非比例阻尼线性结构体系动力分析的拟力实模态叠加法

A MODAL SUPERPOSITION PSEUDO-FORCE METHOD FOR DYNAMIC ANALYSIS OF NON-PROPORTIONALLY DAMPED LINEAR SYSTEMS

对于非比例阻尼线性结构体系,利用体系无阻尼实模态来形成模态响应方程时,得到的模态方程组是关于模态阻尼矩阵耦合的。非比例阻尼可以分成两部分:耗散能量的比例阻尼和转换能量的非比例阻尼。基于这种概念,本文采用了一种拟力实模态叠加法来求解非比例阻尼体系的动力分析,即把前述耦合模态方程中代表非比例阻尼的耦合项作为虚力,放到方程的右端,再运用迭代法进行求解。这种方法综合了经典模态叠加法和拟力法的优点。数值算例表明,此方法具有很好的收敛特性,所得结果精度高。我们认为,这种方法可应用于实际工程分析。

For non-proportionally damped linear systems the modal equations obtained from the undamped eigenvectors are coupled with the modal damping matrix. The non-proportional damping may be divided into two parts: the proportional part for dissipation of energy and the non-proportional part for transformation of .energy. Based on this concept, a modal superposition pseudo-force method for the dynamic analysis of non-proportionally damped systems is presented. In this method, the coupled modal equations are solved by iteration in which the coupling terms are treated as pseudo-force and set to the right side of the equations. The method combines the advantages of the classical modal superposition method and the pseudo-force method. Numerical examples show good convergence of the process and good acuracy of the computed results.