基于任意四边形单元的约束阻尼板的模态分析

约束层阻尼技术目前广泛应用于薄壁结构的减振降噪中，关于约束阻尼板的有限元分析基本采用矩形或三角形单元，但用于模拟不规则形状结构时，会带来形状拟合上的困难或精度上的不足。基于离散Kirchhoff理论和Layer-wise层合板理论，利用Hamilton原理推导了约束阻尼板的任意四边形单元，并在此基础上考虑粘弹性材料本构的频率相关性，给出了约束阻尼结构复特征值问题的迭代求解算法。数值算例对不同形状的约束阻尼板结构进行了模态分析，通过与解析解、实验结果及有限元结果的对比，表明了本文单元的有效性和对不规则形状结构的适用性。

Modal analysis of the plate treated with constrained layer damping based on an arbitrary quadrilateral element

Constrained layer damping (CLD) treatments are widely used for vibration and noise reduction of thin-walled structures.Despite extensive applications in finite element analysis of plates treated with CLD,the rectangular element and triangle element are challenged by irregular structural forms or low accuracy.In this paper,based on the discrete Kirchhoff and layer-wise laminate theories,an arbitrarily quadrilateral element for the constrained layer-damped plate is developed using Hamilton''s principle.On this basis,considering the frequency dependent characteristics of viscoelastic materials,an iterative algorithm for complex eigenvalue problem of the structures with CLD treatment is given.Numerical examples are presented to do modal analysis of the CLD plates with different shapes.By comparing with the analytical solution,the experimental results and the finite element results,the effectiveness and the applicability of this method to irregular structural forms are verified.