正交各向异性声源膜板的自由振动特性分析  

Free vibration characteristics analysis of orthotropic sound source plates

作　　者：王久法 WANG Jiufa(Yichang Testing Technique Research Institute,Yichang 443099,China)

机构地区：[1]宜昌测试技术研究所,湖北宜昌443099

出　　处：《振动与冲击》2021年第22期216-220,266,共6页Journal of Vibration and Shock

基　　金：国家自然科学基金(51775057,51875049);湖南省自然科学杰出青年基金(2019JJ20017);长沙理工大学道路灾变防治及交通安全教育部工程研究中心开放基金资助项目(kfj170401)。

摘　　要：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。最后进行数值计算,研究了该方法的收敛性能,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,验证了该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。Based on the Mindlin plate theory,the vibration model of orthotropic sound source plates was established.The vibration displacement and the cross-sectional rotations of the mid-plane were expressed as the linear combination of a double Fourier cosine series and an auxiliary series by using the improved Fourier series method.The use of these supplementary series was to solve the discontinuity problem which encountered in the displacement partial differentials along the edges.Then the vibration matrix equation of orthotropic sound source plates was derived and the vibration characteristics were obtained by solving the general matrix equation.Finally,the convergence performance of the method was studied,and the vibration characteristics of the plates under classical boundary conditions were calculated.The accuracy of the method was verified by the comparison with the results in the available literature.The influence of boundary conditions was analyzed,which provides support to 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 

分 类 号：TP533[自动化与计算机技术]