Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity

International Journal of Mechanical Sciences

Volumn 50, Issue 3, 2008, Pages 389-404

  Ghayesh, M H ^a   Khadem, S E ^a  

^a TARBIAT MODARES UNIVERSITY   (Iran)

Author keywords

Axially moving beam; Bifurcation; Multiple scales method; Non linear vibration; Stability

Indexed keywords

BIFURCATION (MATHEMATICS); NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; THERMAL EFFECTS;

AXIALLY MOVING BEAM; MULTIPLE SCALES METHOD; NON-LINEAR VIBRATION;

VIBRATION ANALYSIS;

EID: 39549115447     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmecsci.2007.10.006     Document Type: Article

References (34)

1. Mote Jr. C.D. On the non-linear oscillation of an axially moving string. Journal of Applied Mechanics 33 (1966) 463-464
2. Ames W.F., Lee S.Y., and Zaiser J.N. Non-linear vibration of a traveling threadline. International Journal of Non-linear mechanics 3 (1968) 449-469
3. Thurman A.L., and Mote Jr. C.D. Free, periodic, non-linear oscillation of an axially moving strip. Journal of Applied Mechanics 36 (1969) 83-91
4. Tabarrok B., Leech C.M., and Kim Y.I. On the dynamics of an axially moving beam. Journal of Franklin Institute 29 (1974) 201-220
5. Wickert J.A., and Mote Jr. C.D. Classical vibration analysis of axially continua. Journal of Applied Mechanics 57 (1990) 447-738
6. Wickert J.A. Non-linear vibration of a traveling tensioned beam. International Journal of Non-linear Mechanics 27 (1992) 503-517
7. Stylianou M., and Tabarrok B. Finite element analysis of an axially moving beam, Part I: time integration. Journal of Sound and Vibration 178 (1994) 433-453
8. Pakdemirli M., Ulsoy A.G., and Ceranoglu A. Transverse vibration of an axially accelerating string. Journal of Sound and Vibration 169 (1994) 179-196
9. Oz H.R., Pakdemirli M., and Ozkaya E. Transition behavior from string to beam for an axially accelerating material. Journal of Sound and Vibration 215 3 (1994) 517-578
10. Stylianou M., and Tabarrok B. Finite element analysis of an axially moving beam, Part II: stability analysis. Journal of Sound and Vibration 178 (1994) 455-481
11. Oz H.R., and Pakdemirli M. Vibrations of an axially moving beam with time-dependent velocity. Journal of Sound and Vibration 27 (1999) 239-257
12. Chakraborty G., Mallik A.K., and Hatwal H. Non-linear vibration of a traveling beam. International Journal of Non-linear Mechanics 34 (1999) 655-670
13. Pakdemirli M., and Ozkaya E. Approximate boundary layer solution of a moving beam problem. Mathematical and Computer Applications 2 3 (1998) 93-100
14. Parker R.G. Supercritical speed stability of the trivial equilibrium of an axially-moving string on an elastic foundation. Journal of Sound and Vibration 221 2 (1999) 205-219
15. Pellicano F., and Zirilli F. Boundary layers and non-linear vibrations in an axially moving beam. International Journal of Non-linear Mechanics 33 4 (1998) 691-711
16. Oz H.R., Pakdemirli M., and Boyaci H. Non-linear vibrations and stability of an axially moving beam with time-dependent velocity. International Journal of Non-linear Mechanics 36 (2001) 107-115
17. Chen L.Q., Zhang N.H., and Zu J.W. Bifurcation and chaos of an axially moving viscoelastic string. Mechanics Research Communications 29 (2002) 81-90
18. Shin C., Chung J., and Kim W. Dynamic characteristics of the out-of-plane vibration for an axially moving membrane. Journal of Sound and Vibration 286 (2005) 1019-1031
19. Chen L.Q., Zhabo W.J., and Zu J.W. Simulation of transverse vibrations of an axially moving string: a modified difference approach. Applied Mathematics and Computation 166 (2005) 596-607
20. Zhang N.H., and Chen L.Q. Non-linear dynamical analysis of axially moving viscoelastic string. Chaos, Solitons and Fractals 24 (2005) 1065-1074
21. Chen L.Q., and Zhao W.J. A conserved quantity and the stability of axially moving non-linear beams. Journal of Sound and Vibration 286 (2005) 663-668
22. Chen L.Q., and Yang X.D. Steady state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models. International Journal of Solid and Structures 42 (2005) 37-50
23. Kartik A., and Wickert J.A. Vibration and guiding of moving media with edge wave imperfections. Journal of Sound and Vibration 291 (2006) 419-436
24. Sze K.Y., Chen S.H., and Huang J.L. The incremental harmonic balance method for nonlinear vibration of axially moving beams. Journal of Sound and Vibration 281 (2005) 611-626
25. Ribeiro P., and Manoach E. The effect of temperature on the large amplitude vibrations of curved beams. Journal of Sound and Vibration 285 (2005) 1093-1107
26. Avsec J., and Oblak M. Thermal vibrational analysis for simply supported beam and clamped beam. Journal of Sound and Vibration 308 (2007) 514-525
27. Boresi A.P., and Sidebottom O.M. Advanced mechanics of materials (1985), Wiley, New York
28. Ghayesh M.H., and Khadem S.E. Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation. Structural Engineering and Mechanics, International Journal 27 1 (2007) 17-32
29. 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
30. Thomsen J.J. Vibrations and stability (2003), Germany, Springer
31. Nayfeh A.H. Problems in perturbation (1993), Wiley, New York
32. Nayfeh A.H., and Mook D.T. Nonlinear oscillation (1979), Wiley, New York
33. Nayfeh A.H. Introduction to perturbation techniques (1981), Wiley, New York
34. Nayfeh A.H., and Pai P.F. Linear and non-linear structural mechanics (2004), Wiley, New York