非线性边界条件下具非线性耗散粘弹性梁方程的整体解
发布时间：2018-08-06 17:55
【摘要】：本文考虑材料的粘性效应和非线性外阻尼,对一类轴向载荷和横向载荷作用下具非线性耗散项的粘弹性梁方程进行研究,采用Galerkin方法,证明了该方程在非线性边界条件下整体解的存在唯一性.全文结构如下:第一章介绍了本文所研究问题的背景和来源,以及本文的主要研究内容和研究结果.第二章介绍了本文的一些基础知识,包括基本空间和它们的关系,以及一些引理、概念和基本假设等.第三章采用Galerkin方法,研究了在非线性边界条件下具耗散粘弹性梁方程的初边值问题,得出该整体解的存在唯一性.第四章应用Galekin方法,在前面的基础上研究了具粘性非线性边界条件下梁方程的初边值问题,并求证出了该方程的整体解.第五章对本文的研究内容进行了展望.
[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.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：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.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
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