Rub-induced non-linear vibrations of a rotating large deflection plate

Abstract

This paper uses a semi-analytical approach to investigate the frequency response, bifurcation, and chaos of a rotating large deflection plate subjected to rub-induced non-linear vibrations. The general equations are coupled with the lateral displacement and two in-plane stretch variables and were derived using Hamilton's principle with consideration given to the centrifugal stiffening effect. The accuracy of the solution method is demonstrated through a comparison of modal characteristics found in the literature. Special attention is given to the influence of friction coefficients, the rubbing force amplitude and the contact load time on rub-induced non-linear vibrations. The results show that the frictional effect in tip-rub is the main source of rub-induced non-linear vibrations for the rotating large deflection plate. Increases in the rubbing force amplitude and the contact load time produce more non-linear effects such as more paths to chaos and a jump phenomenon, and intensify the vibration of the system.