解非线性振动问题的摄动谐波平衡法

本文在谐波平衡法的基础上,引进摄动的思想,得出了用解析法解非线性振动问题的一个新的有效方法——摄动谐波平衡法。该方法无需对解的形式及谐波系数的量级预先有所了解,这是谐波平衡法所不能比拟的。另外,该方法使非线性振动问题的求解过程变得简单,只涉及解线性代数方程的运算,不必求解微分方程,这又比Lindstedt-Poincare方法、多尺度方法优越。

The Method of Perturbation-Harmonic Balance for Solving Nonlinear Oscillations

In this paper, perturbation technique is introduced into the method ofHarmonic Balance. A new and effective method called Perturbation-HarmonicBalance is obtained. A great deal solutions and the order of harmoniccoefficients do not need to be known previously, using the method imcom-parable to the method of Harmonic Balance. On the other hand, the procedureof solving nonlinear oscillations becomes very simple. Using the method it isnot related to solution of differential equation, and then it is superior toLindstedt-Poincar(?) and multiple scales.