Dynamic stability of an axially accelerating viscoelastic beam

被引:79
作者
Chen, LQ [1 ]
Yang, XD
Cheng, CJ
机构
[1] Shanghai Univ, Dept Mech, Shanghai 200436, Peoples R China
[2] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China
基金
中国国家自然科学基金;
关键词
axially accelerating beam; viscoelasticity; method of averaging;
D O I
10.1016/j.euromechsol.2004.01.002
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
This work investigates dynamic stability in transverse parametric vibration of an axially accelerating viscoelastic tensioned beam. The material of the beam is described by the Kelvin model. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The Galerkin method is applied to discretize the governing equation into a infinite set of ordinary-differential equations under the fixed-fixed boundary conditions. The method of averaging is employ to analyze the dynamic stability of the 2-term truncated system. The stability conditions are presented and confirmed by numerical simulations in the case of subharmonic and combination resonance. Numerical examples demonstrate the effects of the dynamic viscosity, the mean axial speed and the tension on the stability conditions. (C) 2004 Elsevier SAS. All rights reserved.
引用
收藏
页码:659 / 666
页数:8
相关论文
共 14 条
[1]   VIBRATIONS OF BELTS AND BELT DRIVES [J].
ABRATE, S .
MECHANISM AND MACHINE THEORY, 1992, 27 (06) :645-659
[2]   DYNAMIC STABILITY OF PIPES CONVEYING PULSATING FLUID [J].
ARIARATNAM, ST ;
NAMACHCHIVAYA, NS .
JOURNAL OF SOUND AND VIBRATION, 1986, 107 (02) :215-230
[3]   FLEXURAL INSTABILITIES IN AXIALLY MOVING BANDS [J].
ASOKANTHAN, SF ;
ARIARATNAM, ST .
JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 1994, 116 (03) :275-279
[4]  
Bishop R., 1979, MECH VIBRATION
[5]  
Bogoliubov NN., 1961, Asymptotic methods in the theory of non-linear oscillations (In Russian)
[6]  
Marynowski K., 2002, Journal of Theoretical and Applied Mechanics, V40, P465
[7]   Kelvin-Voigt versus Burgers internal damping in modeling of axially moving viscoelastic web [J].
Marynowski, K ;
Kapitaniak, T .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2002, 37 (07) :1147-1161
[8]   Transition behaviour from string to beam for an axially accelerating material [J].
Oz, HR ;
Pakdemirli, M ;
Ozkaya, E .
JOURNAL OF SOUND AND VIBRATION, 1998, 215 (03) :571-576
[9]   On the vibrations of an axially travelling beam on fixed supports with variable velocity [J].
Öz, HR .
JOURNAL OF SOUND AND VIBRATION, 2001, 239 (03) :556-564
[10]   Vibrations of an axially accelerating beam with small flexural stiffness [J].
Özkaya, E ;
Pakdemirli, M .
JOURNAL OF SOUND AND VIBRATION, 2000, 234 (03) :521-535