轴向运动梁在轴向载荷作用下的动力学特性研究

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振动与冲击 ›› 2016, Vol. 35 ›› Issue (19) : 75-80.

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陈红永1，李上明2

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The effect of axial load on dynamic characteristics of axially moving Timoshenko beam

Chen Hongyong 1 Li Shangming 2

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摘要

研究了轴向运动Timoshenko梁在轴向载荷作用下的振动特性。首先通过考虑轴向拉压载荷作用，根据Timoshenko梁理论和Hamilton原理建立了梁的横向振动控制微分方程，推导了简支-简支边界条件下的梁的无量纲频率随轴向载荷的变化关系，采用新的无量纲化形式消除了无载荷作用下控制方程的奇异性。通过微分求积法进行数值求解并对结果进行验证，分析结果表明：无载荷作用下，长细比越大，越易达到失稳状态；在相同运动速度下，受压状态时比受拉状态下更易达到失稳；临界速度随着轴向载荷的绝对值的增大而减小。通过研究探索了影响临界速度和临界载荷的因素以及两者的关系，对于轴向受载运动系统设计具有一定指导意义。

关键词：轴向运动Timoshenko梁；轴向载荷；横向振动；微分求积法

Abstract

The effects of axial load on vibration characteristics of axially moving Timoshenko beam are investigated. The differential governing equation of transverse vibration of axially moving beam with considering the axial load is established on the base of Timoshenko beam theory and Hamilton’s principle. The dynamic characteristics of different slenderness beams with axial load and pinned-pinned boundary conditions are investigated. The dimensionless frequencies of beam are calculated numerically with differential quadrature method (DQM), and compared with the analytical solutions to verify. The results show: The beam is easier to reach unsteady state when its factor of slenderness is larger with the boundary condition of no load; The beam reaches unsteady state easier under the effect of compressive load rather than tensile load. The critical speed decreases while the absolute value of axial load increases. Through the investigation on the influence factor and the relationship between the critical load and the critical velocity, the results have practical importance on the design of the axially moving systems.

Key words: axially moving Timoshenko beam; axial load; transverse vibration; differential quadrature method

关键词

轴向运动Timoshenko梁

/ 轴向载荷 / 横向振动 / 微分求积法

Key words

axially moving Timoshenko beam

/ axial load / transverse vibration / differential quadrature method

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陈红永1，李上明2. 轴向运动梁在轴向载荷作用下的动力学特性研究[J]. 振动与冲击, 2016, 35(19): 75-80

Chen Hongyong 1 Li Shangming 2. The effect of axial load on dynamic characteristics of axially moving Timoshenko beam[J]. Journal of Vibration and Shock, 2016, 35(19): 75-80

