Li–He’s modified homotopy perturbation method coupled with the energy method for the dropping shock response of a tangent nonlinear packaging system

This paper couples Li–He’s homotopy perturbation method with the energy method to obtain an approximate solution of a tangent nonlinear packaging system. A higher order homotopy equation is constructed by adopting the basic idea of the Li–He’s homotopy perturbation method. The energy method is used...

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Bibliographic Details
Published inJournal of low frequency noise, vibration, and active control Vol. 40; no. 2; pp. 675 - 682
Main Authors Ji, Qiu-Ping, Wang, Jun, Lu, Li-Xin, Ge, Chang-Feng
Format Journal Article
LanguageEnglish
Published London, England SAGE Publications 01.06.2021
Sage Publications Ltd
SAGE Publishing
Subjects
Approximation
Energy methods
Packaging
Perturbation methods
Runge-Kutta method
energy method
approximate solution
Li–He’s homotopy perturbation method
Tangent nonlinear differential equation
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Summary:This paper couples Li–He’s homotopy perturbation method with the energy method to obtain an approximate solution of a tangent nonlinear packaging system. A higher order homotopy equation is constructed by adopting the basic idea of the Li–He’s homotopy perturbation method. The energy method is used to improve the maximal displacement and the frequency of the system to an ever higher accuracy. Comparison with the numerical solution obtained by the Runge–Kutta method shows that the shock responses of the system solved by the new method are more effective with a relative error of 0.15%.
ISSN:1461-3484
2048-4046
DOI:10.1177/1461348420914457