Analysis of A Forced Strongly Non-Linear Two-Degree-of-Freedom System By Means of The Power Series Method

M. Abu-Hilal's picture
Journal Title, Volume, Page: 
Journal of Sound And Vibration Volume 241, Issue 4, 5 April 2001, Pages 635-642
Year of Publication: 
M. I. Qaisi
Mechanical Engineering Department, Jordan University, Amman, Jordan
M. Abu-Hilal
Department of Mechanical and Industrial Engineering, Applied Sciences University, Amman, 11931, Jordan
Current Affiliation: 
Department of Mechanical Engineering, Faculty of Engineering, An-Najah National University, P.O. Box 7, Nablus, West Bank, Palestine
Preferred Abstract (Original): 

A power-series solution is presented for the periodic motion of an undamped strongly non-linear two-degree-of-freedom system excited by harmonic forces. The analysis is facilitated by transforming the time variable into an harmonically oscillating time. The frequency of the new time variable is determined by observing the equality between the rate of change of dynamical energy and the power delivered by the forces. The results show good agreement with the modified Lindstedt–Poincaré method and the incremental harmonic balance method.

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