Active Impact Sound Isolation with Floating Floors. Gonçalo Fernandes Lopes

Active Impact Sound Isolation with Floating Floors Gonçalo Fernandes Lopes Outubro 009

Active impact sound isolation with floating floors Abstract The users of buildings are, nowadays, highly demanding about the level of overall comfort and acoustic comfort in particular. However, most buildings do not ensure sufficient isolation against the transmission of low frequency impact noise, i.e. between 0 and 00 Hz. In this frequency range, the classic theories of room acoustics, where vibration and sound fields are assumed to be diffuse, do not apply. Both floors and rooms exhibit a clearly modal behaviour. One simple way to reduce impact sound transmission is to use floating floors. Unfortunately, this solution may be counterproductive at low frequencies. It is also observed that the same floor solution can exhibit different dynamic behaviours in different rooms, thus bringing additional difficulties to the designing process. It is then important to define a typified floating floor system designed to accommodate the specific conditions of the application site. In this thesis, the use of a floating floor cover with an elastic layer configured by inner-tubes with enclosed air at pressure depending on the requirements of the source and rooms, is proposed. Keywords: Sound insulation; Impact sound; Floating floors; Loss factor; Rubber; Air-Cushion. Introduction Mechanical vibration or footfall exhibit, in general, important energy contents for frequencies below 00 Hz. Floor vibration modes also occur at these frequencies. Additionally, for current rooms in dwellings and similar buildings, the sound fields generated by impact excitation of floors also exhibit a modal behaviour below 00 Hz, with significant sound pressure differences within the room volumes. The modal behaviour of both floors and sound fields yields modal coupling effects which can then lead to significant sound amplification at certain frequencies. Sound amplification also can result from modal selection due to the point of impact. Unfortunately, normalised methods for both measurement and prediction of impact sound isolation are based on the classical theories of room acoustics, which assume diffuse sound fields and infinite panels. Thus, there are floors which comply with present regulations and yet yield annoyance due to excessive noise levels at low frequencies. Floating floors, consisting of a cover layer on a resilient one applied on the structural base floor, are generally used to improve impact sound isolation. These systems are efficient for high mass floating layers and for low stiffness and high damping resilient layers. However, the properties of materials currently used as resilient layers do not comply totally with the above requirements, which may lead to amplification of impact sound noise at frequencies below 00 Hz. The combination of the effects described above justifies the search for a floating floor system able to adapt to the specific conditions of the application site, thus exhibiting an efficient performance

also at low frequencies. In the present thesis, a semi-active floating floor system based on the ability to control the stiffness and damping of the resilient layer is proposed. This will be achieved by using inner-tubes as a resilient layer associated to a system of controlling the pressure of the enclosed air. Analytical model for prediction of the dynamic behaviour of floating floors In Figure 1, a floating cover (1) is considered on a resilient layer applied on a base floor (). h 1 µ 1 m 1 h 0 µ h m Figure 1 Floating cover above resilient layer applied on a base floor. The vibration field v,x generated on the base floor by a point force F applied on the floating floor is given, according to Neves e Sousa [1], by v x, ( ) ( ) ( ) 4ω F ω m n 1 ( 0 φm n y0,z0 φm n y,z 1 1 1 1 y,z j m1 b c ω -ω )( ω -ω ) 1 1= I,m 1n 1 II,m 1n = (1) 1 where b and c (m) are the floor dimensions, ω (rad/s) is the angular frequency, ϕ m1n1 are the floor mode shape functions; and the denominator of the sum is given by ( ω -ω )( ω -ω ) = [ ω ( 1+ jη1) + ω10 ( 1+ jη0 ) -ω ] K I,m 1n1 II,m 1n 1 1,m 1n1 L [ ω ( 1+ jη ) + ω ( 1+ jη ) -ω ]-ω ( 1+ jη ),,m1n 1 0 0 10 0 () The natural frequencies ω 1,m1n1 and ω,m1n1 correspond to the top and base floors alone, whereas ω 10 and ω 0 are the natural frequencies of the one degree-of-freedom mass-spring systems made

