Propagation of Structure-borne Sound in Lightweight Gypsum Board Walls

Transcription

1 Propagation of Structure-borne Sound in Lightweight Gypsum Board Walls Stefan Schoenwald, Eddy Gerretsen, Heiko J. Martin Eindhoven University of Technology, NL-56 MB Eindhoven, Den Dolech 2, The Netherlands, pren ISO 1848 describes two different methods to measure the vibration reduction index K ij of junctions of building elements. Both methods are applicable to junctions of heavy, monolithic building elements, but only the indirect method that uses airborne sound seems to be practical for junctions of lightweight, assembled building elements, like framed gypsum board walls, so far. In the scope of a current research project at Eindhoven University of Technology to adopt the so-called direct method that is based on the measurement of structure-borne sound to junctions of such kind of elements, basic research is carried out at framed gypsum board walls to characterize the structure-borne sound propagation and the dynamic response of lightweight, assembled structures. Two in its geometry identical walls the first one with a metal frame and the second one with a wooden frame are built stepwise and also changes are made in the structure to determine the way structure-borne sound propagates in this type of elements as well as to find construction details that have influence on it. According to the frequency range different measurement techniques, like experimental modal analysis, power balance measurements and wave number measurements, have been applied to investigate the dynamic behaviour itself and to measure the material properties of the assembled structures in situ. The obtained knowledge will be used to find an appropriate analytical model of the structure and finally to describe appropriate conditions for the application of the direct-method of pren ISO Introduction Currently at Eindhoven University of Technology a research project is carried out on the measurement of the vibration reduction index K ij (EN 12354) of junctions of lightweight double leaf framed building structures, like for example gypsum board walls. The focus of the project is set on the adoption of the socalled direct measurement method of structure-borne sound according to pren ISO 1848 to this type of structures. Generally, the methods of EN and pren ISO 1848 are valid for all types of building elements [1]. But unfortunately, an interpretation as 1 st order statistical energy analysis (SEA) model, like for heavy monolithic building elements [2], does not hold for lightweight, framed ones because basic SEA conditions are not fulfilled. Nevertheless, it is possible to determine K ij if the level difference of sound power radiated by surfaces of two coupled lightweight building elements is known. The sound power level difference can be determined from the measured velocity level difference and a correction term to take into account different radiation efficiencies below the coincidence frequency f c. This correction seems to be important since the coincidence frequency of lightweight framed building elements is usually high. If the velocity level difference could be determined with an appropriate effort of time, then also the direct method of pren ISO 1848 is practical for junctions of lightweight framed building elements. To reach this goal an experimental study is carried out at gypsum board walls to obtain basic knowledge about the propagation of structure-borne sound and parameters that have influence on it. In this paper the course of the experimental study as well as some preliminary results for the total loss factor η of lightweight walls are presented. 2 Experimental study In the experimental study the change of the characteristics of the bending wave field, of elastic properties and of the radiation efficiency due to structural changes at lightweight, framed gypsum board walls is investigated. 2.1 Description of test set-up Two geometrical almost identical gypsum board walls are built in a former reverberation chamber of the acoustics laboratory at the Eindhoven University of Technology. The walls and ceiling of the chamber were covered with absorbents to avoid back coupling of sound that is radiated by the test specimens. The length of both walls is 4,2 m and their height is 2,6 m. One consists of a usual metal frame (channels: UW/CW 75 x,6 mm) and the other one of a wooden frame (wood studs: 69 mm x 45 mm). The spacing of the studs is,6 m unless otherwise provided. Common gypsum board (2,6 m x,6 m x 12,5 mm) is used for the cladding and further the joints of the 1925

