STRUCTURE-BORNE SOUND PROPAGATION ACROSS A DOUBLE LEAF TIMBER-FRAME WALL

Transcription

1 STRUCTURE-BORNE SOUND PROPAGATION ACROSS A DOUBLE LEAF TIMBER-FRAME WALL Fabian Schöpfer, Andreas R. Mayr, Ulrich Schanda Laboratory for Sound Measurement LaSM, University of Applied Sciences Rosenheim, Hochschulstr. 1, 8324 Rosenheim, Germany. fabian.schoepfer@fh-rosenheim.de Carl Hopkins Acoustics Research Unit, School of Architecture, University of Liverpool, L69 7ZN, UK. With the increasing mechanization of buildings, it is necessary to be able to predict both the structure-borne sound power input from building machinery and the subsequent propagation of structure-borne sound in the building. This paper considers lightweight constructions and describes the results of an experimental study in the laboratory on a T-junction that was constructed from a timber joist floor and two double leaf timber-frame walls. The focus in this paper is on the vibrational behaviour of one of the timber-frame walls. To assess the vibration pattern and the propagation of structure-borne sound, the surface velocity levels were measured on a grid on both leaves of the wall with point force excitation on one side. This grid allowed calculation of structural intensity vectors. The influence of elements such as the timber studs and tongue and grooved joints between the boards were apparent in different frequency regions. Experimental modal analysis was carried out using measurements on both leaves of the wall, giving information about the coupling in different frequency regions. The results give insight into how such a timber-frame wall could be modelled using statistical energy analysis. 1. Introduction In recent years timber-frame constructions have become ever more important especially with the potential to build multi-story dwellings. With the energetic optimization of buildings, the amount of service equipment such as heating devices, heat pumps or ventilation systems is increasing. Such appliances act as structure borne-sound sources in the building and can cause annoyance to the occupants. This provides a challenge for engineers and architects to ensure the required sound insulation between the dwelling units. To fulfil legal requirements on sound insulation, calculation models are necessary to predict the sound propagation in the design stage. However, at present there is a lack of validated prediction tools for this purpose. To develop a model for the calculation of sound propagation through double leaf lightweight constructions, a detailed knowledge about the vibrational characteristics of such structures is necessary. Therefore, this paper focuses on the vibrational behaviour of a double leaf timber frame wall when it is excited with a structure-borne source. ICSV22, Florence, Italy, July 215 1

2 2. Test rig In the course of an ongoing research project a lightweight test rig was constructed in the Laboratory for Sound Measurement (LaSM) at the University of Applied Sciences in Rosenheim. The test rig forms a T-junction from two timber-frame walls and timber joist floor. The frame construction was designed in cooperation with the timber-house manufacturer Regnauer and has common stud spacing and cross sections of the building elements. The stud spacing is 62.5 cm for the wall studs and floor joists. The cross sections for the frame elements are 9 cm x 6 cm for the wall studs and 24 cm x 6 cm for the floor joists. The framework of the walls is constructed from vertical studs with a cross-bar at the bottom and top of the wall. In-between the studs no cross-bars are inserted. To simplify later modelling stages, the walls and the floor only have a single layer of sheathing material without any insulation in the cavities. The chosen sheathing material is chipboard to avoid the use of orthotropic board materials such as plasterboard or oriented strand board (OSB). The 19 mm chipboard panels are screwed on the framework construction at 35. cm centres. The single chipboard panels are connected with tongue and groove joints without glue in the joints. The whole test rig is isolated from the rest of the building with elastic supports underneath the wall in the basement and floor joists. 3. Experimental work The experimental study presented in this paper was conducted on the timber-frame wall in the lower floor of the T-junction. This wall has a length of 5.6 m and a height of 2.6 m with eight bays in-between the vertical beams. The boundary along the bottom edge of the wall sits on an elastic interlayer. At the top edge of the wall the floor joists are rigidly connected to the wall beams with one screw for each joist. The beams at the two side edges of the wall are not fixed to any other supports. 3.1 Measurement set-up For the experimental investigations a single point excitation was applied using an electrodynamic shaker at one end of the wall. To investigate structure-borne sound power input and propagation, the source was attached to the chipboard (a) in a bay and (b) above a stud. In the bay the shaker was connected to the wall using a small aluminium plate with a threaded hole being glued to the structure with cyanoacrylate adhesive. On the stud the aluminium plate was screwed through the chipboard into the studs in addition to cyanoacrylate adhesive. The vibrational response of the wall was measured with accelerometers at the intersection points of a regular grid across the whole wall. The same grid was applied to both surfaces (source and receiver) of the structure. Along the length of the wall the grid spacing was 1.4 cm due to the stud spacing of 62.5 cm. Hence every sixth measurement position is above the centre line of a wall stud. Along the height of the wall the grid spacing was 11. cm. This results in a total number of 49 x 24 measurement positions for each surface. 24 accelerometers were used so the surface velocity levels were determined in a series of measurements with a set of 12 accelerometers being moved along each wall leaf. At the excitation point the input force was measured with a force transducer, along with the acceleration by averaging the signal from two accelerometers on either side of the force transducer. The excitation signal was white noise in order to ensure sufficient vibration level above background at all points. For this measurement a multi-channel FFTanalyser was used and the narrow band FFT-spectra of the accelerations were integrated to output velocities for further processing in Matlab. 3.2 Vibrational behaviour of the timber frame wall The measured grid data provides the opportunity to investigate the distribution of velocity levels across the structure on both wall leaves. By referencing to the input force for example it is also possible to assess the phase relations and therefore the modal coupling of both leaves of the wall. 2 ICSV22, Florence, Italy, July 215

