Periodic Solutions to the Vibration Equation of a Beam with a Rigidly Clamped Endpoint and an Elastically Fixed Endpoint

We study the problem of finding a time-periodic solution to Euler–Bernoulli quasilinear equation describing vibrations beam subject stretching along horizontal axis. The boundary conditions correspond case rigidly clamped and elastically fixed endpoints. nonlinear term is power growth. Using variational method, we establish existence an unbounded sequence periodic solutions.