A combined modal / finite element analysis technique for non-linear beam dynamic response under harmonic excitation

Abstract

A method is proposed for modelling multi-mode large deflection beam response. Significant savings in computational time can be obtained compared with the direct integration nonlinear finite element method. The deflections from a number of static nonlinear finite element test cases are transformed into modal co-ordinates using the modes of the underlying linear system. Regression analysis is then used to find the unknown nonlinear modal stiffness coefficients. The governing nonlinear equations of motion are completed by including finite element derived modal mass, and an arbitrary damping model. The response of the beam to excitation of an arbitrary nature may then be found using time domain numerical integration. The work presented here extends upon the work of previous researchers to include non-coupled multi-modal response, and the effect of buckling due to axial loads.

The proposed method is applied to the case of a homogeneous isotropic beam, which is simply supported and axially constrained at both ends. For the case of steady state harmonic excitation, results are compared with the direct integration nonlinear finite element method.