轴向运动三参数黏弹性梁弱受迫振动的渐近分析

王波

doi:10.3879/j.issn.1000-0887.2012.06.010

轴向运动三参数黏弹性梁弱受迫振动的渐近分析

doi: 10.3879/j.issn.1000-0887.2012.06.010

王波

上海应用技术学院机械工程学,上海 200235

基金项目: 国家自然科学基金资助项目(10972143)；上海高校青年教师培养资助计划(YYY11040)；上海市教育委员会重点学科建设资助项目(J51501)

详细信息

通讯作者:
王波(1982—),男,辽宁盘锦人,讲师,博士(Tel: +86-21-60873024; E-mail: b.wang@live.com).

中图分类号: O326
计量
- 文章访问数: 1453
- HTML全文浏览量: 94
- PDF下载量: 862
- 被引次数: 0
出版历程
- 收稿日期: 2011-05-09
- 修回日期: 2012-02-29
- 刊出日期: 2012-06-15

Asymptotic Analysis on Weakly Forced Vibration of an Axially Moving Viscoelastic Beam Constituted by Standard Linear Solid Model

WANG Bo

School of Mechanical Engineering, Shanghai Institute of Technology,Shanghai 200235, P.R.China

摘要

摘要: 研究了轴向运动三参数黏弹性梁的弱受迫振动．建立了轴向运动三参数黏弹性梁受迫振动的控制方程．使用多尺度法渐近分析了运动梁的稳态响应，导出了解稳定性边界方程、稳态振幅的表达式以及稳态响应非零解的存在条件．依据Routh-Hurwitz定律决定了非线性稳态响应非零解的稳定性．
- 轴向运动梁 /
- 弱受迫振动 /
- 三参数模型 /
- 多尺度法 /
- 稳态响应
Abstract: The weakly forced vibration of an axially moving viscoelastic beam was investigated. The viscoelastic material of beams was constituted by the standard linear solid model with the material time derivative involved. The nonlinear equations governing the transverse vibration were derived from dynamical, constitutive, and geometrical relations. The method of multiple scales was applied to determine the steady-state response. The modulation equation was derived from the solvability condition of eliminating secular terms. Closed-form expressions of the amplitude and existence condition of nontrivial steady-state response were derived from the modulation equation. The stability of nontrivial steadystate response was examined via RouthHurwitz criterion.
- axially moving beam /
- weakly forced vibration /
- standard linear solid model /
- method of multiple scales /
- steady-state response

HTML全文

参考文献(26)

[1]	Chen L Q. Nonlinear vibrations of axially moving beams[C]Evans T. Nonlinear Dynamics. INTECH, Croatia, 2010: 145-172.
[2]	Pasin F. Ueber die stabilitt der beigeschwingungen von in laengsrichtung periodisch hin und herbewegten stben[J]. Ingenieur-Archiv, 1972, 41(6):387-393.
[3]	z H R, Pakdemirli M, zkaya E. Transition behavior from string to beam for an axially accelerating material[J]. Journal of Sound and Vibration, 1998, 215(3): 571-576.
[4]	z H R. On the vibrations of an axially traveling beam on fixed supports with variable velocity[J]. Journal of Sound and Vibration, 2001, 239(3): 556-564.
[5]	Suweken G, van Horssen W T. On the transversal vibrations of a conveyor belt with a low and time-varying velocity—part Ⅱ: the beam like case[J]. Journal of Sound and Vibration, 2003, 267(5/6): 1007-1027.
[6]	Pakdemirli M, z H R. Infinite mode analysis and truncation to resonant modes of axially accelerated beam vibrations[J]. Journal of Sound and Vibration, 2008, 311(3/5): 1052-1074.
[7]	Chen L Q, Yang X D, Cheng C J. Dynamic stability of an axially accelerating viscoelastic beam[J]. Eur J Mech A/Solid, 2004, 23(4): 659-666.
[8]	Chen L Q, Yang X D. Stability in parametric resonances of an axially moving viscoelastic beam with time-dependent velocity[J]. Journal of Sound and Vibration, 2005, 284(3/5): 879-891.
[9]	Yang X D, Chen L Q. Stability in parametric resonance of axially accelerating beams constituted by Boltzmann’s superposition principle[J]. Journal of Sound and Vibration, 2006, 289(1/2): 54-65.
[10]	Chen L Q, Yang X D. Vibration and stability of an axially moving viscoelastic beam with hybrid supports[J]. Eur J Mech A/Solid, 2006, 25(6): 996-1008.
[11]	Maccari A. The asymptotic perturbation method for nonlinear continuous systems[J]. Nonlinear Dynamics, 1999, 19(1): 1-18.
[12]	Boertjens G J, van Horssen W T. On interactions of oscillation modes for a weakly non-linear undamped elastic beam with an external force[J]. Journal of Sound and Vibration, 2000, 235(2): 201-217.
[13]	Chen L Q, Lim C W, Hu Q Q, Ding H. Asymptotic analysis of a vibrating cantilever with a nonlinear boundary[J]. Sci China Ser G-Phys Mech Astron, 2009, 52(9): 1414-1422.
[14]	Chen L Q, Yang X D. Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models[J]. Int J Solids Struct, 2005, 42(1): 37-50.
[15]	Yang T Z, Fang B, Chen Y, Zhen Y X. Approximate solutions of axially moving viscoelastic beams subject to multi-frequency excitations[J]. International Journal of Non-Linear Mechanics, 2009, 44(2): 230-238.
[16]	Ding H, Chen L Q. Nonlinear models for transverse forced vibration of axially moving viscoelastic beams[J]. Shock and Vibration, 2011, 18(1/2): 281-287.
[17]	Chen L Q, Ding H. Steady-state transverse response in coupled planar vibration of axially moving viscoelastic beams[J]. ASME Journal of Vibration and Acoustics, 2010, 132(1): 011009.
[18]	Mockensturm E M, Guo J. Nonlinear vibration of parametrically excited, viscoelastic, axially moving strings[J]. ASME J Appl Mech, 2005, 72(3): 374-380.
[19]	Chen L Q, Yang X D. Bifurcation and chaos of an axially accelerating viscoelastic beam[J]. Chaos, Solitons and Fractals, 2005, 23(1): 249-258.
[20]	Hou Z, Zu J W. Non-linear free oscillations of moving viscoelastic belts[J]. Mech Mach Theory, 2002, 37(9): 925-940.
[21]	Fung R F, Huang J S, Chen Y C, Yao C M. Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed[J]. Comput Struct, 1998, 66(6): 777-784.
[22]	Ha J L, Chang J R, Fung R F. Nonlinear dynamic behavior of a moving viscoelastic string undergoing three-dimensional vibration[J]. Chaos, Solitons & Fractals, 2007, 33(4): 1117-1134.
[23]	Chen L Q, Chen H. Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model[J]. J Eng Math, 2010, 67(3): 205-218.
[24]	Chen L Q, Ding H. Steady-state responses of axially accelerating viscoelastic beams: approximate analysis and numerical confirmation[J]. Sci China Ser G-Phys Mech Astron, 2008, 51(11): 1701-1721.
[25]	Ding H, Chen L Q. On two transverse nonlinear models of axially moving beams[J]. Sci China Ser E-Tech Sci, 2009, 52(3): 743-751.
[26]	Chen L Q, Jean W Z. Solvability condition in multi-scale analysis of gyroscopic continua[J]. Journal of Sound and Vibration, 2008, 309(1/2): 338-342.