Experimental approach on natural frequency of window vibration induced by low frequency sounds

Transcription

1 INTER-NOISE 216 Experimental approach on natural frequency of window vibration induced by low frequency sounds Tetsuya DOI 1 ; Keiichiro IWANAGA 1 ; Michiko JIMBO 2 1 Kobayasi Institute of Physical Research, Japan 2 Gakushuin University, Japan ABSTRACT Low frequency sound may cause environmental problems such as window rattling and human feeling indoors. In previous studies, we conducted field experiments to investigate transmission of low frequency sound into a test building by using a transportable device that could generate low frequency sounds down to 2 Hz. Results showed that windows of the test building vibrate easily at around 1 Hz. However the reason has not been clarified. In this study, we conducted a field experiment in which we used same test building and low frequency sound source to verify the spring-mass system model, by supposing windows to be mass and air inside the room to be spring. Results show, natural frequency of window vibration is not only affected by the factor of the spring-mass system, but may also be affected by the factor of stiffness of windows. Keywords: Low frequency sound, Insulation, I-INCE Classification of Subjects Numbers: , INTRODUCTION The low frequency sound generated from sonic boom, tunnel blasting, water discharge from dams, and helicopter operations might cause various environmental problems such as window rattles and human feeling. In 22, Ochiai et al investigated rattling of windows and doors in actual houses [1]. They found that windows and doors rattle easily in the frequency range of 5 to 2 Hz, and that frequency differs depending on the different windows and doors. However, the reason for this difference has not been made clear. In 212 and 214, we conducted field experiments using low frequency sound source and a test building, and found that windows (sliding glass doors) of the test building vibrate easily at around 1 Hz, and found that sound pressure level indoors becomes uniform under 2 Hz [2][3]. In these frequency ranges, it is possible to consider the vibration of windows and doors using the spring-mass system model. In the spring-mass model, windows and doors act as mass, and an air indoors act as spring. On the other hand, when windows and doors vibrate, they bend and have counter-force because of stiffness effect, and so, it is also possible that they have natural frequency. However, the spring-mass system model and this assumption have not yet been verified by experiments. In this study, we conducted two types of field experiments using a test building to investigate the reason for natural frequency of sliding glass door vibration. In the experiment A, the relationship between room volume of the test building and natural frequency of doors was investigated to verify about spring-mass system model. In the experiment B, the relationship between displacement of doors and counter-force was investigated to grasp stiffness effect of doors. 2. PROCEDURE OF MEASUREMENT 2.1 Experiment A (effect of spring-mass system) To investigate spring-mass system related to indoor air and door vibration, field experiment A was conducted by using impulsive sound source and a test building. 1 doi@kobayasi-riken.or.jp 116

2 INTER-NOISE Impulsive sound source Impulsive sound source (ISS) was used in this study. Figure 1 shows the overview of the ISS. It is composed of an air tank constructed by an aluminum cylinder with.26 m of internal diameter and.5 m of length. One end of the cylinder is closed and the other end is open. The polyester-made membrane, which is attached on the open side, bursts due to the pressure in the tank. In order to reduce sound reflection which produces echoes inside the cylinder after the first impulsive sound, the cylinder was filled with acoustic absorbing material. Figures 2 and 3 show the sound pressure waveform and the frequency characteristic of impulse sound respectively, which are measured at 4 m distance from the sound source. The pulse width of the measured sound pressure wave is about 1 ms and the maximum sound pressure amplitude is about 6 Pa, which corresponds to the maximum SPL of 15 db. As shown in Fig. 2, a clear impulse sound is obtained by the effect of the acoustic absorbing material inserted in the tank. The frequency characteristics shown in Fig. 3 also indicate that the impulse sound has sufficient acoustic power in the infra-low frequency range below 2 Hz. Aluminum ring Aluminum tube Opening 26mm Absorption material Air inlet 5mm Rubber Rubber Polyester sheet Figure 1 Configuration of impulsive sound source ms Time (S) Figure 2 Waveform of impulsive sound (r = 4 m) /3 Oct.band center frequency(hz) Figure 3 Spectrum of impulsive sound (r = 4 m) 117

