具非线性边界耗散和结构阻尼的梁方程的整体解  

Global Solutions of Beam Equation with Nonlinear Boundary Dissipations and Structural Damping

作　　者：王银珠[1] 杨茂财[2] 王旦霞[2] 

机构地区：[1]太原科技大学应用科学学院,山西太原030024 [2]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2016年第1期10-14,18,共6页Journal of North University of China(Natural Science Edition)

基　　金：太原科技大学2014年校博士科研启动基金项目;山西省自然科学基金资助项目(2015011006;2015011003)

摘　　要：考虑材料的粘性效应、介质阻尼和外部阻尼、转动惯量,建立了一类更广泛的具有外部载荷的Kirchhoff型非自治梁方程,研究了其在一定的非线性边界条件和初始条件下系统的初边值问题,利用经典Galerkin方法,结合先验估计和Sobolev空间理论,证明了上述系统的整体解的存在性和唯一性,为这类梁方程解的合理的Galerkin截断提供了理论依据,也为实际工程提供了设计依据.Simultaneously, considering the viscous effect of material, damping of medium and external damping, and rotational inertia, a kind of more general Kirchhoff type non-autonomous beam equation with external load was established. Under certain nonlinear boundary conditions and initial conditions, the initial-boundary value problem of the nonlinear non-autonomous beam equation was studied. By u- sing classical Galerkin method, combining the prior estimate and the Sobolev space theory and some inequality skills, the existence and uniqueness of the global solutions for the above-mentioned system were proved. Furthermore, the result provides the theoretical basis for this kind of beam equation reasonable Galerkin truncation, also provides the design basis for the practical engineering. Key words： structural damping; rotational inertia; nonlinear boundary; Galerkin method; global solutions

关 键 词：结构阻尼 转动惯量 非线性边界 GALERKIN方法 整体解 

分 类 号：O175.27[理学—数学]