Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay (Communications in Mathematical Research, 2020)
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 establishthe existence of periodic solutions in time for a damped Rayleigh beam modelwith time delay, which is treated as a bifurcation parameter. The main proofis based on a Lyapunov-Schmidt reduction together with the classical implicitfunction theorem. Moreover, we give a sufficient condition for a direction ofbifurcation.
Keywords: Beam equations; damping; time delay; periodic solutions.