基于图胞映射法的齿轮非线性随机系统全局特性数值解研究
发布时间：2019-03-04 19:12
【摘要】：本文研究的落脚点是基于图胞映射法的齿轮非线性随机系统全局特性分析。研究的重点是图胞映射法、精细积分法以及齿轮非线性随机系统模型。 对于图胞映射法的研究主要集中在第二章和第三章。首先以改进的简单胞映射算法为例介绍了胞映射法的基本原理、基本概念以及其应用；然后系统的研究了以广义胞映射法为基础的图胞映射法,发现图胞映射法能够反应更多的非线性系统的特征信息,具有更广的用途；最后应用图胞映射法研究了单自由度非线性齿轮系统的全局特征,取得了良好的效果。 第四章主要基于精细积分法研究了含随机激励的非线性随机齿轮系统的随机响应过程。在非线性齿轮系统模型中,引入一个平稳随机激励过程,其响应也必为随机过程。应用精细积分法可得到随机响应在各离散时间点上的期望和相关矩阵的值。 非线性齿轮系统结构的随机性也普遍存在,应用精细积分法并不能解决此类随机响应问题,而图胞映射法对解决此类问题有着天然的优势,在第五章即做了这方面的尝试。运用Monte Carlo随机模拟法对随机参数进行采样,运用数值积分法得到在不同采样参数下胞之间的映射关系,然后就可运用图胞映射算法得到随机非线性齿轮系统的全局特性图。 在前面的研究中,先后建立了两类随机系统模型,一类是含随机激励的随机系统模型,一类是参数具有随机性的随机系统模型。第六章也进行了简单的实验对比研究。
[Abstract]:In this paper, the global characteristic analysis of gear nonlinear stochastic system based on graph cell mapping method is studied. The research focuses on graph cell mapping method, precise integration method and gear nonlinear stochastic system model. The research of graph cell mapping mainly focuses on the second chapter and the third chapter. Firstly, taking the improved simple cell mapping algorithm as an example, the basic principles, basic concepts and applications of the cell mapping method are introduced. Then the graph-cell mapping method based on the generalized cell mapping method is studied systematically. It is found that the graph-cell mapping method can reflect more characteristic information of the nonlinear system and has a wider application. Finally, the global characteristics of the single-degree-of-freedom nonlinear gear system are studied by using the graph cell mapping method, and good results are obtained. In chapter 4, the stochastic response process of nonlinear stochastic gear system with random excitation is studied based on the precise integration method. In the model of nonlinear gear system, a stationary random excitation process is introduced, and its response must also be stochastic process. The expectation of random response at each discrete time point and the value of correlation matrix can be obtained by using the precise integration method. The randomness of the structure of nonlinear gear system also exists, and the application of precise integration method can not solve this kind of random response problem. The graph cell mapping method has natural advantages to solve this kind of problem. In the fifth chapter, the attempt is made in this respect. The random parameters are sampled by Monte Carlo random simulation method, and the mapping relations between cells under different sampling parameters are obtained by numerical integration method. Then the global characteristic diagram of random nonlinear gear system can be obtained by using graph cell mapping algorithm. In the previous study, two kinds of stochastic system models have been established, one is stochastic system model with random excitation, the other is stochastic system model with random parameters. The sixth chapter also carries on the simple experiment contrast research.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH132.41
本文编号：2434550
[Abstract]:In this paper, the global characteristic analysis of gear nonlinear stochastic system based on graph cell mapping method is studied. The research focuses on graph cell mapping method, precise integration method and gear nonlinear stochastic system model. The research of graph cell mapping mainly focuses on the second chapter and the third chapter. Firstly, taking the improved simple cell mapping algorithm as an example, the basic principles, basic concepts and applications of the cell mapping method are introduced. Then the graph-cell mapping method based on the generalized cell mapping method is studied systematically. It is found that the graph-cell mapping method can reflect more characteristic information of the nonlinear system and has a wider application. Finally, the global characteristics of the single-degree-of-freedom nonlinear gear system are studied by using the graph cell mapping method, and good results are obtained. In chapter 4, the stochastic response process of nonlinear stochastic gear system with random excitation is studied based on the precise integration method. In the model of nonlinear gear system, a stationary random excitation process is introduced, and its response must also be stochastic process. The expectation of random response at each discrete time point and the value of correlation matrix can be obtained by using the precise integration method. The randomness of the structure of nonlinear gear system also exists, and the application of precise integration method can not solve this kind of random response problem. The graph cell mapping method has natural advantages to solve this kind of problem. In the fifth chapter, the attempt is made in this respect. The random parameters are sampled by Monte Carlo random simulation method, and the mapping relations between cells under different sampling parameters are obtained by numerical integration method. Then the global characteristic diagram of random nonlinear gear system can be obtained by using graph cell mapping algorithm. In the previous study, two kinds of stochastic system models have been established, one is stochastic system model with random excitation, the other is stochastic system model with random parameters. The sixth chapter also carries on the simple experiment contrast research.
【学位授予单位】：中南大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：TH132.41
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