of the source will only cause problems when the source s operating frequency lies within a frequency band with a matching source-structure mobility. 1 INTRODUCTION An operating machine of any kind produces a sound field p in the machinery room in two ways. First, there is the airborne sound pa. This is the sound which is directly radiated from the vibrating parts of the machine into the air. It can be characterized by the airborne sound power level Wa. Since the equipment is always attached to a supporting structure, there will be vibrations of the machine which are injected into that structure. On its turn, the structure will radiate these vibrations as structure-borne sound ps into the air. This is the second contribution to the sound field in the machinery room, which can be characterized by the structure-borne sound power level Ws. a address: pieter.schevenels@bwk.kuleuven.be

2 In most domestic buildings, one is generally less interested in the sound field in the machinery room than in the sound field in other rooms of the building. The sound field in a receiver room, due to the airborne and structure-borne sound power level of the machine, is determined by various transmission paths between the source room elements and the receiver room elements. Concerning installation noise, a European standard is being developed by WG2 of technical committee CEN/TC126. This standard will be part 5 of the future EN 12354, which in general describes how to estimate the acoustic performance of buildings from the performance of elements. In the draft standard, the normalized structure-borne sound pressure n,s,ij for the transmission path between supporting building element i and radiating element j in the receiving room is determined as [1]: D R S i ref n,s,ij = Ws,inst,i sa,i ij,ref 1lg 1lg (1) Sref 4 A where Ws,inst,i is the installed structure-borne sound power level of the source at element i, D sa,i is the adjustment term from structure-borne to airborne excitation for element i, R ij,ref is the reference flanking sound reduction index for transmission from element i to element j, S i is the area of element i and S ref and A ref are reference areas of 1 m². For the case of a single contact point and a single degree of freedom, the installed structure-borne sound power can be written: Re { Y } 2 sf i Ws,inst,i = 1lg 2 Wref Ys + Yi v (2) where v sf is the r.m.s. free velocity at the contact point, Y s is the source mobility and Y i is the mobility of the receiving element i. By use of the reception plate method [2 6], which uses a force source assumption ( Ys Y i ), this becomes: Ws,inst,i Re{ Y } 1lg i = Wsn + (3) Y,rec where Wsn is the normalized structure-borne sound power into a 1 cm thick concrete reception plate and Y,rec is the characteristic mobility of a virtual infinite 1 cm thick concrete plate, taken as 51 6 m/ns. Wsn can be written as: Wsn Y = + (4) Ws,rec 1lg,rec Re{ Y } rec in which Re{ Yrec} is the real part of the mobility of the reception plate at the connection point. Ws,rec is calculated out of the energy balance of the reception plate: ( η π fm S ) = 1 lg (5) Ws,rec rec rec rec v,rec

3 in which v,rec is the spatially averaged vibration velocity level (reference 11 9 m/s) and η rec, m rec and S rec are respectively the loss factor, the mass per unit area and the area of the reception plate. For the case of multiple contact points and/or multiple degrees of freedom, adapted versions of equations (2 4) exist [7]. 2 EXPERIMENTA SETUP The reception plate, used for the experiments described in this paper, is located at the Belgian Building Research Institute (BBRI). It measures 2 x 2.8 m², has a thickness of 1 cm and a minimum loss factor of 8 % below Hz. Therefore the plate complies with the requirements in draft standard pren [8]. A FitVibe 6 (Figure 1 and 2), which is a vibrating therapy appliance, is used as a vibrational source. It is designed to produce vertical vibrations with an amplitude up to 3 mm and frequencies between and 6 Hz, adjustable in steps of 1 Hz. The mechanism used consists of two motors, each connected to several concentric elliptical elements, that rotate in opposite sense and lift the vibrating plate twice at each turn. The size of the vibrating plate is x 41 cm. Figure 1: The FitVibe 6 on the reception plate. Figure 2: A schematic view of the FitVibe 6. In order to consider realistic scenarios, the FitVibe 6 is evaluated with and without a person standing on the top plate. To simulate this person, a barrel of water is put upon a 1 cm thick damping mat. This damping mat avoids drifting of the load and simulates in some way the damping effects of the body. Figure 3: Wooden floor and concrete floor between transmission rooms.

