本文選題：結(jié)構(gòu)阻尼　切入點：熱彈耦合梁　出處：《太原理工大學》2017年博士論文

【摘要】：本文利用Galerkin方法、Sobolev空間理論、整體吸引子和一致吸引子等理論,研究了四類復雜彈性梁方程(組)系統(tǒng)的初邊值問題以及這些系統(tǒng)的長時間整體動力行為最本質(zhì)的概念吸引子的存在性。首先,利用Galerkin方法結(jié)合一些先驗估計和不等式技巧和Sobolev空間理論等給出了四類不同系統(tǒng)的整體解的存在性唯一性,從而定義了三類不同的自治無窮維動力系統(tǒng)的半群和一類非自治無窮維動力系統(tǒng)的雙參數(shù)過程族;其次,通過先驗估計結(jié)合一些不等式技巧等,給出了復雜彈性梁結(jié)構(gòu)所確定的三類不同的自治無窮維動力系統(tǒng)的有界吸收集的存在性和一類非自治無窮維動力系統(tǒng)的一致有界吸收集的存在性;最后,通過證明了三類自治無窮維動力系統(tǒng)所對應(yīng)的解半群是漸近光滑的和一類非自治無窮維動力系統(tǒng)過程族是一致漸近緊的,從而根據(jù)整體吸引子和一致吸引子的存在性定理,證明了工程上應(yīng)用廣泛的復雜彈性梁結(jié)構(gòu)所確定的具結(jié)構(gòu)阻尼的兩類熱彈耦合梁方程組系統(tǒng)的整體吸引子和非線性邊界條件下一類自治單個彈性梁方程系統(tǒng)的整體吸引子和一類具有局部阻尼的非自治單個彈性梁方程系統(tǒng)的一致吸引子的存在性。具體內(nèi)容如下:1.第一章介紹了吸引子研究的必要性和研究的現(xiàn)狀,以及彈性梁結(jié)構(gòu)所確定的無窮維動力系統(tǒng)的研究現(xiàn)狀。2.第二章介紹了本文中用到的一些基本定義、一些常用的基本不等式以及一些基本引理。3.第三章給出了具有結(jié)構(gòu)阻尼的n維熱彈耦合梁方程組在齊次邊界條件及初始條件下系統(tǒng)的初邊值問題和整體吸引子的存在性;4.第四章對于具有熱記憶項的熱彈耦合梁方程組在齊次邊界條件及一定的初始條件下的系統(tǒng),通過引入一個新的加權(quán)空間,把非自治系統(tǒng)自治化,給出了系統(tǒng)的整體解和整體吸引子的存在性;5.第五章給出了非線性邊界條件下單個彈性梁方程在一定的初始條件下系統(tǒng)的的整體解和整體吸引子的存在性;6.第六章給出了非線性邊界條件下具局部阻尼的非自治單個彈性梁方程在一定的初始條件下系統(tǒng)的一致有界吸收集和一致吸引子的存在性。
[Abstract]:In this paper, the theory of Sobolev space, the global attractor and the uniform attractor are discussed by using the Galerkin method. In this paper, we study the existence of the most essential concept attractors for four classes of complex elastic beam equations (systems) and the most essential concept attractors for the long time global dynamic behavior of these systems. The existence and uniqueness of global solutions for four different systems are obtained by using the Galerkin method and some prior estimators and inequality techniques as well as Sobolev space theory. The semigroup of three kinds of autonomous infinite dimensional dynamical systems and the two-parameter process family of a class of nonautonomous infinite dimensional dynamical systems are defined. The existence of bounded absorption sets for three classes of autonomous infinite dimensional dynamical systems determined by complex elastic beam structures and the existence of uniformly bounded absorption sets for a class of nonautonomous infinite dimensional dynamical systems are given. By proving that the solution Semigroups corresponding to three kinds of autonomous infinite dimensional dynamical systems are asymptotically smooth and that the process families of a class of nonautonomous infinite dimensional dynamical systems are uniformly asymptotically compact, the existence theorems of global attractors and uniform attractors are obtained. It is proved that the global attractor of two classes of thermoelastic coupled beam equations with structural damping and the integral of a class of autonomous single elastic beam equations under nonlinear boundary conditions determined by the widely used complex elastic beam structures in engineering are proved. The existence of uniform attractors for a class of nonautonomous single elastic beam equation systems with local damping. As well as the research status of infinite dimensional dynamic system determined by elastic beam structure. The second chapter introduces some basic definitions used in this paper. Some general inequalities and some basic Lemma .3. in chapter 3, the initial-boundary value problem and global attractor of n-dimensional thermoelastic coupled beam equations with structural damping under homogeneous boundary conditions and initial conditions are given. Chapter 4 for the systems of thermoelastic coupled beam equations with thermal memory under homogeneous boundary conditions and certain initial conditions, By introducing a new weighted space, the nonautonomous system can be autonomous. The global solution and the existence of the global attractor of the system are given. Chapter 5 gives the existence of the global solution and the global attractor of the system under certain initial conditions under the nonlinear boundary conditions. In the chapter, the uniformly bounded suction collection and the existence of uniform attractors for a nonautonomous single elastic beam equation with local damping under certain initial conditions are given under nonlinear boundary conditions.
【學位授予單位】：太原理工大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：O19

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相關(guān)期刊論文 前1條

1 王素萍;紹旭馗;;梁方程的一致緊吸引子[J];鄭州大學學報(理學版);2016年01期

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本文編號：1699865