建立在同伦基础之上的一种非线性分析方法(2)——单自由度守恒系统周期的通用公式

A KIND OF NONLINEAR ANALYTICAL METHOD BASED ON HOMOTOPY (Part 2) - General Formulations of the Period of Conservative Single-Degree-Freedom System

本文以非线性的单自由度守恒系统为例,描述了一种新的非线性分析方法。此方法建立在光滑映射的基础上,不依赖于小参数,从而特别适合于求解不具有小参数的强非线性问题。本文所给近似公式的精确度对参数值的变化不敏感,对任意大小的参数都是一致有效的。

In this paper, a kind of new nonlinear analytical method is described by using nonlinear conservative system with single-degree-freedom as a simple example. The proposed method is based on smooth mapping and homotopy in topology and is independent upon small or large parameters at all, so that it can be applied to solve strongly nonlinear problems not containing any small or large parameters. The two formulations given in this paper are insensitive to the values of the parameters and is uniformly valid for any values of the parameters.