【摘要】：本文研究的落腳點(diǎn)是基于圖胞映射法的齒輪非線性隨機(jī)系統(tǒng)全局特性分析。研究的重點(diǎn)是圖胞映射法、精細(xì)積分法以及齒輪非線性隨機(jī)系統(tǒng)模型。 對于圖胞映射法的研究主要集中在第二章和第三章。首先以改進(jìn)的簡單胞映射算法為例介紹了胞映射法的基本原理、基本概念以及其應(yīng)用；然后系統(tǒng)的研究了以廣義胞映射法為基礎(chǔ)的圖胞映射法,發(fā)現(xiàn)圖胞映射法能夠反應(yīng)更多的非線性系統(tǒng)的特征信息,具有更廣的用途；最后應(yīng)用圖胞映射法研究了單自由度非線性齒輪系統(tǒng)的全局特征,取得了良好的效果。 第四章主要基于精細(xì)積分法研究了含隨機(jī)激勵(lì)的非線性隨機(jī)齒輪系統(tǒng)的隨機(jī)響應(yīng)過程。在非線性齒輪系統(tǒng)模型中,引入一個(gè)平穩(wěn)隨機(jī)激勵(lì)過程,其響應(yīng)也必為隨機(jī)過程。應(yīng)用精細(xì)積分法可得到隨機(jī)響應(yīng)在各離散時(shí)間點(diǎn)上的期望和相關(guān)矩陣的值。 非線性齒輪系統(tǒng)結(jié)構(gòu)的隨機(jī)性也普遍存在,應(yīng)用精細(xì)積分法并不能解決此類隨機(jī)響應(yīng)問題,而圖胞映射法對解決此類問題有著天然的優(yōu)勢,在第五章即做了這方面的嘗試。運(yùn)用Monte Carlo隨機(jī)模擬法對隨機(jī)參數(shù)進(jìn)行采樣,運(yùn)用數(shù)值積分法得到在不同采樣參數(shù)下胞之間的映射關(guān)系,然后就可運(yùn)用圖胞映射算法得到隨機(jī)非線性齒輪系統(tǒng)的全局特性圖。 在前面的研究中,先后建立了兩類隨機(jī)系統(tǒng)模型,一類是含隨機(jī)激勵(lì)的隨機(jī)系統(tǒng)模型,一類是參數(shù)具有隨機(jī)性的隨機(jī)系統(tǒng)模型。第六章也進(jìn)行了簡單的實(shí)驗(yàn)對比研究。
[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.
【學(xué)位授予單位】：中南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2011
【分類號】：TH132.41

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 申永軍,楊紹普,潘存治,邢海軍;參外聯(lián)合激勵(lì)下直齒輪副的非線性動力學(xué)[J];北京交通大學(xué)學(xué)報(bào);2005年01期

2 趙巖,林家浩,曹建華;轉(zhuǎn)軸系統(tǒng)平穩(wěn)隨機(jī)地震響應(yīng)的變異性分析[J];工程力學(xué);2002年02期

3 唐進(jìn)元;陳思雨;鐘掘;;一種改進(jìn)的齒輪非線性動力學(xué)模型[J];工程力學(xué);2008年01期

4 張旭方;張義民;韓麗;黃素珍;;隨機(jī)外激勵(lì)作用下非線性系統(tǒng)響應(yīng)演變概率密度[J];固體力學(xué)學(xué)報(bào);2009年02期

5 陳炎,黃小清,羅文結(jié);非自治非線性杜芬系統(tǒng)的隨機(jī)振動[J];華南理工大學(xué)學(xué)報(bào)(自然科學(xué)版);2000年01期

6 林家浩,易平;線性隨機(jī)結(jié)構(gòu)的平穩(wěn)隨機(jī)響應(yīng)[J];計(jì)算力學(xué)學(xué)報(bào);2001年04期

7 趙巖,林家浩,曹建華;轉(zhuǎn)子系統(tǒng)的平穩(wěn)/非平穩(wěn)隨機(jī)地震響應(yīng)分析[J];計(jì)算力學(xué)學(xué)報(bào);2002年01期

8 林家浩,張亞輝,孫東科,孫勇;受非均勻調(diào)制演變隨機(jī)激勵(lì)結(jié)構(gòu)響應(yīng)快速精確計(jì)算[J];計(jì)算力學(xué)學(xué)報(bào);1997年01期

9 張鎖懷,李憶平,丘大謀;用諧波平衡法分析齒輪耦合的轉(zhuǎn)子—軸承系統(tǒng)的動力特性[J];機(jī)械工程學(xué)報(bào);2000年07期

10 孫月海,張策,潘鳳章,陳樹勛,黃永強(qiáng);直齒圓柱齒輪傳動系統(tǒng)振動的動力學(xué)模型[J];機(jī)械工程學(xué)報(bào);2000年08期

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