Nonlinear vibration analysis of axially moving strings in thermal environment

Document Type : Research Article

Authors

1 bProfessor of Mechanical Engineering , Isfahan University of Technology, Isfahan

2 M.S.c. Student, Mechanical Engineering Department, Isfahan University of Technology, Isfahan

3 Assistant Professor of Mechanical Engineering , Isfahan University of Technology, Isfahan

Abstract

In this study, nonlinear vibration of axially moving strings in thermal environment is investigated. The vibration haracteristics of the system such as natural frequencies, time domain response and stability states are studied at different temperatures. The velocity of the axial movement is assumed to be constant with minor harmonic variations. It is presumed that the system and the environment are in thermal equilibrium. Using Hamilton’s principle, the system equation of motion, and t[1]he boundary conditions are derived and then solved by applying Multiple Time Scales (MTS) method. The effect of temperature on the vibration characteristics of the system such as linear and nonlinear natural frequencies, stability, and critical speeds is investigated. Considering ideal and non-ideal boundary conditions for the supports, nonlinear vibration of the system is discussed for three different excitation frequencies. The bifurcation diagrams for ideal and non-ideal boundary conditions are presented under the influence of temperature at various speeds.

Highlights

• Nonlinear vibration of axially moving strings in thermal environment is investigated.

• Ideal and non-ideal boundary conditions for the supports is considered.

• With ideal boundary conditions, bifurcation phenomenon always occurs.

• Natural frequencies and critical speeds decrease if the temperature increases.

Keywords

Main Subjects


[1] R. Sack, Transverse oscillations in travelling strings, British Journal of Applied Physics, 5 (1954) 224.
[2] F.R. Archibald, A. Emslie, The vibration of a string having a uniform motion along its length, Journal of Applied Mechanics, 25 (1958) 347-348.
[3] W.L. Miranker, The wave equation in a medium in motion, IBM Journal of Research and Development, 4 (1960) 36-42.
[4] C. Mote, Stability of systems transporting accelerating axially moving materials, Journal of Dynamic Systems, Measurement, and Control, 97 (1975) 96-98.
[5] A. Ulsoy, C. Mote, Vibration of wide band saw blades, Journal of Engineering for Industry, 104 (1982) 71-78.
[6] M. Pakdemirli, A.G. Ulsoy, A. Ceranoglu, Transverse vibration of an axially accelerating string, (1994).
[7] R.-F. Fung, J.-S. Huang, Y.-C. Chen, The transient amplitude of the viscoelastic travelling string: an integral constitutive law, Journal of Sound and Vibration, 201 (1997) 153-167.
[8] R.-F. Fung, J.-S. Huang, Y.-C. Chen, C.-M. Yao, Nonlinear dynamic analysis of the viscoelastic string with a harmonically varying transport speed, Computers & Structures, 66 (1998) 777-784.
[9] L.-Q. Chen, H. Chen, Asymptotic analysis on nonlinear vibration of axially accelerating viscoelastic strings with the standard linear solid model, Journal of Engineering Mathematics, 67 (2010) 205-218.
[10] M.H. Ghayesh, Nonlinear transversal vibration and stability of an axially moving viscoelastic string supported by a partial viscoelastic guide, Journal of Sound and Vibration, 314 (2008) 757-774.
[11] E.M. Mockensturm, J. Guo, Nonlinear vibration of parametrically excited, viscoelastic, axially moving strings, Journal of Applied Mechanics, 72 (2005) 374-380.
[12] L.-Q. Chen, N.-H. Zhang, J.W. Zu, Bifurcation and chaos of an axially moving viscoelastic string, Mechanics Research Communications, 29 (2002) 81-90.
[13] L. Zhang, J. Zu, Nonlinear vibration of parametrically excited moving belts, part I: dynamic response, Journal of Applied Mechanics, 66 (1999) 396-402.
[14] L.-Q. Chen, W. Zhang, J.W. Zu, Nonlinear dynamics for transverse motion of axially moving strings, Chaos, Solitons & Fractals, 40 (2009) 78-90.
[15] M. Lepidi, V. Gattulli, Static and dynamic response of elastic suspended cables with thermal effects, International Journal of Solids and Structures, 49 (2012) 1103-1116.
[16] A. Yurddaş, E. Özkaya, H. Boyacı, Nonlinear vibrations of axially moving multi-supported strings having non-ideal support conditions, Nonlinear Dynamics, 73 (2013) 1223-1244.
[17] K. Marynowski, T. Kapitaniak, Dynamics of axially moving continua, International Journal of Mechanical Sciences, 81 (2014) 26-41.
[18] R.A. Malookani, W.T. van Horssen, On resonances and the applicability of Galerkin׳ s truncation method for an axially moving string with time-varying velocity, Journal of Sound and Vibration, 344 (2015) 1-17.
[19] X.-D. Yang, H. Wu, Y.-J. Qian, W. Zhang, C.W. Lim, Nonlinear vibration analysis of axially moving strings based on gyroscopic modes decoupling, Journal of Sound and Vibration, 393 (2017) 308-320.
[20] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.