板振動吸音に関する考察 : 周辺固定円形板モデルの解析

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In this paper a model for panel vibration type sound absorbing materials is prepared, and the effects of some physical quantities of panel materials, the depth of an air-space backing and the acoustic impedance of a rear wall on sound absorption characteristics of the system are studied through theoretical analysis. The model for the panel acoustic system adopted in this paper has a cylindrical form including a circular panel with its circumference clamped (see Fig. 1). In Fig. 1 the plane sound wave travels in the plus z-direction and is normally incident on the panel surface. It is assumed that the acoustic impedance of the panel surface in a static state and that of the inner surface of the cylinder are both infinite, while the rear wall has a finite acoustic impedance. In addition it is presumed that the modes of vibration other than axisymmetric vibration with circular nodes are not allowed for the panel. In theoretical analysis of the above system, we begin with solving an equation for forced vibration of the circular panel. Then the wave equation in the cylindrical region on the left side of the panel (Region I), and the equation on the right side of the panel (Region II) are solved. Boundary conditions are expressed by Equations (19), (20) and (21) for Region I, and by Equations(25), (19)' and (20)' for Region II. As a result Equation (22) for Region I, and Equation (26) for Region II are obtained. On the other hand, Equation (30) is derived on the assumption that the driving force exerted on the panel arises from the pressure difference between both sides of the plate. Multiplying both sides of Equations (22), (26) and (30) by the m-th normal function for vibration of the circular panel with its circumference clamped, for density integration all over the panel surface results in Equation (37) for obtaining a vector C with an element C_n, which is the amplitude of the reflected wave of the n-th mode of vibration propagated in Region I. If these C'_ns are known by numerical calculation, the sound absorption coefficients of the system can estimated. Comparisons between calculated values and measured values by the standing wave tube method of the sound absorption coefficients of circular plates of vinyl chloride are presented in Fig. 4, and Fig. 5. Since these figures show good agreement, we next study the effects of the modulus of elastidty, thickness, density and loss factor of panel materials, the depth of an air-space backing, and the acoustic impedance of a rear wall on the sound absorption characteristics of the system by the same method of calculation. The sound absorption characteristics are expressed by three quantities defined as follows. (1) Relative frequency deviation Δf=(f_<res>. - f_<pro>. , where f_<res>. is the lowest resonance frequency of the system and f_<pro>. is the lowest natural frequency of the panel. (2) Sharpness Q of the lowest peak in the sound absorption characteristics. (3) Absorbed energy A. This is the energy absorbed in the band width of 400 Hz around the lowest resonance frequency of the system. The results are as fol1ows : (1) There is a linear relation between the modulus of elasticity, and Q and Δf, but A shows a constant value independently of the modulus of elasticity (see Fig. 6). (2) Q increases but A decreases with an increase in the thickness of panel material. When a panel is thin, however, Q and A change little Δf varies notably with a change in the hickness of panel material, that is, the thinner a panel is, the larger Δf is. This may be attributed to the movement of the second peak of the sound absorption characteristic toward the lower frequency region with the lowest peak remaining nearly stationary, thus getting these two peaks to get closer with a decrease in the thickness of a panel (see Fig. 7). (3) Δf and Q are independent of the density of panel material (see Fig. 8). (4) A loss factor of panel material has a great effect on the second peak of th
社団法人日本音響学会の論文
1974-05-01

板振動吸音に関する考察 : 周辺固定円形板モデルの解析

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