2 Forum Acusticum 25 Budapest gypsum boards are taped and filled. Mineral wool (flow resistance 5 kns/m 4, density 16 kg/m 3 ) with a thickness of 6 mm is placed in the cavities as absorbent. The test walls are connected to adjacent structures using standard construction details with elastic interlayer and point connections. The lower edge of the specimens is placed on the heavy concrete floor of the test chamber. The upper edge of the test specimens is free. One vertical edge of each wall is connected to the concrete walls of the test chamber. A wooden board was used to adjust the slight inclination of the walls of the former reverberation room. The other vertical edge is fixed at a rectangular hollow steel channel (length 2,8 m, width/height 12 mm, thickness 4 mm), that is bolted to the floor and filled with sand to increase its mass. The upper end of the support is attached with steel bars to the walls of the test facility. 2.2 Structural changes In the course of the study the test walls are built in steps and structural modifications are made to investigate their influence on the dynamic response of the wall. Five regarded situations are shown in Table 1. Table 1: Structural modifications at the test specimens Notation Modification S1 Frame Stud spacing,6 m S2 Frame Stud spacing,3 m S3 Frame Stud spacing,6 m Mineral wool 6 mm between studs S4 Frame Stud spacing,6 m Both sides, single Mineral wool 6 mm S5 Frame Stud spacing,6 m Both sides, single For reference measurements also were carried out at single gypsum boards that are used to build the test walls. The gypsum boards were hanging with rubber bands suspended in an open test hall of the acoustics laboratory. The resonance frequency of the massspring system was low and thus the two suspensions have no significant influence on the dynamic response of the boards. Transmission losses to adjacent structures as well as radiation losses can be neglected due to the isolation of the springs and the high critical frequency. Therefore the measured loss factor is close to the internal loss factor of gypsum boards. 3 Total loss factor η The total loss factor η of a structure is the ratio of lost to reversible mechanical energy per radian cycle in a dynamic system. Losses occur inside a structure due to friction as well as at its boundaries due to transmission to adjacent structures or radiation into a fluid medium. 3.1 Transient measurement In this case the total loss factor is calculated from the measured structural reverberation time T s of a structure. 2,2 η = (1) f T s The structural reverberation times were measured with the PC-based measurement software Dirac of Brüel and Kjaer. The structure was excited with a electro-dynamic shaker and the impulse response was measured with accelerometers. The reverberation time is determined by the backward integration from the impulse response [4]. Either a MLS- or sweep signal was used for excitation. The measurements showed that there was no difference in the reverberation times using a MLS- or sweepsignal for excitation when the signal-to-noise-ratio was sufficient. But measurements showed that depending on the specific situation the signal-to-noise-ratio can be improved by the use of either one of the two signals. Generally, the sweep excitation was preferred for testing because of the fact that disturbances, like echoes in the test chamber or background noise, can easily identified by listening. Since the signal-to-noise-ratio should be at least 1 db or better 15 db higher than the chosen decay rate of the reverberation time, only T s,1 or T s,2 was used for the calculation of the total loss factor η. The loss factors are supposed to be used for modeling of the sound propagation along the walls, thus they were determined for every field - the area between two studs of the two walls separately. The number of excitation points, accelerometer positions and averages exceed the requirements given in pren ISO

3 Forum Acusticum 25 Budapest The loss factors shown in the following for the whole test specimens are the averages of their field values. 3.2 Stationary measurement Besides reverberation time measurements also acceleration level measurements were carried out to determine the characteristics of the sound field and to validate the results of the loss factor measurement. Hereby, acceleration levels were determined at the excitation position of the shaker with an impedance head and at roving measurement positions on straight lines along the length axis of the walls through the excitation point. The distance between the roving points was 1 cm. The wall was excited with stationary white noise and the level difference L was measured with a FFT-analyzer (B&K Type 355). 