Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Abstract

Vibrations of a beam can be described as an Euler-Bernoulli beam, or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.