一重板の遮音機構の解析 : 円形板への平面波垂直入射

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The mass law of sound transmission through an infinite single partition is well known, and the mass law for oblique incidence has been derived on the assumption that the partition consists of particles not connected with one another. Cremer pointed out that oblique incidence sound transmission deviates considerably from the mass law above the coincidence frequency, where the inertia of the partition and its stiffness cancel each other. However, there is a resonance contribution to transmission for a finite partition and the transmission characteristics above the critical coincidence frequency f_c are different from those below f_c for any incidence of angle, since the sound radiation of flexural vibration depends on the frequency. Consequently the relation between the vibration and the reaction of the air is very important, and in order to analyze transmission through a finite partition, it is necessary to take account of its stiffness, internal loss, shape, size and surroundings in addition to its mass. This paper presents an analysis and a physical interpretation of transmission of a normally incident plane wave through a circular plate set flush in an infinite rigid baffle, where the internal damping and the reaction of the air to the vibrating plate are taken into account. The theoretical results shown in Figs. 3〜7 are as follows:1)The plate vibrates in such a way that a piston motion and a flexural motion are superposed. 2)The transmission loss T. L. at anti-resonance is nearly equal to that of a circular piston plate, where the amplitude of the flexural vibration is relatively small. 3)The deviation from the mass law occurs at the resonance point because the amplitude of the flexural vibration is very large at this point, and the flexural vibration radiates sound below f_c less than the vibration of an infinite piston does. The deviation for a plate with clamped edges is a little greater than for a plate with supported edges, and the deviation is generally noticeable above f_c when the flexural vibration is damped by the internal loss rather than by the radiation resistance. 4)At lower resonance frequencies, T. L. of the plate with little internal loss becomes apparently negative, which indicates that the equivalent transmission area is larger than the geometric area of the plate by the diffraction effect. 5)At frequencies slightly below the lower resonance frequencies other than the first one, T. L. becomes considerably great, because the flexural vibration cancels the sound radiation of the piston vibration. As a practical illustration, the measured transmission loss of a steel plate with and without attaching a damping material, and the vibration level difference between those two are presented in Figs 8 and 9.
社団法人日本音響学会の論文
1973-04-10

一重板の遮音機構の解析 : 円形板への平面波垂直入射

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