The Determination of Frequencies and Modes of Undamped Structures Using Finiteelement Stiffness and Consistent-Mass Matrices

摘要

An analysis and a computer program which permit determining the natural mode shapes and frequencies for undamped structures are given. The program is designed to operate on stiffness and consistent-mass matrices which are derived from a finite-element representation of the structure, since it has been shown that superior accuracy is achieved compared with conventional lumped-parameter methods with an equal number of idealized elements. The consistent-mass matrix is a symmetric-mass matrix with nonzero offdiagonal elements; it is this symmetric nondiagonal feature which the present analysis handles conveniently. In particular, the present method represents a convenient and economical synthesis of existing methods, and may be used to calculate the natural mode shapes and frequencies for any system which is described by a set of symmetric mass and stiffness matrices. (Author)