3 INTER-NOISE Test building Figure 4 shows the test building used in this experiment. This test building has a typical Japanese wooden construction and its dimensions are 5.1 m wide x 2.1 m deep x 2.5 m high. Horizontally sliding glass doors surrounded by an aluminum frame of 1.6 m wide x 1.8 m high are attached on one of the walls as test specimen. In this study, field experiments for 4 volume conditions of the test building were conducted by installing indoor walls as shown in Fig. 5 to investigate the relationship between natural frequency of doors and room volume. has the smallest indoor volume (3.6m 3 ), and it is 1/6 the volume of the original test building. The wall was made of wood and has 2 mm in thickness, and some wooden pillars were used to secure the position of walls. In our preliminary experiment, it was confirmed that SPL difference for opposite sides of the wall is over 2 db. Figure 4 Test building (v=3.6m 3 ) (v=7.2m 3 ) (v=12.8m 3 ) (v=2m 3 ) Figure 5 Experimental conditions of the test building Measurement Figure 6 shows the arrangement of the sound source and the test building. We measured indoor and outdoor sound pressure by using a low frequency sound meter (RION, XN-12A:.2 Hz 1 khz, XN-1G: 1-5Hz, NA-17: 1-5 Hz). We also measured the displacement of the glass doors by using two laser displacement gauges (KEYENCE LK-G155) as shown in Figs. 5 and

4 INTER-NOISE 216 Test building (5m x 2m) M icrophones Sliding glass doors 4m Laser displacemet gauges 4m Mic. Sound source Figure 6 Arrangement of the sound source and the test building 2.2 Experiment B (stiffness effect of doors) To investigate stiffness effect of sliding glass doors, field experiment B was conducted by using compressed air and the test building used in experiment A. When compressed air flowed into the test building, atmospheric pressure indoor increased, and caused the doors to bend toward the outside, as shown in Fig. 7. We measured indoor and outdoor difference in pressure by using a pressure gauge (CEM, DT-892), and measured displacement of doors by the laser displacement gauge mentioned above. From the measured data, we investigated a relationship between displacement of doors and its counter-force. Although some air leaks out of the building thorough gaps in the sash of the sliding glass doors, measurement is possible because the volumes of incoming and outgoing air are equal. Air tube Air tank Air Test building Difference pressure gauge Laser displacemet gauges Sliding glass doors Figure 7 Overview of the experiment B 119

5 INTER-NOISE Results 3.1 Experiment A Figure 8 indicates time variation of outdoor sound pressure and door displacement. The upper figures are outdoor pressure waveforms, which are 4 m away from the sound source. The same amplitude impulses were observed for each experimental condition. Middle and bottom figures are door vibration waveforms due to impulse sounds. Time period of vibration increases in the order of case 1, 2, 3, 4. Outdoor pressre (a) (Volume=3.6m 3 ) (b) (Volume=7.2m 3 ) Displacement of door (left) Displacement of door (right) Time(s) Time(s) Outdoor pressre (c) (Volume=12.8m 3 ) 8 8 (d) (Volume=2m 3 ) Displacement of door (left) Displacement of door (right) Time(s) Time(s) Figure 8 Time variation of outside sound pressure and door displacement 12

6 INTER-NOISE 216 Figure 9 indicates frequency characteristics of outdoor sounds. These results show that the incident sounds against the test building have a frequency range of 5-2 Hz, and have the same amplitude ±2dB /3 Oct.band center frequency(hz) Figure 9 Frequency characteristics of incident sound radiated from the source Figure 1 shows the averaged results of frequency characteristics for 4 points indoors. In the case that all 4 impulse sounds radiated into the test building are the same amplitude, frequency characteristics of indoor sounds differ depending on the volume conditions of the building. has the smallest volume and its dominant frequency is 16 Hz, which is the highest. A tendency that dominant frequency get lower in the order of case 1, 2, 3, 4 was observed /3 Oct.band center frequency(hz) Figure 1 Frequency characteristics of sound inside the building Figure 11 shows the averaged results of frequency characteristics of left and right door vibration. In this study, we define displacement level (DispL) by calculating displacement of door vibration with the following equation: 2 2 DispL 1 log( X / X ) (1) where, X is root mean square value of door displacement[mm], and X is the reference displacement (2x1-5 [mm]). In these results, the same tendency as indoor sounds was observed, where dominant frequency of door vibration get lower in the order of case 1, 2, 3,

