求解一类含阻尼的强非线性系统的改进多尺度方法

MODIFIED MULTIPLE SCALES METHOD FOR SOLVING A STRONGLY NONLINEAR SYSTEM WITH DAMPING

将改进LP方法参数变换思想直接应用到多尺度方法中,提出一种改进的多尺度方法,对含有阻尼的Duf-fing系统自由振动摄动解进行研究,得出了该类问题摄动解的显示表达式,这是使用MLP方法无法得到的。和数值计算比较的算例表明,所得方法计算结果与数值计算结果非常接近。

Using the approach of parameter transform in the improved Lindstedt-Poincare method,a modified multiple scales method is proposed.Using this method,a strongly nonlinear Duffing system with damping is studied.Its perturbation solution which can not be obtained using the improved Lindstedt-Poincare method is obtained with the new method.An example results using the new method are coincident with those using the numerical method.