A comparative study of the consistent and simplified finite element analyses of Eigenvalue, problems

Abstract

Classical displacement method of the finite element analysis of eigenvalue problems requires the use of consistent and conforming elements. However, simpler approaches based on relaxing the condition of consistency of the element descriptions, such as lumped inertia force method and others are also found to yield satisfactory results. In this paper we make a comparative study of the consistent and simplified approaches with reference to four representative problems. In the simplified approach studied in this paper, the contribution of straining modes in the derivation of the mass and geometric stiffness matrices is neglected and this simplifies their derivation substantially. The results indicate that this simplification introduces only small errors in the eigenvalues.