Nonlinear Eigensolver for Exact Vibration Analysis

by H. A. Smith, Stanford Univ, Stanford, United States,
D. C. Sorensen, Stanford Univ, Stanford, United States,
R. K. Singh, Stanford Univ, Stanford, United States,



Document Type: Proceeding Paper

Part of: Engineering Mechanics

Abstract:

Vibration analysis of structural systems is concerned with accurately predicting the free vibration modes and frequencies of the vibrating system. This analysis process involves two general parts: the dynamic finite element model of the physical system and the numerical algorithm for determining the modal shape and frequency from the model. In many instances, the most appropriate finite element model consists of frequency dependent matrices which require nonlinear eigensolution techniques. This study formulates a nonlinear eigenproblem and numerical solver for determining the natural modes and frequencies of exact finite element models. The eigensolution technique proposed in the paper is a modified form of the Arnoldi method which overcomes numerical difficulties associated with the traditional Arnoldi's method such as loss of orthogonality in the basis vectors, appearance of spurious eigenvalues and the potential untoward growth in storage.

Subject Headings: Finite element method | Vibration | Numerical methods | Dynamic models | Structural systems | Numerical models | Numerical analysis

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