A combined modal/finite element analysis technique for the dynamic response of a non-linear beam to harmonic excitation

In this paper, a method is proposed for modelling large deflection beam res ponse involving multiple vibration modes. Significant savings in computatio nal time can be obtained compared with the direct integration non-linear fi nite element method. The deflections from a number of static non-linear fin ite element test cases are transformed into modal co-ordinates using the mo des of the underlying linear system. Regression analysis is then used to fi nd the unknown coupled non-linear modal stiffness coefficients. The inclusi on of finite element derived modal masses, and an arbitrary damping model c ompletes the governing non-linear equations of motion. The response of the beam to excitation of an arbitrary nature may then be found using time doma in numerical integration of the reduced set of equations. The work presente d here extends upon the work of previous researchers to include non-linearl y coupled multi-modal response. The particular benefits of this approach ar e that no linearization is imposed, and that almost any commercial finite e lement package may be employed without modification. The proposed method is applied to the case of a homogeneous isotropic beam. Fully simply supported and fully clamped boundary conditions are considere d. For the free vibration case, results are compared to those of previous r esearchers. For the case of steady-state harmonic excitation results are co mpared with the direct integration non-linear finite element method using A BAQUS. In all cases, excellent agreement is obtained. (C) 2001 Academic Pre ss.