First, the 1st-order approximate solution of Duffing Equation got by L-P perturbation method is tried to apply for analyzing dropping shock problem in this paper, but the result is not satisfactory. So, based on the 1st-order approximate solution, a novel solution that combines L-P perturbation method with energy method is proposed, and the authors employed a amplitude correction coefficient of which is determined by two peak values to adjust the proportion of basic frequency and high frequency for a given event. The results show that the acceleration-time curve got by this method is very similar to the one got by elliptic integration method, and the accuracy of peak value, waveform and extended period of shock got by this method is satisfactory. In the recent years, there has been much interest in the packaging dynamics, especially in drop shock problem, because the rapid development of packaging industry and serious damage problems of package. The energy method is often used to solve the drop shock problem in packaging dynamics, but it can only obtain the maximum acceleration, neither the waveform nor the extended period of shock can be analyzed. A different method is usually employed for solving the nonlinear drop shock problem is known as the numerical integral method (include elliptic integration method), but it is not only complicated but also can not express the physical meaning in terms of simple functions. Another type of approach to the question is known as the L-P perturbation method, but its 1st-order approximate solution is not suitable to use due to its large error, and the high-order solution is too complicated to apply. So, a novel solution which combine L-P perturbation method and energy method is proposed, the calculated results show that the solution has clear physical meaning and relatively high speed of computation, and the method offered is useful to solve the nonlinear drop shock problem of packaging.
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