of each floor connected to the resilient (elastic) layer. The factors η 0, η 1 and η are the loss factors of the resilient layer and the top and base floors, respectively. The above expressions indicate that both the mass of the floor covering and the stiffness and loss factor of the interlayer play an important role on the performance of the floating floor. Thus, as the mass of the covering layer is mainly controlled by structural limitations, the present study will focus on the properties of the material used as resilient layer. Floating floor systems available in construction A review on the floating floor systems available in construction was made. As pointed out in the above section, the resilient layer has an important contribution to the efficiency of the system. In Table 1, the density (ρ), modulus of elasticity (E), loss factor (η 0 ) and thickness (e) of different materials currently used as resilient layers are shown. Table 1 Properties of floating floor systems available in construction. Material ρ (Kg/m 3 ) E (GPa) η e (m) Rubber 10-50 0,05 0,10-0,17 0,01 Polystyrene 1040-1100 0,30 0,0 0,04 Extrudid polyethylene 3-3 0,0 0,10 0,005 Polyurethane 150-1030 0,0008-0,050 0,30-0,50 0,01-0,05 Polyvinyl chloride 704,5 0,03 0,30-0,50 0,005 Neoprene 1500-1600 0,70-,00 (x10-3 ) 0,10 0,15 Fiberglass 110 0,15-0,30 (x10-3 ) 0,10 0,00 Air cushion - - 0 - Steel spring 03,4 0-0,1* - Proposed semi-active isolation system The challenge was to set-up a floating floor system able to change in an easy way its dynamic properties thus adapting to the excitation and the acoustic characteristics of the rooms below. The idealised system consists of a set of inner-tubes laid linearly between the top and base floors. Two types of covering layers were considered: lightweight concrete rafts or MDF sheets. The proposed solution is illustrated in Figure.

1 3 4 1- Flooring solution; - Concrete raft/mdf sheet; 3- Inner-tube; 4- Base floor. Figure The proposed solution illustration. The inner-tube elements are laid parallel, with constant spacing w s depending on the applied loads and the structural resistance of the covering layer. The mechanical characteristics of the top and base floors remain unchanged during the construction lifetime. Conversely, the properties of the elastic layer can be changed simply by means of a compressor and valves used to control the pressure of the air enclosed in the inner-tubes. In order to assess the behaviour of the air chambers when subjected to compression loads, a model was constructed with the aid of SAP000 []. The D model shown in Figure 3 was considered. This model corresponds to a section of an inner-tube aligned with the z-axis. Membrane finite elements were used. F B A Rubber Air A Figure 3 D model in SAP000 corresponding to a section of an inner-tube.

Point A in Figure 3 is simply supported and corresponds to the contact point between the innertube and the base floor, whereas B corresponds to the contact point between the covering layer and the inner-tube, through which impact forces are transmitted to the air chambers. In Table, the properties considered in the model for rubber and air are shown. Table Considered properties of rubber and air. Material Properties Rubber Air Density ρ (Kg/m 3 ) 1000,000 1,04 Modulus of elasticity E (MPa) 4,00 a 75,00 0,14 a 1,1 Poisson ratio v (-) 0,49 0,001 Damping coefficient ξ (%) 0,050 a 0,00 0,05 As different types of rubber can be used in the inner-tubes, intervals of values for the modulus of elasticity and damping coefficient are given. The effect of these parameters on the performance of the floating system, as well as the effect of the rubber thickness and the air pressure is tested. The considered values are shown in Table 3. RUBBER Table 3 Considered properties of rubber and air. PROPERTIES Modulus of elasticity E b (MPa) 4 40 75 - Damping coefficient ξ b (%) 5 1,5 0 - Thickness e b (m) 0,001 0,003 0,005 - AIR Pressure P (Atm) 1,0,0 4,5 8,0 In order to assess the dynamic stiffness of the inner-tubes for each parametric combination, the model shown in Figure 3 was used. SAP000 was used to perform a modal analysis for a periodic time signal. Thus, the inverse Fast Fourier Transform algorithm was used to obtain an excitation pulse signal from a flat excitation force spectrum. The time response, given as the displacement measured at B along the x-axis was then transformed into a displacement spectrum in order to identify the system resonant frequency. The half-power method was used to assess the global damping of the system. The obtained results were combined in graphs such as the one shown in Figure 4 in order to check the effect of each studied parameter.

