胡海岩
摘要:在许多线性振动的教材和手册中，关于固有振型节点规律表述存在不妥。本文对该问题进行分析，指出必须理解 Гантмахер 和 Крейн 关于固有振型节点定理的前提和局限性。文中详细分析了两自由度系统固有振型节点的规律，给出若干新的结论。基于该规律对一类多自由度组合系统的固有振型进行分析，说明可人为设计结构来满足特定的固有振型阶次与节点数关系。
关键词：固有振型, 节点, 振荡矩阵, 离散系统
On node number of a natural mode⁃shape
Haiyan Hu
Abstract：It is pointed out in this paper that there exist some improper statements on the rule of the nodes of a natural mode-shape in monographs, textbooks and engineering manuals related to linear vibrations. Hence, detailed discussions are made on the theorem of Гантмахер and Крейн about the natural mode-shapes and their nodes, as well as their preconditions in order to call attention from both academia and industries. Afterwards, a complete analysis is made for the node number of the natural mode-shapes of a two degrees of freedom arbitrary linear system. Based on the analysis, the natural mode-shapes of a kind of multiple degrees of freedom composite systems are studied so as to demonstrate a designable relation between the order of a natural mode-shape and the number of its nodes.
Keyword：natural mode⁃shape, node, oscillation matrix, discrete system
原文链接：http://dlxykzxb.cnjournals.net/jdc/article/abstract/20180301?st=search