4 The FitVibe 6 is tested in two transmission rooms at the aboratory of Acoustics at the K.U.euven (Figure 3). Only vertical degrees of freedom in the contact points have been considered. Between the leftmost transmission rooms, a wooden structure of 3 x 3 m² is mounted. This wooden floor consists of a 18 mm thick fibreboard plate supported by seven wooden joists, each with a cross-section of 19 x 7 cm². The bottom side is finished with two gypsum board plates of 12.5 mm thickness. The space in between is filled with 6 cm thick glass wool (17 kg/m³). A part of a model of this wooden floor is shown in Figure 4. Between the rightmost transmission rooms, a concrete floor of 2 x 2 m² and 1 cm thickness is mounted. In a second phase, a floating floor is mounted on this concrete floor. This floating floor consists of a 3 cm thick layer of mineral wool ( kg/m³) and a smaller light-density concrete plate (1 kg/m³) of 1.5 x 1.5 m² and 5 cm thickness. This floating floor, with the loaded FitVibe 6 on top of it, is shown in Figure 5. Figure 4: Model of the wooden floor. Figure 5: oaded FitVibe 6 on the floating floor. Both floors are mounted resiliently with respect to the surroundings, as will be experimentally proven, so flanking sound transmission can be neglected. Therefore the structure-borne sound pressure level in the lower room is only dependent of one transmission path. Written in terms of the equivalent absorption surface A in the lower room, that level becomes: A ps = Ws,inst,i Dsa,i R 1lg (6) 4 where R is the airborne sound insulation between both rooms. First the following characteristics for each floor are measured: oss factor η according to ISO 1-3, Annex E [9] Airborne sound insulation R in accordance with ISO 1-3 [9] Next, on each floor the influence of following parameters is studied: Operating frequency: 24 Hz, Hz, 6 Hz Position: middle of plate, corner of plate oad: kg, 6 kg This has been done by measuring the following variables for each combination of the above parameters: Airborne sound power level Wa in accordance with ISO 3742 for narrow-band sound sources [1] Normalized structure-borne sound power level Wsn into the reception plate [8] Acceleration level a of the floor Mobility Y i of the floor according to ISO 7626 [11] Sound pressure level p in the upper and lower room

5 3 MOBIITIES AND OSS FACTORS Since the sound power injected into a building element i is greatly determined by its mobility value Y i, the mobilities of the investigated floors are discussed first. Due to practicalities, the source mobility Y s hasn t been measured yet. The mobilities of the different floors are measured by use of an electro-dynamic shaker that was hung carefully on a construction in order to avoid any pre-loading of the examined floor. A force sensor is connected to the shaker by a thin threaded rod of 2.5 cm length, in order to allow only perpendicular forces to pass. The other side of the force sensor is screwed into a nut which is glued to the surface of the floor. At the point of interest, an accelerometer is attached. A linear sweep is sent out and impulse responses of the force and acceleration are determined by deconvolution of the received signal with the sent signal. The mobility between point k and point l of element i is defined as [12]: Y i,kl ( ω ) v ( ω) ( ) a ( ω) ( ) i,l i,l = = (7) Fi,k ω jωfi,k ω Since the FitVibe 6 has three contact points, not only point mobilities are important, but also transfer mobilities have to be measured. By using the concept of effective mobilities at the contact points Y i,k and Y s,k, the single point/single degree of freedom formalism can be easily extended [7], so equation (2) becomes: { Yi,k} v Re (8) 2 sf,k Ws,inst,i = 1lg 2 k Wref Y s,k Y + i,k If we use the force source approximation Y s,k Y i,k and more or less equal effective receiver mobilities for the 3 contact points, equation (8) can be simplified: Re 1lg 2 { Yi,k} v sf,k Ws,inst,i 2 W ref k Ys,k (9) For calculating the contact-point-averaged effective receiver mobilities, it is assumed that the forces in the different contact points have equal amplitude. If further a random phase assumption is made, the average real part of the effective receiver mobility becomes independent of transfer mobilities: Re 1 3 { } = i,k Re{ } i,kk Y 3 k= 1 Y (1) where Y i,kk is the point mobility in contact point k of (floor) element i. In the experiments, this random phase assumption seems not to deviate much from the zero phase assumption, which in fact does take into account transfer mobilities. Therefore only the random phase assumption is considered in this paper. All above assumptions are also made in the reception plate method [8], which allows us to calculate the installed structure-borne sound power out of the measured power dissipated