3 3.2.1 Surface velocity levels on both leaves Previous research [1] indicates that the decrease of vibrational energy with distance can be significant with timber-frame structures; hence the surface velocity levels on both wall leaves were measured. The distribution of velocity levels also allows an assessment of the influence of the stiffening wall studs and the joints in the sheathing material on the vibrational behaviour of the structure. Since the measurements at each grid position were not all carried out simultaneously, the response signals at each grid position were normalized to the input force to account for any small changes in the force input. To visualize the results, the narrow band data was summed to give one-third octave band values. The surface velocity levels are shown for the 31.5 Hz, 1 Hz, the 8 Hz and the 25 Hz one-third octave bands in figure 1, for bay and stud excitation respectively. The levels have been normalized to the highest level on the source leaf, which was set to zero decibels. In these figures, the arrow indicates the location of the input force. The thick black lines indicate the position of the wall studs and bars, and the thin black lines indicate the joints between the chipboard panels. Bay excitation 31.5 Hz 1 Hz 8 Hz 25 Hz m/ns (db) -4-5 Stud excitation 31.5 Hz 1 Hz 8 Hz 25 Hz m/ns (db) Figure 1: Distribution of velocity levels on both leaves of the timber-frame wall Concerning the attenuation of vibration along the wall the three selected frequency bands show similar characteristics for bay and stud excitation as well as for both leaves. At 31.5 Hz where the bending wavelength on the chipboard is approximately 1.4 m and therefore larger than the bay spacing, the vibration levels are similar in each bay. The lowest levels occur near the top of the wall where it is rigidly connected to the timber joist floor. With increasing frequency the attenuation with distance gets stronger. At high frequencies (in this case represented by the 25 Hz one third-octave band) there is evidence that the single chipboard panels are no longer rigidly coupled together and ICSV22, Florence, Italy, July 215 3

