窄带外激作用下多自由度非线性动力系统响应的研究

【作者】 尤国伟；

【导师】 徐伟；

【作者基本信息】 西北工业大学 ， 应用数学， 2002， 硕士

【摘要】 本文用解析和数值方法研究了窄带随机噪声外激下非线性系统的响应问题。论文的主要内容如下： 第一章阐明了窄带随机噪声激励下非线性系统响应问题的研究现状，简述了论文的主要内容和结构安排。 第二章和第三章研究了系统（1．1）在窄带随机外部激励下的共振响应问题。主要讨论了w₂≈3w₁，Ω≈3w₁时的情况。对该系统的研究分为两个部分：首先在第二章集中讨论了相应的确定性系统，即v=0时的情况。用多尺度法分离了系统的快变项，并详细推导出以系统振幅为未知数的代数方程组；对得到的代数方程组，由于其复杂性，不能直接进行讨论，而只能借助计算机编程实现对方程的求解；对系统响应的稳定性，也进行了讨论。在第二章基础上，第三章将多尺度法引入到相应的随机系统的研究中；严格推导了系统的约简方程，用矩方法求出稳态解应满足的方程，获得一些结果；并且数值模拟结果与理论推导的结果是一致的；并注意到，与其对应的确定性系统相比较，系统响应从周期解变为近似周期解，系统的相轨线从极限环变为扩大的近似极限环；随着激励带宽的增大，此扩大的近似极限环的宽度将增大。 第四章，给出了全文的总结，并对需要进一步进行的工作做了介绍。更多还原

【Abstract】 In this dissertation, the response in two-degree-of-freedom nonlinear system under random external excitation is investigated by using analytical and numerical method. Some conclusions are obtained. The main contents of the dissertation are as follows:Chapter one summarizes the situation and application of response in nonlinear dynamical system under narrow-band random excitation and presents the main contents and arrangement of the dissertation.In chapter two and chapter three, the response of two-degree-of freedom nonlinear system (1.1) is studied.In chapter two, the case when v = 0 is discussed. The method of multiple scales is used to determine the equations of modulation of amplitude and phase .The steady state response can be obtained by solving a couple of algebraic equations, which have been achieved by careful deduction under some conditions. And because of the complexity of the equations, programs are necessary to solve the equations mentioned above, and certain graphs are presented. Based on chapter two, In chapter three, the method of multiple scales is introduced to the study of the multiple-dimensional nonlinear stochastic systems under random external excitation. Using method of multiple scales, we strictly deduce the equation of modulation of amplitude and phase. The effects of random excitations are analyzed; numerical simulations verify the results. Theoretical and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle.In chapter four we concludes the work and points out some aspects to be further studied.更多还原