非線性邊界條件下具非線性耗散粘彈性梁方程的整體解
發(fā)布時(shí)間：2018-08-06 17:55
【摘要】：本文考慮材料的粘性效應(yīng)和非線性外阻尼,對(duì)一類軸向載荷和橫向載荷作用下具非線性耗散項(xiàng)的粘彈性梁方程進(jìn)行研究,采用Galerkin方法,證明了該方程在非線性邊界條件下整體解的存在唯一性.全文結(jié)構(gòu)如下:第一章介紹了本文所研究問題的背景和來源,以及本文的主要研究?jī)?nèi)容和研究結(jié)果.第二章介紹了本文的一些基礎(chǔ)知識(shí),包括基本空間和它們的關(guān)系,以及一些引理、概念和基本假設(shè)等.第三章采用Galerkin方法,研究了在非線性邊界條件下具耗散粘彈性梁方程的初邊值問題,得出該整體解的存在唯一性.第四章應(yīng)用Galekin方法,在前面的基礎(chǔ)上研究了具粘性非線性邊界條件下梁方程的初邊值問題,并求證出了該方程的整體解.第五章對(duì)本文的研究?jī)?nèi)容進(jìn)行了展望.
[Abstract]:In this paper, considering the viscous effect and nonlinear external damping of materials, a class of viscoelastic beam equations with nonlinear dissipative term under axial and transverse loads is studied. The Galerkin method is used. The existence and uniqueness of the global solution of the equation under nonlinear boundary conditions are proved. The structure of the thesis is as follows: in chapter 1, the background and source of the problems are introduced, and the main research contents and results are also given. The second chapter introduces some basic knowledge of this paper, including basic space and their relations, as well as some Lemma, concepts and basic assumptions. In chapter 3, the Galerkin method is used to study the initial boundary value problem of the viscoelastic beam equation with dissipation under nonlinear boundary conditions, and the existence and uniqueness of the global solution are obtained. In chapter 4, the Galekin method is used to study the initial boundary value problem of the beam equation with viscous nonlinear boundary conditions, and the global solution of the equation is obtained. The fifth chapter looks forward to the research content of this paper.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175
本文編號(hào)：2168526
[Abstract]:In this paper, considering the viscous effect and nonlinear external damping of materials, a class of viscoelastic beam equations with nonlinear dissipative term under axial and transverse loads is studied. The Galerkin method is used. The existence and uniqueness of the global solution of the equation under nonlinear boundary conditions are proved. The structure of the thesis is as follows: in chapter 1, the background and source of the problems are introduced, and the main research contents and results are also given. The second chapter introduces some basic knowledge of this paper, including basic space and their relations, as well as some Lemma, concepts and basic assumptions. In chapter 3, the Galerkin method is used to study the initial boundary value problem of the viscoelastic beam equation with dissipation under nonlinear boundary conditions, and the existence and uniqueness of the global solution are obtained. In chapter 4, the Galekin method is used to study the initial boundary value problem of the beam equation with viscous nonlinear boundary conditions, and the global solution of the equation is obtained. The fifth chapter looks forward to the research content of this paper.
【學(xué)位授予單位】：太原理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175
【參考文獻(xiàn)】
相關(guān)期刊論文 前4條
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2 張建文,張建國,李慶士,蔡中民;具強(qiáng)阻尼非線性粘彈性梁方程的整體解[J];工程數(shù)學(xué)學(xué)報(bào);2003年02期
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相關(guān)碩士學(xué)位論文 前1條
1 班愛玲;具有臨界增長(zhǎng)指數(shù)的阻尼波動(dòng)方程的吸引子和核截面的維數(shù)[D];上海師范大學(xué);2009年
，本文編號(hào)：2168526
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