FORMULATION AND SOLUTION OF THE NONLINEAR, DAMPED EIGENVALUE PROBLEM FOR SKELETAL SYSTEMS

This paper presents and discusses an Arnoldi-based eigensolution techn ique for evaluating the complex natural frequencies and mode shapes fr om frequency dependent quadratic eigenproblems associated with vibrati on analysis of damped structures. The new solution technique is used i n conjunction with a mixed finite element modelling procedure which ut ilizes both the polynomial and frequency dependent displacement fields in formulating the system matrices. This modelling provides the abili ty to represent a frequency dependent damping matrix in vibration anal ysis of skeletal systems. The eigensolution methodology presented here is based upon the ability to evaluate a specific set of parametrized curves for the non-linear eigenvalue problem at given values of the pa rameter. Numerical examples illustrate that this method, used in conju nction with a secant interpolation, accurately evaluates the complex n atural frequencies and modes of the quadratic non-linear eigenproblem and verifies that the new eigensolution technique coupled with the mix ed finite element modelling procedure is more accurate than the conven tional finite element models.