Experiment and simulation studies on sound insulation performance of the wooden component

2.1. Sound pressure method

In this equation, ${\stackrel{-}{L}}_{P_i}$ is the average number of SPL (Sound Pressure Level) inside the reverberation chamber of the incident side; ${\stackrel{-}{L}}_{P_o}$ is the average number of SPL inside the reverberation chamber of the transmission side; $S$ is the unilateral surface area of the wooden component; $A$ is the number of sound absorption inside the reverberation chamber of the transmission side.

According to ISO354 [7], the number of sound absorption can be calculated by Sabine formula, shown as follows:

where $V$ is the volume of the reverberation chamber; $T$ is the reverberation time of the reverberation chamber.

Depending on the size of the laboratory room, four microphones have been arranged separately and symmetrically surrounding the test piece of wooden component. In order to observe the uniformity of diffuse sound field, another microphone has been added in the center of these four microphones, as shown in Fig. 2. During the experiment, pink noise sound source was added in the incident side; after the formation of a stable reverb, simultaneous measurement of SPL of each microphone position was started. Each group of data was recorded for 8 s, measured three times, and the sampling frequency was 65536 Hz. Finally, the average SPL of these five-points was chosen as the incidence SPL and transmission SPL.

Fig. 2The test schematic of sound pressure method

The reverberation time has been tested after that. The reverberation time is the time required between sound source stops sounding and the acoustic energy density indoor falls to 60 dB. Keep the microphone position in the transmission side to be the same and add the same pink noise sound source. During the experiment, pink noise has been given for 3 s at first; after the sound source stopped sounding, the SPL decay process was measured immediately. Each group of data was recorded for 8 s and measured three times; the sampling frequency was 65536 Hz. The reverberation time was taken into Eq. (3) to calculate the sound absorption.

The incidence SPL and transmission SPL, the sound absorption (obtained by the experiment) were taken into Eq. (2) to calculate the sound insulation of these wooden components.

2.2. Sound intensity method

Fig. 3The comparison for the transmission loss of two kinds of method

In order to verify the accuracy of sound pressure method, we also used sound intensity method in this experiment. The sound intensity method include two procedure, one is to measure the average SPL of five-points in the incident side (like the measure process of sound pressure method), the other one is to obtain the radiation sound intensity $I_o$ of test pieces through using sound intensity probe to do near-field surface scanning of the specimen in the transmission side. The sound insulation calculating formula of sound intensity method is as follows:

Compare transmission loss obtained by these two kinds of method, the result is shown in Fig. 3.

As can be seen from Fig. 3, the results have a good agreement measured by these two kinds of method separately. It indicates that there was no presence of errors during the experiment and the test results are reliable.

3.1. Damping loss factor measurement

The definition of damping loss factor $\eta$ is the ratio of energy consumption caused by system damping property and the whole energy storage of the system, consists of three independently loss factor [8]:

where ${\eta }_s$ is the structure loss factor caused by the interior friction of system material; ${\eta }_r$ is the loss factor caused by the sound radiation damping of system vibration; ${\eta }_b$ is the loss factor caused by connection damping of system boundary.

In this measurement, pulse attenuation method [9, 10] has been used to measure the damping loss factor of the test pieces; the test device is shown in Fig. 4. As is shown in Fig. 4, the test piece chosen is rectangular plate. When a rectangular plate subjects to a lateral force, several bending vibration will come into existence; the vibration formula can be written as follows [11, 12]:

where ${\varsigma }_0(x,y,t)$ is the particular solution to a given excitation force; ${\omega }_{mn}$ is the angular frequency of harmonic vibration in $(m,n)$ mode; phase angle ${\phi }_{mn}$ and fixed coefficient $A_{mn}$ will be determined by the initial condition when the plate vibrates; ${\delta }_{mn}$ is the corresponding attenuation factor.

The information of plate vibration was measure by vibration acceleration sensors. For a given mode of vibration, the acceleration signal decayed exponentially; ${\delta }_{mn}$ is the slope of this envelope decay curve.

The signal processing method of this trial was to perform an FFT transform towards the acceleration signal to obtain the angular frequency ${\omega }_{mn}$ of each harmonic vibration at first. Then with the help of Butterworth band pass filter, several free-damped vibrations corresponding to each harmonic vibration mode would be isolated as follows:

After that, through taking square and taking natural logarithm, a new signal would be obtained from the filtered signal:

Finally, polynomial fitting would be done towards the new time-domain signal curve; the corresponding decay factor $-2{\delta }_{mn}$ would then be determined by the slope of the fitting curve; the damping loss factor of the rectangular plate could be calculated by the following equation:

During the measurement, each test piece has 6 vibration test points and 30 hammer attack points. Each test point recorded 10 s vibration decay process at one time and the whole measurement process has been done for 3 times; the sampling frequency was 16384 Hz. The damping loss factor of this wooden component is shown in Fig. 5.

Fig. 4The test schematic diagram of damping loss factor

Fig. 5Damping loss factor of the wooden component

3.2. Simulation model establishment

Two sound cavities have been established on both sides of the wooden component to simulate the actual reverberation chambers. Compared to the traditional finite element method, the calculating efficient of AML is relatively high. In AML, transmission loss can be extracted directly, without the need to acquire an indirect calculation. The final 3D model is shown in Fig. 6.

Fig. 6AML simulation model of the transmission loss

The comparison between the experiment transmission loss and the simulation was shown in Fig. 7.

