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電磁場中載流薄板的分岔和混沌電子書
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資料類別
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公共管理畢業(yè)論文（設(shè)計(jì)） |
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課程(專業(yè))
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運(yùn)籌學(xué)與控制論 |
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關(guān)鍵詞
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Menikov 函數(shù)|平均法 |
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適用年級
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大學(xué) |
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身份要求
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普通會員 |
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金 幣
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40 �。�金幣如何獲得？） |
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文件格式
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pdf |
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文件大小
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6240K |
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發(fā)布時間
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2009-05-19 21:26:00 |
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預(yù)覽文件
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無 |
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下載次數(shù)
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0 |
| 發(fā)布人 |
lcw |
內(nèi)容簡介：
電磁場中載流薄板的分岔和混沌電子書
摘 要
分岔和混沌是非線性系統(tǒng)最重要而又最基本的特性，幾乎在所有涉及非線性科學(xué)的領(lǐng)域中，都存在著分岔現(xiàn)象和混沌運(yùn)動。隨著現(xiàn)代高新科技的發(fā)展，板、殼等結(jié)構(gòu)元件處于電磁場環(huán)境中的情況已是屢見不鮮，這種電磁場與力學(xué)場相互耦合的一個基本特征就是非線性特性。論文在分析和總結(jié)非線性微分動力系統(tǒng)分岔和混沌研究現(xiàn)狀的基礎(chǔ)上，對電磁場中橫向磁場和機(jī)械載荷共同作用下載流矩形薄板的非線性行為進(jìn)行了研究。主要內(nèi)容如下：首先，簡要介紹了混沌運(yùn)動的國內(nèi)外研究現(xiàn)狀，論文研究的主要內(nèi)容以及判定通向混沌運(yùn)動的Melnikov 方法，并給出了幾種常用的Melnikov函數(shù)。其次，針對橫向電磁場中三邊簡支一邊自由和一對邊簡支一對邊固定載流矩形薄板，建立了單模態(tài)下薄板的非線性運(yùn)動方程。利用Melnikov函數(shù)法對其單模態(tài)位移模式下的混沌運(yùn)動進(jìn)行了分析。得到了非線性動力系統(tǒng)在無擾動情況下的平衡點(diǎn)及在有擾動的情況下，發(fā)生Smale 馬蹄意義下的混沌的臨界條件。并利用Matlab 程序模擬了滿足此臨界條件的非線性系統(tǒng)的混沌運(yùn)動。最后，對橫向電磁場中三邊簡支一邊自由和一對邊簡支一對邊固定載流矩形薄板，建立了雙模態(tài)下薄板的非線性運(yùn)動方程。利用平均法求得板在雙模態(tài)下的分岔點(diǎn)，并討論了分岔點(diǎn)的穩(wěn)定性情況。進(jìn)一步從理論上討論了利用單、雙模態(tài)位移模式模擬非線性行為的差異。
關(guān)鍵詞 薄板；Menikov 函數(shù)；平均法；電磁場；分岔；混沌；臨界載荷；電流密度
目 錄
摘要···············································································································I
Abstract ·········································································································· II
第 1 章 緒論···································································································· 1
1.1 課題的提出及意義··············································································· 1
1.2 混沌運(yùn)動的研究現(xiàn)狀及前景······························································· 2
1.2.1 混沌研究簡介················································································· 2
1.2.2 薄板混沌運(yùn)動簡介········································································· 4
1.3 論文的結(jié)構(gòu)安排··················································································· 6
第2 章 混沌研究的基本方法········································································· 7
2.1 Melnikov 方法簡介·············································································· 7
2.2 Melnikov 函數(shù)及混沌判斷依據(jù)的推導(dǎo)··············································· 7
2.3 常用的Melnikov 函數(shù)······································································· 12
2.4 本章小結(jié)···························································································· 14
第3 章 載流矩形薄板的混沌分析······························································· 15
3.1 基本方程···························································································· 15
3.2 三邊簡支一邊自由載流矩形薄板的混沌運(yùn)動·································· 18
3.2.1 動力方程······················································································ 18
3.2.2 混沌運(yùn)動分析··············································································· 19
3.2.3 算例分析······················································································ 24
3.3 一對邊簡支一對邊固定載流矩形薄板的混沌運(yùn)動·························· 26
3.3.1 動力方程······················································································· 26
3.3.2 混沌運(yùn)動分析················································································ 27
3.4 本章小結(jié)···························································································· 40
第4 章 載流矩形薄板的雙模態(tài)分岔分析··················································· 41
4.1 三邊簡支一邊自由載流矩形薄板的雙模態(tài)分析······························ 41
4.1.1 基本方程······················································································ 41
4.1.2 雙模態(tài)分岔分析··········································································· 42
4.2 一對邊簡支一對邊固定載流矩形薄板的雙模態(tài)分析······················ 48
4.2.1 基本方程······················································································ 48
4.2.2 雙模態(tài)分岔分析··········································································· 50
4.3 本章小結(jié)···························································································· 55
結(jié)論············································································································ 56
燕山大學(xué)理學(xué)碩士學(xué)位論文
VI
參考文獻(xiàn)········································································································ 58
攻讀碩士學(xué)位期間承擔(dān)的科研任務(wù)與主要成果·········································· 62
致謝············································································································ 63
作者簡介········································································································ 64
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