In this paper, a comparison is made between direct and indirect perturbation approaches to solve the non-linear vibration equations of a piezoelectrically actuated cantilever microbeam. In this comparison, the equation of motion is considered according to Euler-Bernoulli theory with considering the non-linear geometric and inertia terms resulted from shortening effect. In the direct perturbatio...

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.

This paper is devoted to the study of periodic solutions for a semilinear Euler-Bernoulli beam equation with variable coefficients. Such mathematical model may be described infinitesimal, free, undamped in-plane bending vibrations thin straight elastic beam. When frequency $\omega =\frac{2\pi}{T}$ rational, some properties operator coefficients are investigated. We obtain existence when nonline...