As can be seen from Fig. 7, in the low frequency range below 160 Hz, the simulation results have a relatively large difference with experiment results and the maximum difference is 5 dB. This phenomenon was mainly caused by boundary condition differences between simulation process and the experiment.

During the experiment, the boundary condition is shown in Fig. 1, in which the wooden component was fixed by multi-point constraints and all-around was sealed with sludge. However, the simulation process could only simplified the actual boundary conditions instead of maintain full consistency with the experiment.

Fig. 7The comparison between experiment and simulation of the transmission loss

In the high frequency range above 160 Hz, boundary conditions no longer play a dominant role and thus these two kinds of result have a good agreement. In summary, the overall simulation trend is consistent with experiment, which indicates AML method is effective in predicting the sound insulation performance of wooden component.

4.1. Surface treatment

A layer of organic polymer material has been sprayed on the surface of wooden component, as shown in Fig. 8.

Fig. 8The sectional view for wooden component before and after surface treatment

Transmission loss of this wooden component before and after surface treatment has been tested and compared in Fig. 9.

As can be seen from Fig. 9, the surface treatment makes transmission loss of wooden component increase about 1 dB throughout the whole frequency band. In order to further analyze the reasons for this phenomenon, the damping loss factor for wooden component before and after surface treatment has been measured, as shown in Fig. 10.

As can be seen from Fig. 10, the damping loss factor for wooden component after surface treatment has an apparently increase, which would improve the sound insulation of wooden component to some extent.

Fig. 9The transmission loss for wooden component before and after surface treatment

Fig. 10Damping loss factor for wooden component before and after surface treatment

4.2. Sound package

A 1 mm thick layer of rubber material has been affixed to one side of wooden component, as shown in Fig. 11; transmission loss then was measured and compared to the bare board before, as shown in Fig. 12.

Fig. 11The sound package of wooden component

As can be seen from Fig. 12, after affixing a 1 mm thick layer of rubber material, the sound insulation of wooden component increases about 2 dB throughout the whole frequency band, because rubber has good viscoelastic which can effectively decay vibration and improve sound insulation performance.

Fig. 12The transmission loss curve before and after the sound package

4.3. Change the thickness of wooden component

While the material properties of wooden component were remained unchanged, the thickness of wooden component was changed from 15 mm to 24 mm (the step length is 3 mm); the transmission loss curves under different thickness have been obtained and shown in Fig. 13.

As can be seen from Fig. 13, with the increase of thickness, transmission loss shows a rising trend in the frequency band under 500 Hz; however, transmission loss decreases in general with the increase of thickness in the frequency band between 500 Hz and 1000 Hz.

The average transmission loss under each thickness has been calculated to be 26.03 dB, 26.84 dB, 27.05 dB and 27.51 dB. This result showed that the average transmission loss had small changes when the thickness increased from 18 mm to 24 mm. Therefore, it’s recommended to set the thickness of wooden component to 18 mm to avoid increasing weight and reducing product performance.

Fig. 13The comparison of the transmission loss for wooden component with different thickness

4.4. Change the elasticity modulus of wooden component

While other parameters of wooden component remained unchanged, the elasticity modulus was changed from 3.0×10⁹ Pa to 7.5×10⁹ Pa (the step length is 1.5×10⁹ Pa); the transmission loss curves under different elasticity modulus have been obtained and shown in Fig. 14.

As can be seen from Fig. 14, with the increase of elasticity modulus, the general trend of transmission loss is not clear in the frequency band under 500 Hz; mainly because it’s in the area of quality control at this time where the sound insulation performance is mainly controlled by overall quality and the change of elasticity modulus doesn’t affect the quality itself. On the other hand, transmission loss decreases apparently with the increase of elasticity modulus in the frequency band between 500 Hz and 1000 Hz, because transmission loss is no longer controlled by quality in this area.

The average transmission loss under each elasticity modulus has been calculated to be 27.47 dB, 26.84 dB, 25.92 dB and 25.41 dB. This result showed that the average transmission loss decreased when the elasticity modulus increased from 3.0×10⁹ Pa to 7.5×10⁹ Pa while the rigidity of wooden component is reduced gradually at the same time. Therefore, considering rigidity and sound insulation performance, it’s recommended to choose the wooden component whose elasticity modulus is 4.5×10⁹ Pa.

Fig. 14The comparison of the transmission loss for wooden component with different modulus

4.5. Change the density of wooden component

While the elasticity modulus and thickness of wooden component remained unchanged, the density of wooden component was changed from 500 kg/m³ to 800 kg/m³ (the step length is 100 kg/m³); transmission loss curves under different density have been obtained and shown in Fig. 15.

Fig. 15The comparison of the transmission loss for wooden component with different density

As can be seen from Fig. 15, with the increase of density and frequency, transmission loss shows an apparently rising trend in the frequency band under 630 Hz; however, the transmission loss decreases in general with the increase of frequency above 630 Hz. On the other hand, the transmission loss also shows a slow rising trend with the increase of density in the frequency band above 630 Hz.

The average transmission loss under each density has been calculated to be 22.63 dB, 24.99 dB, 26.94 dB and 27.96 dB. This result showed that the average transmission loss increased when the density increased from 500 kg/m³ to 800 kg/m³ while the rate of increase reduced. Therefore, considering the lightweight and sound insulation performance request, it’s recommended to choose the wooden component whose density is 700 kg/m³.

Fig. 16The graphics interface of the datebase for sound insulation performance