一般边界条件下矩形薄板振动声辐射特性分析

基于改进傅立叶级数方法,将矩形板振型函数表示为包含正弦三角级数的改进傅立叶级数,从而有效地克服结构在边界处存在的不连续性,建立了一般边界条件下矩形薄板结构振动声辐射的分析方法,并对薄板结构的振动声辐射特性进行了研究。文中还建立了薄板结构的位移容许函数,然后基于最小势能原理求解了系统的Lagrange函数,最后利用Rayleigh-Ritz法对方程求解从而获得薄板自由振动的模态信息;在此基础上,基于Rayleigh积分公式推导出了薄板振动、辐射声压和声功率的表达式,研究了结构特性参数及边界条件对薄板振动声辐射的影响,通过有限元软件和参考文献的比对分析,验证了改进方法的正确性和有效性。

Analysis of vibration and acoustic radiation characteristics for rectangular plates with general boundary conditions

Based on the theory of plates, a new method called Improved Fourier Series Method (IFSM) is presented to study the vibration and acoustic characteristics of rectangular plates with arbitrary boundary conditions. The plate admissible functions is presented, which is invariantly sought as an improved Fourier cosine series, and a sine series is introduced to overcome the discontinuities of the structure. And then the Lagrange equation is established according to the principle of the minimum potential energy. Finally, by us-ing the Rayleigh-Ritz technique the vibration characteristics can be easily acquired. Under these circum-stances, with the help of Rayleigh integral formula, the expressions of sound pressure and acoustic power are derived. The effects of structural parameters and boundary conditions that have great impact on the acous-tic radiation are also studied. The comparisons among numerical simulation results, which obtained with FEM and reposed in literatures, validate the correctness of the method.