3.3 Measurement results The total loss factor measured for situation S1 is in both cases constant in the whole frequency range that is regarded (Figure 1). The loss factor is for the metal stud wall about,15 and for the wood frame wall about,2. The loss factor of the elastically suspended gypsum boards was about,1 in the whole frequency range. At Hz in all three cases a small peak is visible. Those peaks are differently strongly pronounced and caused by high radiation losses at the coincidence frequency f c. The results clearly indicate that at the walls additional transmission losses occur to the frame and adjacent structures. In case of the wood frame wall those losses are higher. The loss factors are in all three cases bigger than the one of heavy, monolithic structures, like for example concrete (~,1).,8,7,6,5,4,3,2, WF.S1 MS.S1 Gypsum board Figure 1: Loss factor of wood frame wall (WF) and metal stud wall (MS) for situation S1 compared to gypsum board The results of the measurements for situation S2 are not explicitly shown in this paper, because the loss factors do not change significantly if the stud spacing is decreased by additional studs. Only the peak at coincidence frequency shifts to 25 Hz at both walls. A dramatically increase of the loss factor occurs at low and middle frequencies in situation S3 if mineral wool is placed between the studs (Figure 2 and Figure 3). At 1 Hz the loss factor has a maximum at about,6 for the wood frame wall and at about,8 for the metal stud wall. The loss factor decreases exponentially to the high frequencies. Above Hz the curves fit well to the previous situations without absorbent between the studs.,8,7,6,5,4,3,2, WF.S3 WF.S4 WF.S Figure 2: Change of loss factor of wood frame wall (WF) due to structural changes To confirm the increase of the loss factor at low and middle frequencies the acceleration level decay with distance to a point source on a line along the length axis of the wood frame wall is shown for situation S1 and S3 at 25 Hz and 4 Hz in Figure 4. The source is located at the center of the rightmost field. At 25 Hz also the level decay increases when the absorbent is added. The difference between the two regarded situations is about 1 db in the leftmost fields. At 4 Hz the level decay does not change over the whole plate.,8,7,6,5,4,3,2, MS.S3 MS.S4 MS.S Figure 3: Change of loss factor of metal stud wall (MS) due to structural changes The reason for the increase of the loss factor due to the absorbent will be discussed in the following section. 1927

4 Forum Acusticum 25 Budapest In situation S4 the cavities of the test walls are closed by attaching claddings on the second side of the frames. In the frequency range below 16 Hz the loss factors decrease relative to the previous situation, but still exceed the ones in the situations without absorbent in the cavity. At the wood frame wall an increase of the loss factor can be found in the middle frequency range between 2 Hz and 8 Hz, whereas above 8 Hz the loss factors are slightly lower than the ones measured at situation S4. The curve of the metal stud wall on the other hand fits in the frequency range above 8 Hz very well to the one of situation S4. Also here an interpretation of the measurement results follows in the next section. Level Difference [db] Hz 4 Hz ,9-3,6-3,3-3, -2,7-2,4-2,1-1,8-1,5-1,2 -,9 -,6 -,3,,3 Distance to Source [m] HS.S1 HS.S3 Figure 4: Level decay along length axis of wall with reference to excitation point (vertical lines: studs, solid: also joint of gypsum boards) Finally, in situation S5 the mineral wool was removed from the cavities of the test walls. The loss factors of the wood frame wall drop and are equal to those of situation S1. Except in the range above 2 Hz lower values are measured. In the frequency range below 2 Hz the loss factors of the metal stud wall also drop, but still are around,2 and thus higher than the ones of situation S1. The loss factors of the metal stud wall above 2 Hz fit well to those of the wood frame wall. 3.4 Damping mechanisms The significant increase of the loss factor when an absorbent is placed between the sutds is investigated further. Close to the surface of an infinite, uniform plate with free propagating bending waves periodic changes of regions of high and low pressure are caused by the movement of the plate. Below the coincidence frequency the acoustical wavelength is bigger than the bending wavelength of a plate. Thus, a rapidly decaying near field is present, where the pressure changes induce an airflow parallel to the plate surface No sound propagates away from the plate surface. In case of a finite plate the same mechanisms occur except that sound can be radiated by regions of the plate where pressure compensation does not fully take place, like for example at boundaries or discontinuities. If a layer of porous material is placed in front of the surface of the plate the flow resistance of the medium is increased and energy losses occur due to above described gas-pumping effects in the near field. Principally, the additional losses can be seen as radiation losses into a dissipative medium. A fluid-dynamic model introduced by Cummings [5] was used to estimate the losses that are caused by this effect in the absorbent between the studs. A layer of porous