A new analytical technique to find periodic solutions of non-linear systems

Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for [ x ( 0 ) = a 0 , x ˙ ( 0...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2007-10, Vol.42 (8), p.1035-1045
Main Authors: Alam, M. Shamsul, Emdadul Haque, Md, Bellal Hossain, Md
Format: Article
Language:English
Subjects:
Asymptotic solution
Harmonic balance
Periodic solution
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Summary:Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for [ x ( 0 ) = a 0 , x ˙ ( 0 ) = b 0 ] ) while the existing solution is determined for a particular case, especially for [ x ( 0 ) = a 0 , x ˙ ( 0 ) = 0 ] . The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2007.05.007