文档介绍：太原理工大学硕士研究生学位论文 y-7884哇1 非线性边界条件下粘弹性粱方程的整体动力学摘要目前,一方面,由于实际问题及其它学科的推动,另一方面,由于数学自身发展的深入,,: (1)首先,对固体力学中某些无穷维动力系统的研究现状及研究方法进行了总结与评述,尤其是对无穷维动力系统的门槛一一解的存在唯一性进行了重点评述,并对系统能量的指数衰减进行了总结. (2)其次,在Woinowsky-Krieger提出的具轴向力效应的杆振动模型的基础上,对于弹性梁,若同时考虑材料的粘性效应,介质阻尼;几何非线性,物理非线性;并在弹性梁上施加轴向载荷的作用,我们建立了一个更一般的粘弹性梁方程. (3)对于所建立的非线性粘弹性梁方程: 讧+“(4)+p心(4)+rift一(村(丘卜‘1’12如+JⅣ(矗u(1Lh(1)出))u(2)_0 我们利用了Galerkin方法,在非线性边界条件(a): u(o,t)=u(2)(O,∞=u(1)(f,t)=0 “(3’(f,f)+lai￡(3’(f,t)=,(u(f,f)) 及初始条件; 太原理工大学硕士研究生学庄论i: u(o,0)=uo(z),u(z,O)=ul(z) 下给出了解的存在唯一性,及它对初值的连续依赖性,(b): Ⅱ(0,t)=u(2:(o,f)=小1’(z,t)=0 “(3)(z,t)+础(3)(f,t)=g(i(z,t)) 下的解的存在唯一性及它对初值的连续依赖性. 关键词:粘弹性梁,非线性边界,整体解,Galerkin方法, 指数衰减太原理工大学硕士研究生学位论文 THE GLOBAL DYNAMICS oF ELASTIC BEAM EQUATIoN WITH NoNLINEAR BoUNDARY CoNDITIoNS ABSTRACT Atpresent】with thedevelopment ofpractical problems andsome othersciences on the one hand,and with thead- vancement ofmathematics itself 012 the research on infinite—dimensionaldynamic systems has e one ofthe important subjects ofdynamic the— sispresents some research on nonlinear elastic infinite— dimensional dynamic systems ofsolidmechanics and we give the proof ofexistence and the asymptotic behavior under certain initialboundary details will go as follows: Firstly,the current study situation and research meth— ods about general infinite-dimensional dynamic systems aresummarized )the thresh— oldoftheinfinite—dimensionaldynamic systems--the exis— tence,uniqueness ofsolutions has been , theexponential decay oftheenergy issummarized. SecondlNon thebasisofWoinowsky—-Krieger barvibra— III 太原理工大学硕士研究生学位论文 tionmodel with axialforceeffect,simultaneously consld— ering theviscous effectofmaterial;geometrical nonlinear— ity;physical nonlinearity;periodical axialloads;we set up a more general nonlinear equation about viscous elastic beam. Fortheno