Nonlinear free transverse vibrations of axially moving Timoshenko beams with two free ends

被引：0
作者：
Biao Li
YouQi Tang
LiQun Chen
机构：
[1] Shanghai Institute of Applied Mathematics and Mechanics,Department of Mechanics
[2] Shanghai University,undefined
来源：
Science China Technological Sciences | 2011年 / 54卷
关键词：
nonlinear transverse vibration; Timoshenko beam; complex mode approach; method of multiple scales; internal resonances;
D O I：
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学科分类号：
摘要：
In this paper, nonlinear transverse vibrations of axially moving Timoshenko beams with two free ends are investigated. The governing equations and the associated boundary conditions are derived by the extended Hamilton principle. The method of multiple scales is applied to analyze the nonlinear partial differential equation. The natural frequencies and modes are investigated by performing the complex mode approach. The effect of natural frequencies with the stiffness and the axial speeds are numerically demonstrated. The solvability conditions are established for the cases of without and with 3:1 internal resonances. The relationships between the nonlinear frequencies and the initial amplitudes at different axial speeds and the nonlinear coefficients are showed for the case of without internal resonances. The effects of the related coefficients are demonstrated for the case of 3:1 internal resonances.
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页码：1966 / 1976
页数：10
相关论文
共 42 条
  • [1] Chen S. H.(2007)Multidimensional Lindstedt-Poincaré method for nonlinear vibration of axially moving beams J Sound Vib 306 1-11
  • [2] Huang J. L.(2009)Using the extended Melnikov method to study the multi-pulse global bifurcations and chaos of a cantilever beam J Sound Vib 319 541-569
  • [3] Sze K. Y.(1965)A study of band saw vibrations J Franklin Institute 276 430-444
  • [4] Zhang W.(1999)Vibrations of an axially moving beam with time dependent velocity J Sound Vib 227 239-257
  • [5] Yao M. H.(2001)On the vibrations of an axially traveling beam on fixed supports with variable velocity J Sound Vib 239 556-564
  • [6] Zhang J. H.(2000)Vibrations of an axially accelerating beam with small flexural stiffness J Sound Vib 234 521-535
  • [7] Mote C. D.(2002)Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method J Sound Vib 254 782-789
  • [8] Öz H. R.(1973)Transverse modes and frequencies of beams translating between fixed end supports J Mech Eng Sci 15 159-164
  • [9] Pakdemirli M.(1986)Steady state response of anaxially moving strip subjected to astationary lateral load J Sound Vib 107 155-165
  • [10] Öz H. R.(2008)Natural frequencies, modes and critical speeds of axially moving Timoshenko beams with different boundary conditions Intl J Mech Sci 50 1448-1458
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