6 in the reception plate and the averaged effective receiver mobilities in both cases. Equations (3) and (4) can then be combined to: Ws,inst,i { Yi,k} { Yrec,k} Re Ws,rec + 1lg (11) Re In Figure 6, this averaged real part of the effective receiver mobility is shown for a corner and middle position of the FitVibe 6 on the wooden floor, the concrete floor and the floating floor. Also the average real part of the mobility of the reception plate is shown. Average real part of effective receiver mobility [m/ns] Wooden floor (corner) Wooden floor (middle) Concrete floor (corner) Concrete floor (middle) Floating floor Reception plate 1-7 Figure 6: Effective mobilities of the different floors for different positions of the source. From this figure can be seen that the mobility of the wooden floor is the highest of all mobilities, except at lower frequencies. There is a small difference between the two different positions on this wooden floor around the frequencies from 125 to Hz. This is due to (the first) resonances of the wooden floor, which are most distinct in the middle of the floor. The loss factor η lies between.5 (at the lower frequencies) and.3 (at the higher frequencies). The mobility of the concrete floor at higher frequencies is more or less the same as that of the reception plate, no matter what the position of the source is. This is because for both the concrete floor as for the reception plate the characteristic value for the mobility of a 1 cm thick concrete floor is attained at higher frequencies. At lower frequencies, the mobility of the concrete floor is much larger than that of the reception plate, due to the very low lowfrequency loss factor η of the concrete floor. This loss factor is deduced from the acceleration impulse response and lies between.3 and.1. Therefore it appears to be dominated by the material damping of the concrete itself, which typically has values around.2. In other words, there is no much structural energy loss at the borders of the plate, which confirms the assumption that the plate is resiliently mounted. The mobility of the floating floor is, as expected, much lower than the other mobilities. Moreover, the basic resonance frequency of the floating floor system can clearly be seen at

7 Hz and at its harmonics 16 Hz and 315 Hz. The loss factor η doesn't differ much from the loss factor found in the concrete floor by itself. 4 CACUATED AND MEASURED SOUND PRESSURE EVES In this section, measured values of the sound pressure level p in the lower room are compared with calculated values. The calculated values are obtained by use of the draft standard pren and a reception plate method complying with the requirements in draft standard pren These values are the logarithmic sum of an airborne sound pressure component pa and a structure-borne sound pressure component ps. In all experiments, pa in the lower room has been found to be much lower than or equal to ps in that room. Nevertheless, the total calculated sound pressure value p will be used for the following comparisons. Since loss factor measurements have shown all floors are mounted quite resiliently, only the direct sound transmission from upper to lower room needs to be taken into account. This simplification has also been validated by measurements of the acceleration levels a on the test floors themselves and at a point on the surrounding carrying floor while the source was operating, where the latter a has been found to be considerably lower. 4.1 Wooden floor Although the conditions for applying the reception plate method may be expected to be invalid, it has nevertheless been applied to the case of the wooden floor for illustrative reasons and for reason of completeness. In Figure 7, the calculated and measured sound pressure level p in the lower room are shown for two operating frequencies, with the unloaded source at the corner of the wooden floor. p [db()] (re Pa) 6 24 Hz - corner - kg (calc.) (42.4 db(a)) 24 Hz - corner - kg (meas.) (72.7 db(a)) p [db()] (re Pa) 6 Hz - corner - kg (calc.) (52.4 db(a)) Hz - corner - kg (meas.) (6. db(a)) Figure 7: Calculated and measured sound pressure level in the lower room with the source on the wooden floor. (Curves are plot in db(), global values are given in db(a).) At higher frequencies, the calculated results seem to underestimate the measured results to a very large extent. The reason is that the reception plate method, which is used to obtain the calculated results, assumes the building element to have a low mobility, so that the force source assumption would be valid. From Figure 6, it is clear that this is probably not the case, since the wooden floor mobility is high at higher frequencies. Therefore, it is expected that, at higher frequencies, the source mobility Y s is not sufficiently higher than the mobility of the wooden floor. At low frequencies though, where the mobility Y i is lower, the correspondence between calculated and measured sound pressure levels is rather decent. This means that, at lower frequencies, the source mobility Y s is larger than the mobility of the wooden floor.