7 INTER-NOISE /3 Oct.band center frequency(hz) Figure 11 Frequency characteristics of door vibration Figure 12 shows the dominant frequencies of door vibration which are obtained from FFT analysis. In this figure, the horizontal axis indicates room volume. From the results, it is found that dominant frequency of door vibration decreases as room volume increases. Fig. 13 shows the results for 1 Hz in which displacement level is subtracted from SPL indoors. Therefore, this figure indicates the relationship between displacement of doors and indoor sound pressure. From this figure, one can see that small displacement generates large sound pressure when the room is small. These relationships are inversely proportional to room volume, meaning door vibration and indoor sound pressure are affected by the spring-mass system Room volume (m 3 ) Figure 12 Dominant frequency of door vibration Room volume (m 3 ) Figure 13 Relationship between door displacement and indoor pressure 122

8 INTER-NOISE Experiment B Figure 14 shows bending displacement of doors when atmospheric pressure increases. Force F against glass panes is calculated by multiplication of pressure difference inside and outside the building by the area of the doors. X stands for the displacement of doors, and is calculated by averaging the displacement of the center points of the left and right glass pains. There is a tendency that force F is proportional to the displacement of doors. Proportionality coefficient kglass stands for the magnitude of counter force (i.e. stiffness effect) when glass pane is bent by pressure. In actuality, glass panes slide when X is small because there are gaps at the top of doors. However, in this study these effects were ignored for simplification F = kglass X k=8.66* x1 1x1-4 2x1-4 3x1-4 Displacement X (m) Figure 14 Relationship between door displacement and counter force 4. Discussion From the results of experiment A and B, we investigated the relationship of the effect of spring-mass system and stiffness effect. Figure 15 shows the relationship between force F against glass panes and displacement X of doors in experiment A. Force F is calculated by multiplication of RMS (root mean square) value of sound pressure obtained from SPL as shown in Fig. 1 by the area of the doors. Displacement X is the RMS value calculated from the displacement level, as shown in Fig F = k X k = kair1 k = kair2 k = kglass case1 case2 case3 1 k = kair3 case4 k = kair4 x1 1x1-5 2x1-5 Displacement X (m) Figure 15 Relationship between force against glass panes and displacement of doors in experiment A In this figure, proportionality coefficient kair means magnitude of air spring. kair increases in the order of case 4, 3, 2, 1. This means that air spring strengthens as room volume decreases. The dotted line in Fig. 15 indicates kglass, which is stiffness effect of the glass pane obtained from experiment B. By comparing these data, it is found that air spring of case 3 is the same as the stiffness of glass panes. 123

9 INTER-NOISE 216 Figure 16 shows the relationship between proportionality coefficient k obtained in Fig. 15 and room volume. Kglass, which indicates stiffness of glass, is constant, and does not depend room volume. On the other hand, kair, which indicates air spring, weakens as volume increases. From these relationships, we found that contribution of air spring increases as room volume decreases, whereas contribution of stiffness of glass increases as room volume increases. For the test building used in this experiment, the contribution of both effects become equal in case 3 (12.8m 3 ). 2.x1 5 kair kglass 1.x1 5.x Room volume (m 3 ) Figure 16 Relationship between effect of air spring and stiffness effect 5. Summary In this study, field experiments using a test building and sound source were conducted to investigate the mechanism of natural frequency of door vibration due to low frequency sounds. Results indicate that dominant frequency of door vibration deceases as room volume increases. Therefore, the effect of spring-mass system, where spring is assumed as air and mass as doors, was confirmed. Furthermore, another field experiment using the same test building was conducted to investigate the effect of stiffness of glass doors. Results indicate that stiffness effect is greater than effect of air spring when room volume exceeds 12.8m 3. From the results of these two sets of experiments, we conclude that not only air spring effect, but also stiffness effect should be taken into consideration in order to understand the dominant frequency of door vibration. REFERENCES 1. Ochiai et al., On the threshold level of rattling fittings due to low frequency sound pressure level, Journal of INCE/J, Vol. 26, No. 2, pp , 22 (In Japanese). 2. Doi et al., Experimental approach on transmission of low-frequency sound into a building, Proceeding of Internoise (214). 3. Doi et al., Distribution of low frequency sound pressure level inside a building, Proceeding of Autumn Meet. Acoust. Soc. Jpn., pp , 212 (in Japanese). 124