Non-linear vibrations of a clamped beam with initial deflection and initial axial displacement, Part I: Theory

Abstract

Theoretical analyses are presented for non-linear vibrations of a clamped beam under uniformly distributed periodic lateral loading, with the effects of both initial deflection and initial axial displacement taken into consideration. The problem is first reduced to that of a finite degree of freedom system with the Galerkin procedure, the steady state solutions of which are obtained by applying the harmonic balance method. Actual calculations are carried out for the three degree of freedom system with symmetric modes and the frequency response characteristics are determined under various initial axial displacements including the post-buckled case. Effects of both initial deflection and initial axial displacement on the static deflection as well as the lower natural frequencies are also clarified.