Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String

ZHAO Wei-jia; CHEN Li-qun; Jean W Zu

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2006 > 27(1): 21-27

ZHAO Wei-jia, CHEN Li-qun, Jean W Zu. Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String[J]. Applied Mathematics and Mechanics, 2006, 27(1): 21-27.

Citation:

ZHAO Wei-jia, CHEN Li-qun, Jean W Zu. Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String[J]. Applied Mathematics and Mechanics, 2006, 27(1): 21-27.

Citation:

ZHAO Wei-jia, CHEN Li-qun, Jean W Zu. Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String[J]. Applied Mathematics and Mechanics, 2006, 27(1): 21-27.

PDF( 2235 KB)

Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String

1.
Department of Mathematics, Qingdao University, Qingdao 266071, P. R. China;

Received Date: 2003-05-30
Rev Recd Date: 2005-09-06
Publish Date: 2006-01-15

Abstract

Abstract

Finite difference method is presented to simulate transverse vibrations of an axially moving string.The equation of motion is derived first.By discretizing the governing equation and the equation of stress_strain relation at different frictional knots,two linear sparse finite difference equation systems are obtained.The two resulting difference schemes can be calculated alternatively,which make the computation much more efficient.The numerical method makes the nonlinear model easier to deal with and of truncation errors.It also shows stability for small initial values,so it can be used in analyzing the nonlinear vibration of viscoelastic moving string effectively.Numerical examples are presented to demonstrate the efficiency and the stability of the algorithm,and dynamic analysis of a viscoelastic string is given by using the numerical results.
- axially moving strings,
- transverse vibration,
- viscoelastic,
- finite difference,
- alternating iterative,
- dynamical analysis

FullText(HTML)

References(11)

References

[1]	陈立群，Zu J W.轴向运动弦线的横向振动及其控制[J].力学进展，2001，31(4):535—546.
[2]	Abrate A S.Vibration of belts and belt drivers[J].Mech Mach Theory,1992,27(6):645—659. doi: 10.1016/0094-114X(92)90064-O
[3]	Zhang L,Zu J W.One-to-one auto-parametric resonance in serpentine belt drive systems[J].J of Sound and Vibration,2000,232(4):783—806. doi: 10.1006/jsvi.1999.2764
[4]	Zhang L,Zu J W.Non-linear Vibrations of parametrically excited viscoelastic moving belts[J].Part Ⅰ:Dynamic resonse.J of Applied Mechanics,1999,66(2):396—402.
[5]	ZHAO Wei-jia,CHEN Li-qun.A numerical algorithm for nonlinear vibration analysis of a viscoelastic moving belt[J].International J.of Nonlinear Science and Numerical Simulation,2002,3(2):139—144.
[6]	Beikmann R S,Perkins N C，Ulsoy A G.Free vibration of serpentine belt drive system[J].J of Vibration and Acoustics,1996,118(3):06—413.
[7]	Ni Y Q,Lou W J，Ko J M.A hybrid pseudo-force/Laplace transform method for non-linear transient response of suspended cable[J].J of sound and vibration,2000,238(2):189—214. doi: 10.1006/jsvi.2000.3082
[8]	Chen T M.The hybrid laplace transform/finite element method applied to the quasi-static and dynamic analysis of vicoelastic timoshenko beams[J].International J Numerical Method in Eng,1995,38:509—522. doi: 10.1002/nme.1620380310
[9]	Gobat J I,Grosenbaugh M A.Comput methods appl[J].Mech Engrg,2001,190(37/38):487—489.
[10]	Marchuk G I.Methods of Numerical Mathematics[M].New York:Springr-Verlag,1981.
[11]	CHEN Li-qun,ZHAO Wei-jia.A computation method for nonlinear vibration of axially accelerating viscoelastic strings[J].Applied Mathematics and Computation,2005,162:305—310. doi: 10.1016/j.amc.2003.12.100