Abstract The radiation sound field of the plate with general boundary conditions backed by the acoustic cavity is investigated theoretically. The displacement function of the plate is generally expressed as a 2-D Fourier cosine series with additional terms. The addition terms could be used to accelerate the convergence rate of the present method and to account for the discontinuity of the displacement at the boundaries. The vibro-acoustic coupling between the vibration of the plate and the sound field on both sides of the plate is fully taken into consideration by adopting the Hamilton's principle. The sound pressure in the cavity is expressed as a 3-D Fourier series with additional terms which is used to account for the continuity between the velocity of the plate and the sound pressure on the plate. The sound radiation power of the plate can be obtained by using the Rayleigh integral. By means of Fast Cosine Transform, the quadruple integrals of the sound radiation power of the plate is reduced to several single integrals, which effectively avoids the time-consuming calculation. The influence of parameters on sound radiation power, such as boundary conditions, the sizes of the cavity, acoustic medium inside the cavity and the mounting position of the plate, are studied.

中文翻译：

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来自矩形腔背板的声辐射

摘要 从理论上研究了声腔支持的具有一般边界条件的板的辐射声场。板的位移函数通常表示为带有附加项的二维傅立叶余弦级数。加法项可用于加快本方法的收敛速度并说明边界处位移的不连续性。采用汉密尔顿原理，充分考虑了板的振动与板两侧声场之间的振声耦合。腔中的声压表示为带有附加项的 3-D 傅立叶级数，这些项用于说明板速度与板上声压之间的连续性。板的声辐射功率可用瑞利积分求得。通过快速余弦变换，将板声辐射功率的四重积分缩减为几个单积分，有效避免了耗时的计算。研究了边界条件、空腔尺寸、空腔内的声介质、板的安装位置等参数对声辐射功率的影响。