Periodic Vibrations of a Beam with Rigidly Sealed Ends

Abstract

We study the problem of searching periodic solutions to the Euler–Bernoulli equation governing vibrations of a beam with the boundary conditions corresponding to the case of rigidly sealed beam ends. The nonlinear term satisfies the nonresonance condition at infinity. We establish the existence and uniqueness of a solution. To prove the results, we use topological methods (the Leray–Schauder principle) as well as variational methods (the mountain pass theorem).