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

Publish Year: 1393
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:

JR_JACM-1-1_001

تاریخ نمایه سازی: 9 خرداد 1396

Abstract:

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

Authors

Hamid M. Sedighi

Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University Golestan Street, Ahvaz, 61357-43337, Iran

Farhang Daneshmand

Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2K6 Department of Bioresource Engineering, McGill University, 21111 Lakeshore Road, Sainte-Anne-de-Bellevue, Quebec, Canada H9X 3V9 School of