参考文献

[1] Mote C D. A study of band saw vibrations [J]. Journal of the Franklin Institute. 1965, 279: 430-444.
[2] Wickert J A. Non-linear vibration of a traveling tensioned beam[J]. International Journal Non-Linear Mechanics. 1992, 27: 503-517.
[3] Huang J L, Su R K L, Li W H et al.Stability and bifurcation of an axially moving beam tuned to three-to-one internal resonances[J]. Journal of Sound and Vibration, 2011,330(3):471-485.
[4] Chen L Q, Tang Y Q, Lin C W. Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko Beam[J]. Journal of Sound and Vibration, 2010,329(5):547-565.
[5] Ding H, Chen L Q. Galerkin methods for natural frequencies of high-speed axially moving beams[J], Journal of Sound and Vibration.2010, 329(17):3484-3494.
[6] Ding H, Zhang G C, Chen L Q. Supercritical equilibrium solutions of axially moving beams with hybrid boundary conditions[J]. Mechanics Research Communications, 2011, 38(1):52-56.
[7] Ghayesh M H. Nonliear forced dynamics of an axially moving viscoelastic beam with an internal resonance[J]. International Journal of Mechanical Sciences, 2011, 53(11):1022-1037.
[8] Ghayesh M H, Kafiabad H A, Reid T. Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam[J]. International Journal of Solids and Structures, 2012, 49(1):227-243.
[9] Ghayesh M H. Coupled longitudinal-transverse dynamics of an axially accelerating beam[J]. Journal of Sound and Vibration, 2012,331:5107-5124.
[10] Ghayesh M H. Subharmonic dynamics of an axially accelerating beam[J]. Archive of Applied Mechanics, 2012,82: 1169-1181.
[11] Ghayesh M H, Amabili M. Steady-state transverse response of an axially moving beam with time-dependent axial speed[J]. International Journal of Non-Linear Mechanics, 2013, 49: 40-49.
[12] Simpson A. Transverse modes and frequencies of beams translating between fixed end supports[J].Journal of Mechanical Engineering Science, 1973, 15: 159-164.
[13] Tang Y Q, Chen L Q, Yang X D. Natural frequencies modes and critical speeds of axially moving Timoshenko beams with different boundary conditions[J].International Journal of Mechanical Sciences. 2008, 50: 1448-1458.
[14] Bokaian A. Natural frequencies of beams under compressive axial loads[J]. Journal of Sound and Vibration. 1988, 126: 49-65.
[15] Bokaian A. Natural frequencies of beams under tensile axial loads[J]. Journal of Sound and Vibration. 1990, 142:481-498.
[16] Pourtakdoust S H, Assadian N. Investigation of thrust effect on the vibrational characteristics of flexible guided missiles[J].Journal of Sound and Vibration. 2004, 272: 287-299.
[17] Ghayesh M H, Khadem SE. Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity[J]. International Journal of Mechanical Sciences, 2008, 50: 389–404.
[18] 王波. 轴向运动三参数黏弹性梁弱受迫振动的渐近分析[J].应用数学和力学，2012,33(6)：771-780.
Wang Bo. Asymptotic Analysis on Weakly Forced Vibration of an Axially Moving Viscoelastic Beam Constituted by standard Linear Solid Model[J]. Applied Mathematics and Mechanics, 2012,33(6):771-780（in Chinese）.
[19] 李成，姚林泉. 轴向运动超薄梁的非局部动力学分析[J].工程力学, 2013, 30(4): 366-372.
Li Cheng, Yao Quanlin. Nonlocal dynamical analysis on axially travelling ultra-thin beam [J].Engineering Mechanics. 2013, 30(4): 366-372. (in Chinese)
[20] 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, 2007, 28(1): 1-8（in Chinese）
[21] 陈红永，陈海波, 张培强. 轴向受压运动梁横向振动特性的数值分析[J].振动与冲击.2014,33(24): 101-105.
Chen Hong-yong, Chen Hai-bo, Zhang Peiqiang. Numerical analysis of free vibration of an axially moving beam under compressive load [J]. Journal of Vibration and Shock, 2014, 33(24): 101-105.
[22] Guo X X, Wang Z M, Wang Y. et. al. Analysis of the coupled thermoelastic vibration for axially moving beam[J].Journal of Sound and Vibration, 2009, 325: 597–608.
[23] 邱吉宝,向树红,张正平. 计算结构动力学[M]. 合肥：中国科学技术大学出版社, 2009: 31-33.
Qiu Jibao, Xiang Shuhong, Zhang Zhengping. Computational structure dynamics [M].Hefei: University of Science and Technology Press, 2009:31-33. (in Chinese)
[24] Sung K J, Charles W B, Alfred G S. Application of differential quadrature tostatic analysis of structural components [J].International Journal for Numerical Methods in Engineering, 1989, 28: 561-577.
[25] Timoshenko S, Young D H, Weaver W. Vibration problems in engineering [M]. New York: John Wiley & Sons. Inc. Forth Edition. 432-434.
[26] Sun Y X, Fang D N, Ai S K. Thermalelastic damping in micro-beam resonators [J]. International Journal of Solids and Structures. 2006, 43: 3213-3229.