4 that vibration is significantly attenuated across the joint between the panels (NB no glue was used in the tongue and groove connections). Similar findings were made by Nightingale and Bosmans [1] with tongue and grooved OSB panels. The attenuation of velocity levels from one leaf to the other differs between bay and stud excitation except at low frequencies. At 31.5 Hz there are similar velocity levels on both leaves. For bay excitation it can be seen that at 1 Hz, which is above the mass-spring-mass resonance of the double leaf wall, there are differences between the bays which become more apparent at higher frequencies. In contrast, for stud excitation, the differences between both leaves tend to be lower for all selected one-third octave bands. The reason for this is that by applying the excitation above a stud, the leaf on the other side is directly excited by the transmission path through the stud. Therefore the level differences between both leaves are lower for stud excitation compared to bay excitation. The influence of the framework and the screw fixing of the chipboard panels on the vibrational behaviour can be characterised by considering three frequency regions [1]: (a) At very low frequencies (<63 Hz) the vibration levels are distributed uniformly across each leaf that forms the surface of the framework wall and at the stud positions no significant minima can be observed. (b) In the frequency range from 63 Hz to approximately 16 Hz the velocity level is highest near the centres of the bays with the lowest vibration levels above the studs. In this frequency region the chipboard panels behave as if they are line-connected to the studs. The upper limit for periodic point connections to act as line connections can be estimated as λ/2 [1] [2]. In this case study the screw distance is 35 cm which relates to half a bending wavelength on the chipboard panel at approximately 125 Hz. (c) At frequencies above 16 Hz, no significant differences between levels in a bay or above the studs occur. Above 2 Hz strong attenuation occurs at the tongue and groove joints that join adjacent panels Power flow in the framed structure The time-average surface velocity levels give information about the distribution of vibrational energy as shown in the previous section. However, the vibrational energy does not give any insight into the power flow across the wall. The reactive power flow represents the alternating interchange of energy between alternating spatial areas of kinetic and potential energy respectively. Hence the time average of the reactive power flow is zero. However, in any real vibrating mechanical system there are losses due to internal friction, radiation, or boundaries. Therefore there is an active component of the power flow "beneath the seething sea of local reactive energy flux" [3] which transports vibrational energy from sources to sinks. This active component can be visualized by measuring the structural intensity as power per unit width. In this case the two-accelerometer method was applied. From Noiseux [4] this method uses the approximation that the force component is equal to the moment component in the far-field so that the structural intensity can be calculated in the frequency domain for propagation in one direction with equation (1) [5]. (1) Bm 2 I = I(G 12 ) where B is the bending stiffness, m is the mass per unit area, is the transducer spacing. I(G 12 ) is the imaginary part of the cross spectrum between the accelerations of the two transducers lined in the direction of the power flow. To determine the net power flow in x- and y-directions two accelerometer pairs are necessary. For this experiment 24 IEPE-accelerometers each with a mass of 23 grams were used. To avoid mass loading the upper frequency limit for this measurement was estimated to be 1 Hz [6]. Measurements show that the phase difference between all the accelerometers is in the range of ±.2 at frequencies from 5 Hz to 1 Hz with single peaks of ± 1. At frequencies below 5 Hz the phase difference is ± 1. For this experiment a spacing of 33 mm between the centroids of the transducers was used to get a high upper frequency limit. The distance was checked with a spacer when the transducers were mounted to the structure. With a phase difference of 1 and a distance of 4 ICSV22, Florence, Italy, July 215

5 33 mm the combined error from finite difference and phase-mismatch normalized to the actual structural intensity is ±.5 db at 1 Hz [6]. The maximum error in the propagation angle appears at low frequencies where at 31.5 Hz the error is ± 8 and decreases to ± 1.5 at 1 Hz [6]. Due to the narrow spacing of the transducer pairs, the measurement is very time consuming and therefore it was only conducted on the source surface of the wall with bay excitation. The measurement was carried out on a grid with equal spacing of 14 cm in the x- and y-directions. Since the free-field approximation is unlikely to be valid directly above the studs, these points have been omitted. With the probes consisting of four accelerometers the structural intensity was measured in both directions for every point. In total 32 x 18 positions were measured across eight bays which is in contrast to similar investigations by Schoenwald [7] that measured three bays. The narrow band data was summed to give one-third octave band data. In figure 2 in the left-side column the power flow is visualized for the one-third octave bands 31.5 Hz, 1 Hz and 8 Hz Hz y-dimension (m) y-dimension (m) y-dimension (m) x-dimension (m) relative structural intensity level (db) x-dimension (m) relative structural intensity level (db) x-dimension (m) Hz 8 Hz net power flow normalized (db) net power flow normalized (db) net power flow normalized (db) bay with point excitation number of successive studs bay with point excitation number of successive studs bay with point excitation number of successive studs relative structural intensity level (db) -4-5 Figure 2: Net power flow on the source leaf; left column: structural intensity vectors; right column: power flow in x-direction across successive bays ICSV22, Florence, Italy, July 215 5

