自由阻尼处理结构的有限元建模及声辐射分析

用整体划分单元法建立了一种四节点20个自由度自由阻尼处理薄板结构的有限元模型，用能量法推导了单元的刚度和质量矩阵。在用有限元法计算结构的动态响应特性的基础上，将每个单元划分为很多个微元，利用有限元分析得到结构表面振动速度，通过单元的形函数，求出微元上几个点的平均速度，作为微元的振动速度。以每个微元为一单位，分别计算声压和声功率之后叠加起来，即得整个结构的声辐射。算例表明，用此方法分析计算表面阻尼处理结构的动态特性和声辐射是可行的。

Finite Element Modelling and Acoustic Radiation Analysis of Structures with Free Damping Treatment

This paper develops a 4-node 20-freedom finite element for the thin-plate structures with free damping-treatment using integral dividing method. The mass matrix and the stiffness matrix of the elements are derived with energy method. Based on the finite element analysis results of the dynamic properties of the structure, each element is divided into many infinitesimal elements. The velocities of several points of each infinitesimal element are calculated through the element shape function and the velocity distribution obtained from the finite element analysis results. The velocity of each infinitesimal element is considered as the average velocity of the above points. The acoustic pressure and acoustic power of the whole structure are obtained by superposing those of each infinitesimal element. The example given in this paper shows that the method is feasible to calculate the dynamic properties and sound radiation of surface damping-treatment structures.