Stability of axially accelerating viscoelastic beams: multi-scale analysis with numerical confirmations

European Journal of Mechanics, A/Solids

Volumn 27, Issue 6, 2008, Pages 1108-1120

  Ding, Hu ^a   Chen, Li Qun ^a  

^a SHANGHAI UNIVERSITY   (China)

Author keywords

Axially accelerating beam; Instability; Method of multiple scales; Parametric resonance; The finite difference; The material time derivative

Indexed keywords

DIFFERENTIATION (CALCULUS); FINITE DIFFERENCE METHOD; HARMONIC ANALYSIS; NUMERICAL ANALYSIS; PARAMETRIC DEVICES; RESONANCE; SPEED;

ANALYTICAL RESULTS; AXIALLY ACCELERATING BEAM; CONSTITUTIVE RELATIONS; DISCRETIZATION; FINITE DIFFERENCE SCHEMES; FIXED SUPPORTS; GOVERNING EQUATIONS; HARMONIC VARIATION; INSTABILITY; INSTABILITY CONDITIONS; MEAN SPEED; METHOD OF MULTIPLE SCALES; MULTI-SCALE ANALYSIS; NUMERICAL CALCULATIONS; NUMERICAL EXAMPLES; PARAMETRIC RESONANCE; PARAMETRIC RESONANCES; PRINCIPAL PARAMETRIC RESONANCE; ROTATIONAL SPRINGS; THE FINITE DIFFERENCE; THE MATERIAL TIME DERIVATIVE; TIME DERIVATIVES; VISCOELASTIC BEAMS;

DIFFERENCE EQUATIONS;

EID: 50549101850     PISSN: 09977538     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechsol.2007.11.014     Document Type: Article

References (23)

1. Abrate A.S. Vibration of belts and belt drives. Mechanism and Machine Theory 27 (1992) 645-659
2. Boresi A.P., Chong K.P., and Saigal S. Approximate Solution Methods in Engineering Mechanics (2003), Wiley, New York pp. 42-47
3. Chen L.Q., and Yang X.D. Stability in parametric resonances of an axially moving viscoelastic beam with time-dependent velocity. Journal of Sound and Vibration 284 (2005) 879-891
4. Chen L.Q., and Yang X.D. Vibration and stability of an axially moving viscoelastic beam with hybrid supports. European Journal of Mechanics A Solids 25 (2006) 996-1008
5. Chen L.Q., Yang X.D., and Cheng C.J. Dynamic stability of an axially accelerating viscoelastic beam. European Journal of Mechanics A Solids 23 (2004) 659-666
6. Chen L.Q., and Zu J.W. Solvability condition in multi-scale analysis of gyroscopic continua. Journal of Sound and Vibration 309 1-2 (2008) 338-342
7. Čepon G., and Boltežar M. Computing the dynamic response of an axially moving continuum. Journal of Sound and Vibration 300 (2007) 316-329
8. Marynowski K., and Kapitaniak T. Kelvin-Voigt versus Burgers internal damping in modeling of axially moving viscoelastic web. International Journal of Non-Linear Mechanics 37 (2002) 1147-1161
9. Marynowski K. Non-linear vibrations of an axially moving viscoelastic web with time-dependent tension. Chaos, Solitons and Fractals 21 (2004) 481-490
10. Marynowski K. Two-dimensional rheological element in modeling of axially moving viscoelastic web. European Journal of Mechanics A Solids 25 (2006) 729-744
11. Marynowski K., and Kapitaniak T. Zener internal damping in modeling of axially moving viscoelastic beam with time-dependent tension. International Journal of Non-Linear Mechanics 42 (2007) 118-131
12. Mockensturm E.M., and Guo J. Nonlinear vibration of parametrically excited, viscoelastic, axially moving strings. Journal of Applied Mechanics 72 (2005) 374-380
13. Öz H.R. On the vibrations of an axially traveling beam on fixed supports with variable velocity. Journal of Sound Vibration 239 (2001) 556-564
14. Öz H.R., and Pakdemirli M. Vibrations of an axially moving beam with time dependent velocity. Journal of Sound Vibration 227 2 (1999) 239-257
15. Öz H.R., Pakdemirli M., and Özkaya E. Transition behavior from string to beam for an axially accelerating material. Journal of Sound Vibration 215 (1998) 571-576
16. Özkaya E., and Öz H.R. Determination of natural frequencies and stability regions of axially moving beams using artificial neural networks method. Journal of Sound Vibration 252 4 (2002) 782-789
17. Özkaya E., and Pakdemirli M. Vibrations of an axially accelerating beam with small flexural stiffness. Journal of Sound Vibration 234 (2000) 521-535
18. Parker R.G., and Lin Y. Parametric instability of axially moving media subjected to multifrequency tension and speed fluctuations. ASME Journal of Applied Mechanics 68 1 (2001) 49-57
19. Pasin F. Über die Stabilität der Beigeschwingungen von in laengsrichtung periodisch hin und herbewegten Stäben. Ingenieur-Archiv 41 (1972) 387-393
20. Suweken G., and 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. Journal of Sound and Vibration 267 (2003) 1007-1027
21. Wickert J.A., and Mote Jr. C.D. Current research on the vibration and stability of axially moving materials. Shock and Vibration Digest 20 5 (1988) 3-13
22. Yang X.D., and Chen L.Q. Bifurcation and chaos of an axially accelerating viscoelastic beam. Chaos, Solitons and Fractals 23 (2005) 249-258
23. Yang X.D., and Chen L.Q. Stability in parametric resonance of axially accelerating beams constituted by Boltzmann's superposition principle. Journal of Sound and Vibration 289 (2006) 54-65