medium of finite thickness is placed at a small distance in front of the surface of a infinite uniform thin plate. The radiation loss factor is calculated for a gypsum board (thickness: 12,5 mm, density: 72 kg/m 3, Young s modulus: 3x1 9 N/m 2 ) with a porous layer (thickness: 6 mm, flow resistance: 5 knm/s 4 ) in front of it. Between gypsum board and absorbent an air gap with the height of 3 mm was assumed. The calculated radiation loss factor and the difference of the loss factors of situation S1 and S3 are shown in Figure 5. The difference has to be used since in the fluid-dynamic model only losses that occur due to radiation into the absorbent are taken into account. Radiation Loss Factor η [-],8,7,6,5,4,3,2,1 -, Difference MS.S3 - MS.S1 Difference WF.S3 - WF.S1 Radiation Loss factor of fluiddynamic model Figure 5: Increase of loss factor due to absorbent layer (measurements and fluid-dynamic model by Cummings)) At frequencies above 8 Hz the calculated loss factors fit well to the ones measured at the wood frame wall. Further the applied model underestimates the change of the loss factors of the wood frame wall below 8 Hz and the ones of the metal stud wall in the whole frequency range. This might be explained by the fact that only fluid-dynamic effects are taken into account in the model, but also damping effects occur at the walls due to the contact of the plates with the absorbent at part of the area, which cannot be avoided. Further 1928

5 Forum Acusticum 25 Budapest also the finiteness and the non-uniformity of the plate might increase the loss factor. Nevertheless, the model indicates that the increase of loss factors is caused by fluid-dynamic effects and it is very useful for estimating the influence of absorbent layers on the loss factor of a structure. The changes of the loss factors in situation S4 when the cavities are closed can also be explained by a fluiddynamic effects. At frequencies below the massspring-mass frequency f of the wall both leafs of the wall move in phase. Thus, no periodically changing regions of high and low pressure are present in the cavity between the to leafs. No airflow is induced and no energy loss occurs in the porous medium in the cavity. The calculated resonance frequency f is 141 Hz at the wood frame wall and 126 Hz at the metal stud wall. Also a modal analysis was carried out at the wood frame wall, but unfortunately it was not possible to find a single resonance frequency f. Instead a frequency range starting at about 95 Hz was found were different parts of the two leafs began to move out of phase. This explains also the slow decrease of the loss factors below the calculated resonance frequency. 4 Summary and Conclusions The measurements showed that the loss factor has to be taken into account, when the sound propagation along a lightweight double leaf framed structure is regarded. It was shown that the loss factor of a gypsum board wall depends only slightly upon the geometry and material of the frame. A significant increase of the loss factor was found at low and middle frequencies below the coincidence frequency when bulk porous material was placed between the studs of the wall. The additional energy losses are caused by gas-pumping effects in the absorbent layer. In case of a single-leaf framed construction the change of the loss factor can be roughly estimated by a relative simple fluid-dynamic model for an infinite uniform plate, which was introduced by Cummings [5]. Unfortunately, the model cannot be applied to double leaf gypsum board walls, since below the mass-spring-mass frequency of the two leafs a decrease of the loss factor relative to the single leaf situation was found. Finally, the obtained knowledge will be used to adopt the direct measurement method of pren ISO 1848 to junctions of lightweight building structures References [1] S. Schoenwald et al., Aspects of the measurement of K ij at junctions of lightweight assembled structures. Procceedings of CFA-DAGA 24, Strasbourg, pp (24) [2] T. Nightingale, I. Bosmans, Expressions for 1 st order flanking paths in homogenous isotropic and lightly damped buildings, Acta Acustica united with Acustica, Vol. 89. pp (23) [3] M. P. M. van Leth, M. T. P. Ritmijer, Bepaling van de verliesfactor en de buiggolflengte van gipskartonplaten, University of Technology, BPSmaster project, Eindhoven (25) [4] A. Meier: Die Bedeutung des Verlustfaktors bei der Bestimmung der Schalldämmung im Prüfstand, Dissertation RWTH Aachen (2) [5] A. Cummings, Sound radiation from a plate into a porous medium, Journal of Sound and Vibration, Vol No. 3, pp (21) 5 Outlook Beside the presented measurement results further research is and will be done at the test specimens regarding the influence of structural changes on the characteristics of the bending wave field, the elastic properties of the wall and the radiation efficiency. 1929