Extension of the explicit formulation method to deal with nonlinear multi-harmonic vibrations

In this paper an extension of the method proposed by H.Elizalde and M.Imregun [1] to deal with cases with multi harmonic responses is presented. First a review of the original method ( an explicit formulation for nonlinear single harmonic responses ) is presented and then some modifications is included to extend it for multi harmonic cases. To illustrate the performance of the proposed method, two theoretical case studies is conducted, the first one is a three degree of freedom system and the other a clamped-free beam with nonlinear effects at the clamped end. The ability of the proposed method to predict the nonlinear multi harmonic response of these two structures is investigated and good results are obtained.

Keywords:

nonlinear vibrations , describing function , explicit formulation , multi-harmonic