Affiliations: Department of Mechanical Engineering, Faculty of
Engineering, Semnan University, Semnan, Iran | Department of Mechanical Engineering, Babol University
of Technology, Babol, Iran | Department of Civil Engineering, Aalborg University,
Sohngårdsholmsvej 57, 9000 Aalborg, Aalborg, Denmark | Department of Mechanical Engineering, Islamic Azad
University, Semnan Branch, Semnan, Iran
Abstract: In this paper we study the periodic solutions of free vibration of
mechanical systems with third and fifth-order nonlinearity for two examples
using He's Frequency-Amplitude Formulation (HFAF).The effectiveness and
convenience of the method is illustrated in these examples. It will be shown
that the solutions obtained with current method have a fabulous conformity with
those achieved from time marching solution. HFAF is easy with powerful concepts
and the high accuracy, so it can be found widely applicable in vibrations,
especially strong nonlinearity oscillatory problems.
Keywords: Nonlinear vibration, He's frequency-amplitude formulation, periodic solution, approximate frequency
