论文部分内容阅读
There exist many analytical and numerical methods for solving nonlinear dynamical systems.The common approaches include harmonic balance,perturbation and numerical methods such as the Runge-Kutta method.These methods do show their excellence in solving some nonlinear systems but they also inherit certain analytical and/or numerical shortcomings.The classical harmonic balance method normally transforms a nonlinear governing equation into a set of nonlinear equations and hence an explicit analytical solution is in most cases impossible.The perturbation method,on the other hand,requires the presence of small parameters and hence its applicability for strongly nonlinear systems is rather limited.The Runge-Kutta method has no such limitations as discussed above but it only provides numerical solutions without an explicit analytical expression for the systems.Over the last decade,a new approach which is an improved version of the classical harmonic balance method has been developed by the authors for solving strongly nonlinear conservative oscillators and other dynamical systems.The new approach is based on the combination of Newtons method and the harmonic balance,and it has comparatively faster convergence rate.This new approach overcomes the limitations above and explicit,accurate,approximate analytical solutions for many strongly nonlinear dynamical systems have been derived.A number of such cases will be presented.The advantages of this new approach and the approximate solutions will be illustrated.