Ren-He’s method for solving dropping shock response of nonlinear packaging systemReport as inadecuate




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Advances in Difference Equations

, 2016:279

First Online: 28 October 2016Received: 13 August 2016Accepted: 19 October 2016

Abstract

In this paper, Ren-He’s method for nonlinear oscillators is adopted to give approximate solutions for the dropping shock response of cubic and cubic-quintic nonlinear equations arising from packaging system. In order to improve the accuracy of the solutions, a novel technique combining Ren-He’s method with the energy method is proposed, the maximum values of the displacement response and acceleration response of the system are obtained by the energy method, and the approximate solution is corrected. An analytical expression of the important parameters including the maximum displacement, the maximum acceleration of dropping shock response and the dropping shock duration is obtained. The illustrative examples show that the dropping shock response obtained by this method is very similar to the one by the fourth order Runge-Kutta method. The result provides a new simple and effective method for the dropping shock response of a nonlinear packaging system.

KeywordsRen-He’s method energy method displacement maximum value acceleration maximum value dropping shock duration  Download fulltext PDF



Author: An-Jun Chen

Source: https://link.springer.com/







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