On numerical properties of finite element procedures for eigenvalue analysis of elastic vibration in solid structures

Abstract

This study discusses the numerical properties of finite element procedures for eigenvalue analysis of free vibration in elastic solid structures. Exact solutions for a three-dimensional rectangular domain with the slip boundary condition, in which stationary P and S wave modes can be obtained separately, were adopted for comparison with numerical solutions. The distributions and numerical errors of the eigenvalues obtained by different finite element schemes were characterized in detail. Numerical performance was evaluated by utilizing particular stationary P and S wave modes in the cylindrical domain.