Non-linear vibration of a travelling beam

Abstract

Free and forced responses of a travelling slender beam including the non-linear terms are studied. A simple method of calculating the non-linear, non-stationary, complex normal mode is presented. The hardening characteristic and intercoupling of linear modes during the non-linear modal vibration are clearly brought out. The response of the beam, excited by a point harmonic load, is calculated using the non-linear normal modes. A stability analysis is provided to delineate the stable and unstable roots of the response.