## 留言板

 引用本文: 张能辉, 王建军, 程昌钧. 轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法[J]. 应用数学和力学, 2007, 28(1): 1-8.
ZHANG Neng-hui, WANG Jian-jun, CHENG Chang-jun. Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String[J]. Applied Mathematics and Mechanics, 2007, 28(1): 1-8.
 Citation: ZHANG Neng-hui, WANG Jian-jun, CHENG Chang-jun. Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String[J]. Applied Mathematics and Mechanics, 2007, 28(1): 1-8.

• 中图分类号: O322

## Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String

• 摘要: 在考虑初始张力和轴向速度简谐涨落的情况下，利用含预应力三维变形体的运动方程，建立了轴向变速运动弦线横向振动的非线性控制方程，材料的粘弹性行为由Kelvin模型描述．利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数，并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用．数值结果表明，复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度．
•  [1] 陈立群，Zu J W.轴向运动弦线的纵向振动及其控制[J]. 力学进展,2001,31(4):535-546. [2] Pakdemirli M, Ulsoy A G.Stability analysis of an axially accelerating string[J].J Sound Vib,1997,203(5):815-832. [3] 吴俊，陈立群.轴向变速运动弦线的非线性振动的稳态响应及其稳定性[J].应用数学和力学，2004，25(9)：917-926. [4] 周洪刚，朱凌，郭乙木. 轴向加速度运动弦线横向振动的数值计算方法[J].机械强度，2004，26(1)：16-19. [5] CHEN Li-qun,ZHAO Wei-jia,Zu J W. Simulations of transverse vibrations of an axially moving string: A modified difference approach [J].Applied Mathematics and Computation,2005,166(3):596-607. [6] Chen T M. The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams[J].Int J Numerical Method Eng,1995,38(3):509-522. [7] Ni Y Q,Lou W J,Ko J M.A hybrid pseu-force/Laplace transform method for nonlinear transient response of a suspended cable[J].J Sound Vib,2000,238(2):189-124. [8] CHEN Li-qun,ZHANG Neng-hui,Zu J W.The regular and chaotic vibrations of an axially moving viscoelastic string based on 4-order Galerkin truncation[J].J Sound Vib,2003,261(4):764-773. [9] CHEN Li-qun,ZHANG Neng-hui,Zu J W. Bifurcation and chaos in nonlinear vibrations of a moving viscoelastic string[J].Mechanics Research Communications,2002,29(2/3):81-90. [10] CHEN Li-qun,ZHANG Neng-hui.Nonlinear dynamics of axially moving viscoelastic strings based on translating eigenfunctions[A].In:Gutkowski W,Kowalewski T A Eds.The 21st International Congress of Theoretical and Applied Mechanics(IUTAM-ICTAM04)[C].Warszawa: IPPT PAN, 2004,390-391. [11] ZHANG Neng-hui,CHEN Li-qun.Nonlinear dynamical analysis of axially moving viscoelastic strings[J].Chaos, Solitons and Fractals,2005,24(4):1065-1074. [12] CHEN Li-qun, Zu J W, WU Ju,et al.Transverse vibrations of an axially accelerating viscoelastic string with geometric nonlinearity[J].Journal of Engineering Mathematics,2004,48(2):171-182. [13] CHEN Li-qun,WU Jun, Zu J W. Asymptotic nonlinear behaviors in transverse vibration of an axially accelerating viscoelastic string[J].Nonlinear Dynamics,2004,35(4):347-360. [14] Bolotin V V.Non-Conservation Problems of the Theory of Elastic Stability[M].New York: Macmillan,1963. [15] Wickert J A,Mote C D Jr. Classical vibration analysis of axially moving continua[J].ASME J Appl Mech,1990,57(3):738-744.

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##### 出版历程
• 收稿日期:  2005-10-21
• 修回日期:  2006-10-11
• 刊出日期:  2007-01-15

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