文档介绍：太原理工大学硕士研究生学位论文减关键词:Galerkin方法;非线性梁方程;非齐次边界条件;整体解;指数衰万方数据太原理工大学硕士研究生学位论文 GLoBAL SoLUTIoN BoUNDARY CoNDITIoNS FoR BEAM EQUATION WITH MEMORY TERM ABSTRACT At present,with the development ofpractical problems and the advancement of mathernatics itself,the research on infinite-dimensional dynamic systems has e one oftheimportant subjects ofdynamic thispaper,we consider aequation ”甜u一。一/。坤叫uxxxxdT--M(ZL Iu坪dx)钆一oin[0'孙R+ under non-linear boundary conditions which model the vibrations of abeamclamped at z=0 and supported by anon—linearbearing at X= adding only one damping mechanism atz=L,we prove the existence of aglobal details willgoasfollows, (1)Firstly,the current study situation and researchmethods about general infinite— dimensional dynamical system insolidmechanics,and points out theresearch back— ground ofthisarticle,also gave an analysis ofthecorrelation equation. (2)Secondly,on thebasis ofWoinowsky-Krieger beam equation atthehinge model, byadding memory and nonlinear function M,we setup amore general equation about viscous elasticbeam (3)For the vibration ofthe beam model we studied the equation with the initial conditions u(x,0)一uo(z), and the nonlinear boundary conditions ut(x,0)=u1(z) u(0,t)=Ux(o,t)=0 万方数据太原理工大学硕士研究生学位论文 U。。(L,t)=0 札?(叫)一/02坤叫“一(如)d丁一M(/0工Iu坪如)u舢㈡一m(砧))吲让舭㈡) under the above conditions ofinitialboundary value problems. Through transformthe equation,structure theapproximate solution ofthe equa- tion,prior estimate bined with some inequalities ofSoblev space,convergence ofthe equation and take the steps tolimit,To prove that the ex- istence,uniqueness and constant dependence ofglobal studied the expo- nential decay bydefining the energy ofsystem. KEY WORDS: Galerkin method;Non-linear beam equation;Non—homogeneous boundary conditions;Global solution;exponential decay lV 万方数据太原理工大学硕士研究生学位论文目录第一章绪论????????????????????????..(1) 背景知识??????????????????????.(1)