TITLE:
Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators
AUTHORS:
Taher A. Nofal, Gamal M. Ismail, Amal Ali M. Mady, Sayed Abdel-Khalek
KEYWORDS:
Periodic Solution; Nonlinear Oscillators; Energy Balance Method; Variational Iteration Method
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.5 No.10,
October
29,
2013
ABSTRACT: In this paper, we implement a new
approach coupled with the iteration method. This procedure is obtained by combining
He’s
frequency-amplitude formulation and He’s energy balance method into a new iteration procedure such that excellent
approximate analytical solutions, valid for small as well as large values of amplitude, can be determined
for nonlinear oscillators. This study has clarified the motion equation of
nonlinear oscillators by the iteration method to obtain the relationship
between amplitude and angular frequency. We compare the approximate periods
obtained by our procedure with the numerical solution and with other methods
like energy balance
method and variational iteration method. The results show that the
approximations are of extreme accuracy.