基于Mindlin理论，建立了正交各向异性声源膜板的弯曲振动模型。采用改进Fourier级数方法，将声源膜板的横向位移函数和转角函数表示为标准的二维Fourier余弦级数和辅助Fourier级数之和，解决了振动位移函数的偏导数在边界处潜在不连续的问题，在此基础上，推导出正交各向异性声源膜板的振动矩阵方程，声源膜板在任意弹性边界条件下的振动信息可以通过求解一个通用的矩阵方程而得到。最后进行了数值计算，研究了本文方法的收敛性能，计算了声源膜板在经典边界条件下的振动特性，通过与现有文献的计算结果进行比较，验证了本方法的准确性和精确性，并分析了边界条件对声源膜板振动特性的影响，为发声器的优化设计提供支撑。
Abstract
Base on Mindlin plate theory, the vibration model of orthotropic sound source plates is established. and the vibration displacement and the cross-sectional rotations of the mid-plane are sought as the linear combination of a double Fourier cosine series and auxiliary series functions through improved Fourier series method, the use of these supplementary series is to solve the discontinuity problems which encountered in the displacement partial differentials along the edges. Then the vibration matrix equation of orthotropic sound source plates, the vibration characteristics can be obtained by solving the general matrix equation. Finally, the convergence performance of the method in this paper is studied, and the vibration characteristics of the plates under classical boundary conditions are calculated. The accuracy of the method is verified by comparison with the results of the available literature. The influence of boundary conditions is analyzed, which provides support for the optimal design of the sound generator.
关键词
正交各向异性材料 /
声源膜板 /
改进Fourier级数 /
弹性边界条件
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Key words
orthotropic material /
sound source plate /
improved Fourier series /
elastic boundary support
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