Mode Finding in Nonlinear Structural Eigenvalue Calculations

Abstract

The eigenvalue problems resulting from stiffness matrix formulations of structural vibration and buckling problems are nonlinear if substructures are analyzed exactly, or if classical frequency (vibration problems) or load factor (buckling problems) dependent member equations are used. This makes rapid calculation of accurate free vibration or buckling modes difficult. This paper presents several techniques which might overcome this difficulty, examines them theoretically and experimentally, and gives some of the ways in which the more successful techniques can be incorporated in mode finding methods. Coincident eigenvalues (i.e., natural frequencies or critical load factors) are included.