Forced vibration of a beam system with autoparametric coupling effects

Abstract

Small non-linear interactions of the type referred to as autoparametric may have a considerable effect on the pattern of forced vibration response of certain categories of structures exhibiting low damping characteristics. Under conditions of internal resonance these may bring about a complete neutralisation of the normal forced vibration resonance curve with a transfer of energy to an indirectly excited mode. The paper examines non-linear interactions between a pair of beam modes in forced vibration of a simple structure. Steady state solutions are obtained for the non-linear system equations. Measurements of vibratory acceleration and strain on a laboratory model are shown to give good confirmation of the analytical results and show clearly the substantial effects of internal resonance.