有限元/边界元法求解变厚度板的声辐射

Sound Radiation Analysis of Variable Thickness Plate Based on FEM and BEM

利用超参数壳单元建立了变厚度板的有限元方程,并求出谐波激励下板表面的位移响应和速度响应。利用Rayle igh积分公式得到变厚度板的声压,然后将声辐射功率表示为速度响应的正定二次型。将板的声辐射功率对设计变量求导,求出变厚度板声辐射的灵敏度。以厚度线性变化的简支矩形板为例进行了数值仿真,首先研究了倾斜角对固有频率以及板中心点挠度影响,然后进一步研究了激励频率以及倾斜角对板声辐射特性的影响。

The equation of the finite element of the variable thickness plate was established by way of the subperparametric shell element,the displacement response and velocity response of plate in harmonic excitation were obtained by solving the equation of the finite element.The surface acoustic radiation pressure is computed by Rayleigh intergral.Then the acoustic radiation power can be expressed as a positive definite and Hermitian.Finally,the acoustic radiation sensitivity can be acquired by derivation of acoustic power with respect to design variables.Taken a simple supported variable thickness plate as a simulation example,the influence of the inclination angle on natural frequency and plate the central deflection of plate are researched firstly,then the effect of the inclination angle and the exciting frequency upon acoustic radiation is further studied.