8 4.2 Concrete floor In Figure 8, the calculated and measured sound pressure level p in the lower room is shown for the three operating frequencies, with the unloaded source in the middle of the concrete floor. p [db()] (re Pa) 6 24 Hz - middle - kg (calc.) (44.5 db(a)) 24 Hz - middle - kg (meas.) (35.8 db(a)) p [db()] (re Pa) 6 Hz - middle - kg (calc.) (55.2 db(a)) Hz - middle - kg (meas.) (64.4 db(a)) p [db()] (re Pa) 6 6 Hz - middle - kg (calc.) (71.5 db(a)) 6 Hz - middle - kg (meas.) (64.1 db(a)) Figure 8: Calculated and measured sound pressure level in the lower room with the source on the concrete floor. (Curves are plot in db(), global values are given in db(a).) As one could expect out of the bad results with the wooden floor, deviations are probably caused by the low-mobility nature of the source, which leads to an unfulfilled force source assumption. It appears from a quick experiment with a hammer impulse and a spectral analyzer that the concrete floor mobility is the highest in the frequency band of Hz, where its basic resonance frequency is located. In the frequency band around 24 Hz, the floor mobility will most likely be lower, due to the stiffness controlled region in the behaviour of the floor. From Figure 6, it is seen that the floor mobility at the band around 6 Hz is also lower than the mobility at the band of Hz, because of an anti-resonance. The reception plate method experiences problems, but only at an operating frequency of Hz, even though the ratio of the source mobility to the mobility of the floor is independent of the operating frequency. Therefore it is thought that it doesn t really matter if the source mobility comes close to the floor mobility around its (basic) resonance frequencies, as long as the operating frequency of the source isn t situated near one of these resonances. If this happens anyhow, this has an influence on all frequency bands. This might be due to resonances of any kind in the machinery of the source. These resonances are activated because the source mobility Y s will probably match the concrete floor mobility Y i at Hz, which shoots up the global injected power.

