能量矩阵法求解结构振动模态的研究  

Research on structural modal calculation by decomposing the energy matrix

作　　者：李徐钢[1] 左曙光[1] 张敬芬 

机构地区：[1]同济大学汽车学院,上海201804 [2]汉高亚太及中国总部,上海201203

出　　处：《交通科学与工程》2009年第4期69-72,102,共5页Journal of Transport Science and Engineering

基　　金：上海市曙光计划项目(05SG22)

摘　　要：提出一种计算结构模态的新方法.以能量守恒方程为基础,认为线性弹性系统最大振幅处的势能与平衡位置时的动能互相平衡.将弹性系统的势能和动能表达式写成矩阵的形式,对其作一定的变换处理后,通过对其进行特征值分解,可同时得到模态振型和固有频率.两个典型算例的验证表明,该方法是精确可靠的.相比于传统的计算方法,能量矩阵法可更方便地得到弹性系统的各阶模态.A new method for calculating the structural modes is proposed. Based on the energy conservation law, the max kinetic energy of the vibration system is equal to the max potential energy. The kinetic energy and potential energy can be represented in form of matrix and vec- tors. After some transformation on the matrix, the mode-shape and natural frequency can be obtained simultaneously by decomposing the energy matrix. Two examples show that the method is effective, precise and convenient.

关 键 词：能量矩阵 特征分解 固有频率 模态振型 

分 类 号：TB123[理学—工程力学] O326[理学—力学]