板梁耦合振动响应仿真分析

板梁耦合结构是典型的中频振动结构。针对现有的确定性数值分析方法在中频预测的不足,基于波函数法(WBM)理论提出了预测板梁耦合结构的振动响应方法。在Kirchhoff薄板与Euler-Bernoulli梁振动响应基础上,以振动位移与转角为耦合量,运用加权余量法推导了板梁耦合结构的系统矩阵,建立了板梁耦合结构的波函数法模型。以四边固支的矩形板与细长梁耦合结构为例进行了验证,其100Hz时的振动响应位移云图与50~500Hz频响结果表明,相较于有限元(FEM)模型,基于波函数法的板梁耦合结构振动响应模型能有效预测更高频率的振动响应,且该模型有着更高的收敛性,在相同计算精度下,计算成本(模型自由度与计算时间)降低明显。

Simulation analysis of vibration response for coupled plate-beam

Coupled plate-beam structure is a typical structure whose vibration performance is in mid-frequency.Aiming at the shortcomings of the existing deterministic numerical methods in the prediction of the mid-frequency,we proposed a method to predict the vibration response of coupled plate-beam structure on the basis of wave-based method (WBM).First,based on the vibration response of Kirchhoff plate and Euler-Bernoulli beam,the system matrix of coupled plate-beam structure was deduced by using the weighted residual method using the transversal displacement and the torsional angle between plate and beam as the coupling variable.Then the wave-based mathematical model for coupled plate-beam structure was established.Finally,the coupled structure of rectangular plates with four sides clamped and a slender beam was taken as an example to validate the proposed method.The contour of the coupled structure at100 Hz and its frequency response from 50-500 Hz show that compared with finite element method (FEM),the wave-based model for coupled plate-beam structure is more efficient in higher frequency range and has higher convergence.At the same computational accuracy,its computational cost (degree of freedom of model and computational time) decreases significantly.