Homology Design for Eigenvector of Bending Vibration Using Finite Element Method

Abstract

A method of homology design is presented for linear and undamped vibration of elastic structures in eigenvalue problems based on the finite element method. It is aimed at to realize the homologous mode shape, which maintain a prescribed geometrical property in a structure both in standstill and vibrant state. The original eigenvalue problem is separated into two modified eigenvalue problems with square and rectangular coefficient matrices by introducing the homologous mode shape constraint. The governing equation of design change for homologous mode shape is derived by means of the finite element sensitivity analysis of the modified eigenvalue problems. The Moore-Penrose generalized inverse is used for the solution since the coefficient matrix of the governing equation is rectangular. The validity and versatility of the proposed method are demonstrated by the numerical examples of a planar lattice frame.