Eb = 4 MPa Eb = 40 MPa Eb = 75 MPa Eb = 4MPa Eb = 40MPa Eb = 75MPa Eb = 4MPa Eb = 40MPa Eb = 75MPa Eb = 4 MPa Eb = 40 MPa Eb = 75 MPa 0,5 ξ c 0,3 0,1 0,19 0,17 0,15 c 0,13 1 4,5 8 Figure 4 Damping coefficient of the system for ξ b =0,05 depending on P, e b e E b. The damping coefficient and the dynamic stiffness of the system are directly proportional to the other parameters. As expected, the damping coefficient is inversely proportional to the installed air pressure, being this relation more evident for higher rubber thicknesses. On the other hand, the linear relationship between the rubber damping coefficient and that of the system is less evident for high values of the installed air pressure. The dynamic stiffness is directly proportional to the rubber thickness and the air pressure, decreasing slightly when the damping coefficient of rubber increases. P (atm) e b = 1mm e b = 3mm e b = 5mm 0,11 0,09 0,07 0,05 Analysis of the proposed isolation system integrated in a room In the above section, the performance of the system as a function of its dynamic characteristics was studied. In this section, the ability of the system to adapt to the physical conditions of a given room is analysed. Three rooms with current dimensions in dwellings are considered. In Table 4 are shown the dimensions of each room, where the axes x, y and z are those illustrated in Figure 5. x a z c b y Figure 5 Dimensions and axes of the analysed rooms.

The analysis of the floors is based on a comparison of the floor accelerance, which is the point transfer function between the impact force and the acceleration of the base floor. The accelerance of the base floors, predicted at coordinates (3b/8;3c/8), is shown in Figure 6. The base floors were assumed in concrete with E = 30 GPa; ρ = 400 kg/m 3 ; ν = 0. and η = 0.015. µ& & F (kg -1 ) 1,0E-0 1,0E-03 1,0E-04 1,0E-05 1,0E-06 Room Compartimento type I tipo I Room Compartimento type II tipo II Room type III Compartimento tipo III 1,0E-07 0 0 40 60 80 100 10 140 160 180 00 0 f (Hz) Figure 6 Fourier sprectum of the accelerance of the base floors. Floating covers are efficient for frequencies above the cut-off frequency of the floor, f 1. Thus, the proposed floating floor system must exhibit, for each tested configuration, a cut-off frequency as low as possible. The following criteria can be assumed in the appearance order. f 1 = f 1,1 /4; f 1 < f 1,1 ; f 1 < 50 Hz; where f 1,1 (Hz) is the frequency corresponding to the first floor mode. The optimal value of the dynamic stiffness, s (N/m 3 ), of the inner-tubes can be calculated from ( f ) 1 π s = 1 1 + m 1 m (3)

