%0 Journal Article
%T Analytical and Approximate Solutions to the Fee Vibration of Strongly Nonlinear Oscillators
%A Taher A. Nofal
%A Gamal M. Ismail
%A Amal Ali M. Mady
%A Sayed Abdel-Khalek
%J Journal of Electromagnetic Analysis and Applications
%P 388-392
%@ 1942-0749
%D 2013
%I Scientific Research Publishing
%R 10.4236/jemaa.2013.510061
%X <p class=\"MsoNormal\">
	<span lang=\"EN-US\" style=\"font-family:Verdana;\">In this paper, we implement a new
approach coupled with the iteration method. This procedure is obtained by combining
He</span><span lang=\"EN-US\" style=\"font-family:Verdana;\">กฏ</span><span lang=\"EN-US\" style=\"font-family:Verdana;\">s
frequency-amplitude formulation and He</span><span lang=\"EN-US\" style=\"font-family:Verdana;\">กฏ</span><span lang=\"EN-US\" style=\"font-family:Verdana;\">s energy balance method into a new iteration procedure such that excellent
approximate analytical solutions,</span><span lang=\"EN-US\"> </span><span lang=\"EN-US\" style=\"font-family:Verdana;\">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.</span><span lang=\"EN-US\"> </span><span lang=\"EN-US\" style=\"font-family:Verdana;\">We compare the approximate periods
obtained by our procedure with the numerical solution and with other methods
like</span><span lang=\"EN-US\"> </span><span lang=\"EN-US\" style=\"font-family:Verdana;\">energy balance
method and variational iteration method. The results show that the
approximations are of extreme accuracy.</span> 
</p>
%K Periodic Solution
%K Nonlinear Oscillators
%K Energy Balance Method
%K Variational Iteration Method
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=38728