WBM法在薄板弯曲振动分析中的应用

Application of wave based method to plate bending vibration analysis

研究了薄板结构在点力激励下的弯曲振动响应,基于间接Trefftz法,提出了解决薄板弯曲振动响应的波函数方法(WBM).方法原理是:将振动响应展开成全局波函数和非齐次方程特解的线性叠加,这些波函数精确满足方程的齐次部分,随后利用伽辽金法在边界上进行加权残值计算,得到波函数的常数系数.同有限元法相比,WBM法不再需要划分成很小的单元,有更高的计算效率和收敛速度,可以推广到中频段的计算.以一个周边简支矩形薄板为例进行验证,结果表明方法准确且高效.

The bending vibration of a thin plate excited by a point force was described.From indirect Trefftz method,the wave based method is proposed to settle the bending vibration of plate.The vibration are approximated in terms of globe wave functions,which are the exact solutions of the homogeneous parts of the equations and the particular solutions,which are the exact solution of inhomogeneous equations.The contributions of the wave functions to the vibration are determined by applying the boundary conditions in a weighted residual formulation.In contrast with finite element method,WBM needs no discrimination,more efficient and better convergence properties.It is validated that the method is efficient and accurate by a simply supported plate example.