Application of Variational Iteration Method with Energy Method for Nonlinear Equation Arisen from Packaging System

摘要

The variational iteration method (VIM) is widely applied for solving various kinds of nonlinear equations. Despite its simplicity and effectiveness, the accuracy of the method may depend on the iteration steps. However, the more iteration steps one makes, the more complex the results may become. To overcome this shortcoming, a new method combining the VIM with energy method (EM) is proposed and applied to study the nonlinear response of cubic packaging system. The analytical expressions of the important parameters such as the maximum displacement response, the maximum acceleration response of the system, the extended period of the shock, and the conditions for inner resonance of system were obtained. The results show that the maximum of the acceleration and the displacement and the extended period of the shock got by this method are very similar to the ones got by Runge-Kutta method. The result provides the new method for the dropping shock problem of nonlinear packaging system.