9 4.3 Floating floor As one could expect from the lower receiver mobility, the calculations of the source pressure level p agree much more with the measured values than in the case of the concrete floor. This can be seen in Figure 9, where the case of the loaded source is showed. p [db()] (re Pa) 6 24 Hz - 6 kg (calc.) (35.5 db(a)) 24 Hz - 6 kg (meas.) (35.3 db(a)) p [db()] (re Pa) 6 Hz - 6 kg (calc.) (48.5 db(a)) Hz - 6 kg (meas.) (47.3 db(a)) Figure 9: Calculated and measured sound pressure level in the lower room with the source on the floating floor. (Curves are plot in db(), global values are given in db(a).) 5 CONCUSIONS A vibrating therapy appliance has been placed on a concrete floor, a floating floor system and a wooden floor between two vertical transmission rooms. It has been put into operation at frequencies of 24 Hz, Hz and 6 Hz on different positions of the floor. Sound pressure levels in the lower room have been measured and calculated by use of the draft standard pren , together with a reception plate method complying with the requirements in draft standard pren The force source assumption, made by use of the reception plate method, has been discussed for all floors. The wooden floor has the highest mobility and calculations deviate strongly from the measurements, as expected because the force source assumption is not fulfilled. Therefore it is thought that the source mobility doesn t exceed the mobility of the wooden floor sufficiently. The floating floor system has the lowest mobility and the calculations agree much more with the measurements, hereby validating the use of the reception plate method for low floor mobilities. The mobility of the concrete floor lies somewhat in between the two other mobilities and resembles the mobility of the reception plate, at least for higher frequencies. At lower frequencies, the behaviour is largely different in that the concrete floor has a basic resonance frequency at about Hz, while the much more damped basic resonance frequency of the reception plate is about 58 Hz. For operating frequencies of 24 Hz and 6 Hz the used reception plate works rather fine, but for an operating frequency of Hz, bad results are obtained. The resonance of the source on the concrete floor is so pronounced that the predicted results at higher frequency bands have become unreliable. Therefore, it is concluded that a reception plate might still be able to predict the injected sound power level in a building element rather well in case of a low-frequency source with a rather low mobility, as long as this source operates at a frequency where the mobility of the building element still fulfills the condition Ys,k Yi,k.

10 6 ACKNOWEDGEMENTS This work was partly supported by the Belgian Ministry of Economic Affairs. A part of the measurements was done in the frame of a master thesis by Arne Dijckmans and Jeroen Van Minnebruggen. The FitVibe 6 was provided by the company GymnaUniphy. 7 REFERENCES [1] pren :7, Building Acoustics Estimation of acoustic performance of buildings from the performance of elements Part 5: Sound levels due to service equipment, European Committee of Standardization, Brussels, Belgium, (7). [2] M. M. Späh, B. M. Gibbs and H.-M. Fischer, Characterization of mechanical installations in buildings as structure-borne sound sources, Proceedings of the 1 th International Congress on Sound and Vibration (3), pp [3] M. M. Späh, H.-M. Fischer and B. M. Gibbs, Measurement of structure-borne sound power of mechanical installations in buildings, Proceedings of the 11 th International Congress on Sound and Vibration (4), pp [4] E. Gerretsen, Development and use of prediction models in Building Acoustics as in EN 12354, Proceedings of Forum Acusticum 5 (5), pp [5] N. Qi and B. M. Gibbs, Structure-Borne Power from machines in buildings: Prediction of Installed Power from aboratory Measurements, Proceedings of Forum Acusticum 5 (5), pp [6] M. Späh and H.-M. Fischer, New aboratory for the Measurement of Structure-Borne Sound Power of Sanitary Installations, Proceedings of Forum Acusticum 5 (5), pp [7] B. M. Gibbs, N. Qi and A. T. Moorhouse, A Practical Characterisation for Vibro- Acoustic Sources in Buildings, Acta Acustica united with Acustica, 93, (7). [8] pren :7, Acoustic properties of building elements and of buildings - aboratory measurement of airborne and structure borne sound from building equipment Part 1: Simplified cases where the equipment mobilities are much higher than the receiver mobilities, taking whirlpool baths as an example, European Committee of Standardization, Brussels, Belgium, (7). [9] ISO 1-3:1995, Acoustics Measurement of sound insulation in buildings and of building elements Part 3: aboratory measurements of airborne sound insulation of building elements, International Organization of Standardization, Geneva, Switzerland, (1995). [1] ISO 3742:1988, Acoustics Determination of sound power levels of noise sources Precision methods for discrete-frequency and narrow-band sources in reverberation rooms, International Organization for Standardization, Geneva, Switzerland, (1988). [11] ISO :199, Vibration and shock Experimental determination of mechanical mobility Part 2: Measurements using single-point translation excitation with an attached vibration exciter, International Organization for Standardization, Geneva, Switzerland, (199). [12] ISO :1986, Vibration and shock Experimental determination of mechanical mobility Part 1: Basic definitions and transducers, International Organization for Standardization, Geneva, Switzerland, (1986).