Nonlinear transversely vibrating beams by the homotopyperturbation method with an auxiliary term

This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibratingbeams with odd and even nonlinearities using Homotopy Perturbation Method with an auxiliary term(HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumpedmass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the proposedasymptotic approach. It is demonstrated that two terms in series expansions are sufficient to obtain a highlyaccurate periodic solutions. The integrity of the analytical solutions is verified by numerical results.

Keywords:

Homotopy Perturbation Method with an Auxiliary Term , Non-linear vibrating beams , Frequencyamplitude relationship