6 For every point the resulting structural intensity was calculated from the measured x- and y- component. The vectors indicate the direction of the net power flow and their length indicates the intensity magnitude at each point. For clarity the magnitude is also illustrated using the coloured plot. Here the structural intensity level is normalized to the measurement position to the right of the excitation point to show the relative level of the vector magnitudes across the wall surface. The grey bars show the positions of the wall studs and the black lines indicate the tongue and grooved joints between chipboard panels. To quantify the net power flow perpendicular to the vertical wall studs, the x-components were integrated along the height of the wall for each column of measurement points that were positioned immediately to the right of a wall stud as shown in the right-hand side of figure 2 for selected one-third octave bands. In these diagrams the net power flow is normalized to the net power flow into the second bay to identify the decrease across successive studs. The first bay has been omitted since the point source was located there. In the first bay the direction of structural intensity emanates from the excitation point. This behaviour can be observed for all one-third octave bands. At 31.5 Hz all vectors are oriented normal to the wall studs beginning in the second bay with maximum power flow towards the middle axis of the wall. There is no significant decrease of the net power flow with distance. At 1 Hz circulating vectors indicate a vibrational behaviour dominated by standing waves (modes). Therefore a fluctuation of the net power flow occurs as illustrated in figure 2. In the mid-frequency range, in this case represented by the 8 Hz one-third octave band, a strong attenuation with distance occurs, similar to the findings mentioned above. The net power flow in the x-direction decreases monotonically from bay to bay with a decrease of almost -3 db from the second to the eighth bay. 3.3 Coupling between both leaves of the wall The results in section 3.2 give information about the distribution of vibrational energy in the structure. The attenuation with distance could be quantified using the measured velocity levels. In the following section, measured phase relations are used to describe the coupling between the two leaves Simultaneous experimental modal analysis of both leaves To visualize the mode shapes of both leaves separately, the grid data measured according to section 3.1 were used. The narrow band response signals of both leaves were referenced to the input force to determine the phase relationship. These transfer functions were processed in Matlab to visualize the mode shapes of both leafs simultaneously; this is similar to recent work on multi-layer floors by Völtl at LaSM [8]. Three pairs of mode shapes are shown in figure 3 for bay excitation and for stud excitation respectively (initially the attention is on the coloured surface plots). The upper three pairs are for bay excitation, the lower three for stud excitation. The selected mode shapes are plotted over the related frequency on the x-axis. Again the black lines indicate the position of the wall studs. The upper surface plot represents the excited leaf and the lower surface plot represents the other leaf. At low frequencies the mode shapes of both leaves are very similar; there is no influence of the wall studs, and the mode shapes are related to the dimension of the whole wall. In the plots for bay excitation near 8 Hz the source and receiving leaves have approximately mirror-image mode shapes, especially in the first bay. This corresponds to the mass-spring-mass resonance of the double leaf wall at approximately 8 Hz. Hence the phase relation between the leafs is expected to be 18. This was not apparent for the stud excitation as the nodes of the mode shape at approximately 8 Hz for bay excitation tend to fall on the wall studs. Hence this mode is not easily excited by applying the driving force on a stud. Above the mass-spring-mass resonance, there seems to be no correlation between both leaves for bay and stud excitation. 6 ICSV22, Florence, Italy, July 215

