【摘要】 非线性振动理论的传统课题是用近似的分析方法(例如摄动法)或相平面法求解单自由度系统,但其精度和适用范围已渐渐不能满足理论和应用上的需要。近年来,由于计算机的广泛应用和计算方法的改进,对非线性振动的研究在方法上和课题上都有所发展,得到了许多新的结果。在数值方法方面,引人注目的是直接数值积分法的应用,其中把求非线性振动系统的周期解看作常微分方程的边值问题而用打靶方法处理,收敛性和通用很好。性都但在一定条件下,满足确定性方程的稳态解却呈现随机性态。用点变换方法可以研究这种所谓混沌特性。混沌特性在静力学上表现为多重平衡位置,而可用灾变理论进行分类和讨论。更多还原

【Abstract】 The traditional subject in non-linear vibration theory is to solve a one-degree-of- freedom system by means of approximate analytic methods(e.g., the perturbationmethods) or phase-plane method. flat their accuracy and applicability can not fulfil the requirements in theoretical researches and practical applications gradually. Recently, due to the wide application of computers and improvements of the numerical methods the research on non-linear vibrations has been developing both in methods and in subjects, and a lot of new results have appeared. In the field of numerical methode the application of the direct integration method is quite remarkable. The problem of finding periodic solutions of the non-linear vibration systems is regarded as a two-point boundary-value problem and is treated with shooting methods. The convergence and applicability are both quite good. But under certain conditions the steady solutions of the deterministic equations presenta random behaviour. with the help. of the point mapping method the so-called chaotic behaviour can be studied. The chaotic behaviour can be represented as the multi- equilibrium positions saiiically and can be classified and discussed using the catas- trophe theory.更多还原