In Table 4, the obtained optimal stiffnesses of the elastic interlayer are shown for each floor configuration. Table 4 Optimal stiffnesses of the elastic interlayer for each room. Room's m (kg/m) s (N/m) f 1,1 (Hz) f o /4 (Hz) f 1 (Hz) type concrete raft MDF concrete raft MDF I 53 13,5 13,5 100 1 5,7359E+05 1,3945E+05 II 11,5,875,875 100 1,7005E+04 6,5654E+03 III 18,5 4,565 4,565 100 1 6,8011E+04 1,6534E+04 The above values can now be used to select a set of tested solutions (resulting from a particular combination of the parameters considered in Table 3) with similar stiffnesses. For each set of possible solutions, the chosen one corresponds to that with higher damping coefficient. The performance of the resulting floating floor systems was assessed with the help of expression (1) for the considered types of floor covering (lightweight concrete raft with E = 30 GPa and MDF sheets with E =. GPa). Figure 7 shows the Fourier spectrum of the floor accelerance. A slight amplification of acceleration is observed near f 1 when the floating floor is applied, with a significant attenuation of acceleration for higher frequencies. µ/f & 1 (kg ) 1,0E-01 1,0E-0 1,0E-03 1,0E-04 1,0E-05 1,0E-06 1,0E-07 1,0E-08 Lajeta Optimal óptimo c. raft Optimal MDF óptimo MDF No sem isolation rev 0 0 40 60 80 100 10 140 160 180 00 0 Figure 7 Fourier spectrum of the floor accelerance for room type I. f (Hz) The efficiency of the proposed system was compared with that of other traditional passive systems using extruded polyethylene, cork or neoprene as resilient layers. Figure 8 compares the Fourier spectrum of the floors accelerance with that of the proposed floating floor considering a lightweight concrete raft in room II.

µ & 1 /F (kg ) 1,0E-01 1,0E-0 1,0E-03 1,0E-04 1,0E-05 1,0E-06 Inner-tube Câmara-de-ar Polietileno Polyethylene Cork Cortiça 1,0E-07 Neoprene No isolation Neoprene Sem revestimento 1,0E-08 f (Hz) 0 40 60 80 100 10 140 160 180 00 0 Figure 8 Fourier spectrum of the floors accelerance with that of the proposed floating floor considering a lightweight concrete raft in room II. In order to assess the acoustic performance of the proposed floating floor system, the sound pressure field generated in the rooms by the vibrating floors was calculated by 8c0( 1) Cmnφlmn ( x, y, z) jωt p( x, y, z, t) jωρ0 - = - e (4) abc ( ω jδ) -ω l,m,n = 0 lmn + l [ ] where ρ 0 (kg/m 3 ) and c 0 (m/s) are the static density and the speed of sound in air, respectively; ω lmn are the natural acoustic frequencies and ϕ lmn (x,y,z) are the corresponding mode shape functions; δ is a temporal absorption coefficient; and C mn are coupling factors between the floor and the room. In Figure 9, the magnitude of the transfer function between the point impact force applied on the floor and the sound pressure in the room 40 cm away from a corner is shown for the proposed floating floor with the lightweight concrete raft in room II.

p/f (m - ) 1,0E+00 1,0E-01 1,0E-0 1,0E-03 1,0E-04 1,0E-05 1,0E-06 1,0E-07 comp II - betão - câmara de ar comp II - betão - cortiça comp II - betão - polietileno comp II - betão - neoprene 1,0E-08 1 1 41 61 81 101 11 141 161 181 01 1 f (Hz) Figure 9 Transfer function between the point impact force applied on the floor and the sound pressure for the proposed floating floor with the lightweight concrete raft in room II. Figure 9 shows that the sound field is controlled by the modal characteristics of the room, although exhibiting a match between the accelerance spectrum and that of sound transmission. Conclusions A floating floor system based on a rigid covering layer on a set of inner-tubes with controlled enclosed air pressure was proposed and compared with other traditional passive floating floor systems. The proposed system appears to be highly efficient for vibration and thus acoustic isolation. The system has the advantage of being adaptable to the modal behaviour of rooms at low frequencies and also allows the user to change to dynamic loads during the building lifetime. The previous conclusions still require experimental validation. Also the technical and economic viability of the system has yet to be assessed. References [1] Neves e Sousa, A. (005): Low frequency Impact Sound Transmission in Dwellings, Tese de Doutoramento, The University of Liverpool; [] Computers and Structures Inc. (005): Analysis Reference Manual for SAP000 ADVANCED, Berkeley, California, EUA;