7 3.3.2 Use of the Frequency Response Assurance Criterion to assess the coupling between wall leaves The coupling between the two leafs can be assessed by looking at the mode shapes as described in the section before. To quantify the coupling, the Frequency Response Assurance Criterion (FRAC) can be used. The FRAC is described along with other assurance criteria in [9]. This describes a correlation between two complex frequency response functions on the base of the phase relationship. Hence, the FRAC is calculated with the complex transfer functions of both leaves of the timber frame wall according to equation (2) [9]. (2) F RAC ab (f) = Σ Nx x=1σ Ny y=1y a (x, y, f) Y b (x, y, f) 2 [ Σ N x x=1σ Ny y=1y a (x, y, f) Y a (x, y, f) ] [ Σ Nx x=1σ Ny y=1y b (x, y, f) Y b (x, y, f) ] where Y a and Y b are the complex transfer accelerances of the source and receiving leaves respectively. Both are referenced to the input force on the source leaf. N x and N y are the number of measurement positions in x- and y-direction. A value of unity indicates a strong relation between the FRFs, whereas zero will indicate no relationship. FRAC results are shown in figure 3 for bay and stud excitation. FRAC FRAC.9 1 Bay excitation Stud excitation Frequency (Hz) Figure 3: Mode shapes of both leaves of the timber frame wall, together with the Frequency Response Assurance Criterion (FRAC). For bay and stud excitation the strongest coupling appears at low frequencies as described in the previous section. For stud excitation there is a value of almost unity up to 31.5 Hz whereas the value is slightly lower for bay excitation. This is likely to be due to the direct field from the point force that dominates the response on the first bay on the source leaf. In contrast, the receiving leaf is excited by the sound field in the cavity. Both curves drop to values below.2 towards high frequencies. However the curve for stud excitation is above.8 until approximately 63 Hz whereas the curve for bay excitation drops below.8 at approximately 4 Hz. For stud excitation the dominant structural ICSV22, Florence, Italy, July 215 7

8 excitation of the receiving leaf is through the wall stud. This results in stronger coupling compared to the excitation position in a bay. For bay excitation the FRAC value drops to almost zero above the mass-spring-mass resonance (approximately 8 Hz) of the double leaf wall. In conjunction with the earlier results in this paper it is apparent that this wall will need to be modelled differently over different frequency regions. At low frequencies the whole wall might be regarded as a single SEA-subsystem as there is little attenuation of vibrational energy across the wall. With increasing frequency the wall could be modelled as a number of subsystems as the modal response becomes increasingly incoherent. 4. Conclusions In this experimental study on a timber-frame wall, the vibrational behaviour, modal response, decrease in vibration with distance and vibrational power flow have been investigated as well as the coupling of the leaves. To assess the vibration pattern and the propagation of structure-borne sound, the surface velocity levels were measured on a grid on both leaves of the wall with point force excitation on one side. The influence of elements such as the timber studs and tongue and grooved joints between the boards was observed in different frequency regions. Experimental modal analysis was carried out using measurements on both leaves of the wall, giving information about the coupling in different frequency regions. The results give indications about the choice of SEA subsystems for future modelling of the dynamic response of this wall. Acknowledgment This work is part of a research project in cooperation with the University of Applied Sciences Stuttgart and the Acoustics Research Unit at the University of Liverpool. It is funded by the German Federal Ministry of Education and Research in the program FHprofUnt (support code: 3FH89PB2). REFERENCES 1. Nightingale T. R. T., I. Bosmans I.: Vibration response of lightweight wood frame building elements. Building Acoustics, 6 (3/4), p , Craik R. J. M., Smith R. S.: Sound transmission through lightweight parallel plates. Part II: structure-borne sound. Applied Acoustics, 61 (2), p , Fahy F. J.: Sound Intensity. Elsevier; First Edition; Noiseux D. U.: Measurement of power flow in uniform beams and plates, Journal of the Acoustical Society of America, 47 (1), p , Pavić G.: Measurement of structure borne wave intensity. Part I: Formulation of the methods. Journal of Sound and Vibration, 49 (2), 1976, p Hopkins C.: Sound Insulation. Elsevier; First Edition; Schoenwald S.: Investigation of flanking sound transmission in lightweight building structures using a scanning laser vibrometer. Proceedings of Euronoise, Edinburgh, Scotland, Völtl R., Schanda U., Kohrmann M., Buchschmid M., Müller G.: Simultaneous operational vibration analysis of different layers of lightweight timber floors. Proceedings of Internoise, Innsbruck, Austria, Allemang R. J.: The Modal Assurance Criterion - Twenty Years of Use and Abuse, Journal of Sound and Vibration, 211, p , ICSV22, Florence, Italy, July 215