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非线性粘弹性Timoshenko梁动力学行为的分布
引用本文:李根国,朱正佑.非线性粘弹性Timoshenko梁动力学行为的分布[J].上海力学,2001,22(3):346-351.
作者姓名:李根国  朱正佑
作者单位:[1]上海大学,上海200072 [2]上海大学数学系,上海200072
基金项目:上海市科学技术发展基金(98JC14032);上海市教委发展基金资助项目(99A01)
摘    要:本文讨论了有限变形粘弹性Timoshenko梁的动力学行为。首先由Timoshenko梁的理论和分数导数型本构关系给出了梁的控制方程。其次为了便于求解,采用Galerkin方法对系统进行了简化,并比较了1阶和2阶截断系统的动力学性质,它们具有相同的定性性质,说明Galerkin方法的合理性。给出了求解包含分数积分的积分-微分方程的一种新方法,以便求解系统的长时间的解。综合利用非线性动力系统中的经典方法,揭示了梁在有限变形情况下丰富的动力学行为,并分别考察了载荷参数的材料参数对结构的动力学行为的影响。

关 键 词:非线性粘弹性Timoshenko梁  梁控制方程  有限变形  载荷参数  分数导数型本构关系  有限变形  Galerkin方法  分数导数计算方法  动力学行为  非线性积分-微分方程组
修稿时间:2001年2月15日

Analysis of Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beam
LI Gen-guo,ZHU Zheng-you,CHENG Chang-jun.Analysis of Dynamical Behavior of Nonlinear Viscoelastic Timoshenko Beam[J].Chinese Quarterly Mechanics,2001,22(3):346-351.
Authors:LI Gen-guo  ZHU Zheng-you  CHENG Chang-jun
Abstract:The dynamical behaviors of a viscoelastic Timoshenko beam with finite deformation were discussed in details Applying the Timoshenko's theory of beams and the fractional derivative constitutive relation, the governing motion equations were derived. Galerkin method is used to simplify the governing e-quations. The dynamical behaviors of the reduced systems with first order and second order were compared and they are uniform quality. It is shown that Galerkin method is reasonable. A new numerical method for the integro-differential equation included fractional integral was presented, which can be used to get a long-time solution of the equations. The numerical methods in nonlinear dynamics are synthetically applied to reveal plenty dynamical behaviors of the beam with finite deformation. The influences of load and material parameters on the dynamical behavior of the structure are considered respectively.
Keywords:viscoelastic Timoshenko beam  fractional derivative constitutive relation  finite deformation  Galerkin method  numerical method for fractional derivative  dynamical behavior
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