非线性边界条件下具非线性耗散粘弹性梁方程的整体解
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摘要
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。
In this paper,we establish one kind of nonlinear viscous-elastic supported beam subjected to axial forces and transverse load,considering both viscosity effect and nonlinear external daming,and obtain the existence and uniqueness theorem of global solutions for the equations under nonlinear boundary conditions by the Galerkin approach.
In this paper,we establish one kind of nonlinear viscous-elastic supported beam subjected to axial forces and transverse load,considering both viscosity effect and nonlinear external daming,and obtain the existence and uniqueness theorem of global solutions for the equations under nonlinear boundary conditions by the Galerkin approach.
引文
[1]张建国,张建文.具非线性耗散粘弹性梁方程的整体解[J].工程数学学报,2001,18(2):61-68.ZHANG J G,ZHANG J W.The global solutions for the equations of nonlinear viscosity-elasticity beam[J].Chinese Journal of Engineering Mathematics,2001,18(2):61-68.
[2]张建文,张建国,李庆士.具强阻尼非线性粘弹性梁方程的整体解[J].工程数学学报,2003,20(2):30-34.ZHANG J W,ZHANG J G,LI Q S.The global solutions for the equations of strongly damped nonlinear viscosity-elasticity beam[J].Chinese Journal of Engineering Mathematics,2003,20(2):30-34.
[3]张建文,李庆士,蔡中民.具强迫项非线性梁方程解的渐近性[J].应用数学,2001,14(1):60-66.ZHANG J W,LI Q S,CAI Z M.The Asymptotic behavior of solutions for the equations of nonlinear beam with distributed load[J].Mathematica Applicata,2001,14(1):60-66.
[4]王旦霞,张建文,王银珠.非线性边界条件下粘弹性梁方程的整体解[J].中北大学学报(自然科学版),2006,27(2)128-131.WANG D X,ZHANG J W,WANG Y Z.Global solutions to elastic beam equations under nonlinear boundary conditions[J].Journal of North University of China(Natural Science Edition),2006,27(2):128-131.
[5]BALL J M.Initial-boundary value problems for an extensible beam[J].J Math Anal,1973,42:61-68.
[7]BALL J M.Stability theory for an extensible beam[J].J Differ Equa,1973,14(3):399-418.
[6]MA T F.Boundary stabilization for a non-linear beam on elastic bearings[J].Math Appl Sci,2001,24(8):583-594.
[2]张建文,张建国,李庆士.具强阻尼非线性粘弹性梁方程的整体解[J].工程数学学报,2003,20(2):30-34.ZHANG J W,ZHANG J G,LI Q S.The global solutions for the equations of strongly damped nonlinear viscosity-elasticity beam[J].Chinese Journal of Engineering Mathematics,2003,20(2):30-34.
[3]张建文,李庆士,蔡中民.具强迫项非线性梁方程解的渐近性[J].应用数学,2001,14(1):60-66.ZHANG J W,LI Q S,CAI Z M.The Asymptotic behavior of solutions for the equations of nonlinear beam with distributed load[J].Mathematica Applicata,2001,14(1):60-66.
[4]王旦霞,张建文,王银珠.非线性边界条件下粘弹性梁方程的整体解[J].中北大学学报(自然科学版),2006,27(2)128-131.WANG D X,ZHANG J W,WANG Y Z.Global solutions to elastic beam equations under nonlinear boundary conditions[J].Journal of North University of China(Natural Science Edition),2006,27(2):128-131.
[5]BALL J M.Initial-boundary value problems for an extensible beam[J].J Math Anal,1973,42:61-68.
[7]BALL J M.Stability theory for an extensible beam[J].J Differ Equa,1973,14(3):399-418.
[6]MA T F.Boundary stabilization for a non-linear beam on elastic bearings[J].Math Appl Sci,2001,24(8):583-594.