具有结构阻尼的梁振动方程解的存在性与渐近稳定性

发布时间：2018-04-02 21:00

本文选题：结构阻尼　切入点：梁振动方程　出处：《兰州交通大学》2017年硕士论文

【摘要】：本文在Banach空间框架下,运用算子半群理论、不动点定理,研究具有结构阻尼的半线性梁振动方程mild解的存在性,线性及半线性梁振动方程mild?-周期解的存在性与渐近稳定性.本文的主要结果如下:第1章介绍了具有结构阻尼的梁振动方程的研究背景、本文的主要工作以及算子半群理论和非紧性测度等预备知识.第2章给出了凸幂凝聚算子的概念以及不动点定理,在非紧性测度条件以及梁振动方程的解半群是等度连续半群情形下,运用凸幂凝聚算子的不动点定理获得了该问题整体mild解和正mild解的存在性.第3章首先讨论了具有结构阻尼的线性梁振动方程mild?-周期解的存在性与渐近稳定性,获得了线性梁振动方程mild?-周期解的半群表示.其次,在Lipschitz扰动情形下,利用线性梁振动方程周期解的估计,获得了半线性梁振动方程周期解的存在性与渐近稳定性.
[Abstract]:In this paper, using the theory of operator semigroup and fixed point theorem, we study the existence of mild solutions for semilinear beam vibration equations with structural damping, the existence and asymptotic stability of mild-periodic solutions for linear and semilinear beam vibration equations under the framework of Banach spaces.The main results of this paper are as follows: in Chapter 1, the background of the research on the vibration equations of beams with structural damping is introduced. The main work of this paper and the theory of operator Semigroups and the non-compactness measure are also discussed.In chapter 2, the concept of convex power condensate operator and the fixed point theorem are given. In the case of noncompactness measure condition and solution semigroup of beam vibration equation,By using the fixed point theorem of convex power condensate operator, the existence of global mild solution and positive mild solution are obtained.In chapter 3, we first discuss the existence and asymptotic stability of milda-periodic solutions of linear beam vibration equations with structural damping, and obtain the semigroup representation of milda-periodic solutions of linear beam vibration equations.Secondly, in the case of Lipschitz perturbation, the existence and asymptotic stability of periodic solutions of semilinear beam vibration equations are obtained by using the estimation of periodic solutions of linear beam vibration equations.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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