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Transversal forced vibrations of an axially moving sandwich belt system

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Abstract

Based on the author’s previously published results for transversal free vibrations of axially moving sandwich belts described by coupled partial differential equations, which are derived and analytically solved, this paper contains new analytical results, for forced vibrations of the same system excited by transversal external excitation. The transversal forced vibrations of the axially moving sandwich belts are described by the coupled partial nonhomogeneous differential equations. The partial differential equations are analytically solved. Bernoulli’s method of particular integrals and Lagrange’s method of the variations of the constants are used.

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References

  1. Abrate S. (1992). Vibrations of belts and belt drives. Mech. Mach. Theory 27(6): 645–659

    Article  Google Scholar 

  2. Archibald F.R. and Emslie A.G. (1958). The vibration of a string having a uniform motion along its length. Appl. Mech. 25: 347–348

    MATH  Google Scholar 

  3. Chen L.Q., Zaho W.J. and Zu J.W. (2004). Transient responses of an axially accelerating viscoelastic string constituted by fractional differentiation low. J. Sound Vib. 278: 861–871

    Article  Google Scholar 

  4. Hedrih (Stevanović), K.: Transversal Vibrations of Double-Plate Systems. Acta Mechanica Sinica, vol. 22, pp. 487–501. Springer, Heidelberg (hard cower and on line) (2006)

  5. Hedrih (Stevanović), K.: Modes of the Homogeneous Chain Dynamics. Signal Processing, vol. 86, pp. 2678–2702. Elsevier, Amsterdam. ISSN: 0165–1684 www.sciencedirect.com/science/journal/01651684

  6. Hedrih (Stevanović), K.: Transversal Vibrations of the Axially Moving Sandwich Belts. Arch. Appl. Mech. 77, 523–539 (2007). doi:10.1007/s00419-006-0105-x

  7. Hedrih (Stevanović), K.: Vibration Modes of an Axially Moving Double Belt System with Creep Layer. Journal Vibration and Control, Sage, New York (invited and accepted) (2006). http://www.sagepub.com/journal.aspx?pid=258

  8. Hedrih (Stevanović), K.: Eigen Amplitude Vectors and Functions Extended Orthogonality of Small Oscillations Mixed Systems of the Coupled Discrete and Continuous Subsystems. Facta Universitatis, Series Mechanics, Automatic Control and Robotics, vol. 4, No. 17, pp. 225–243. YU ISSN 0534-2009. UDC 534.1:534.012:534.013 (2005). http://facta.junis.ni.ac.yu/facta/macar/macar200501/macar200501-04.html

  9. Hedrih (Stevanović), K.: The Frequency Equation Theorems of Small Oscillations of a Hybrid System Containing Coupled Discrete and Continuous Subsystems. Facta Universitatis, Series Mechanics, Automatic Control and Robotics, vol. 5, No. 1, pp. 25–41. UDC 534.1:534.012:534.013 (2006). http://facta.junis.ni.ac.yu/facta/

  10. Hedrih (Stevanović), K.: Transversal Vibrations of the Axially Moving Double Belt System with Creep Layer, Preprints, 2nd IFAC Workshop on Fractional Differentiation and its Applications, 19–21 July, 2006, Porto, Portugal, pp. 230–235. +CD. IFAC WS 2006 0007 PT, ISBN 972-8688-42-3, 978-972-8688-42-4. ISBN, http://www.iser.ipp.pl (2006)

  11. Hoffmann N. and Gaul L. (2004). A sufficient criterion for the onset of sprag-slip oscillations. Arch. Appl. Mech. 73: 650–660

    Article  MATH  Google Scholar 

  12. Jakšić, N., Boltežar, M.: Viscously damped transverse vibrations of a moving string, Journal of Mechanical Engineering, Strojniški vestnik, pp. 560–569 (2005)

  13. Janković, V.S., Potić, V.P., Hedrih (Stevanović), K.: Parcijalne diferencijalne jednačine i integralne jednačine sa primenama u inženjerstvu (Partial differential equations and integro-differential equations with examples in engineering), Univerzitet u Nišu, str. 347 (1999) (in Serbian)

  14. Lia Y., Dan A. and Christopher D.R. (2002). Adaptive vibration isolation for axiallymoving strings: theory and experiment. Automatica 38: 379–390

    Article  Google Scholar 

  15. Lodewijks, G.: Dynamics of belt systems. Ph.D. Thesis, Delft Universiteitsdrukkerij TU Delft, Delft (1996)

  16. Moon J. and Wickert J.A. (1997). Nonlinear vibration of power transsmition belts. J. Sound Vib. 200: 419–431

    Article  Google Scholar 

  17. Mote C.D. Jr. (1968). Dynamic stability of an axially moving band. J. Franklin Inst. 285(5): 329–346

    Article  MATH  Google Scholar 

  18. Pakdemirli H.R.O.z.M. (1999). Vibrations of axially moving beam with time-dependent velocity. J. Sound Vib. 227(2): 239–257

    Article  MathSciNet  Google Scholar 

  19. Pakdemirli N., Ulsoy A.G. and Ceranoglu A. (1994). Transverse vibration of an axially accelerating string. J. Sound Vib. 169(2): 179–196

    Article  MATH  Google Scholar 

  20. Pausch, M., Pfeiffer, F.: Nonlinear dynamics of chain drive CVT. In: Chien, W.(eds.) Proceedings of the 3rd International Conference on Nonlinear Mechanics, Shanhai, pp. 336–341 (1998)

  21. Pfeiffer, F.: Nonlinear chain dynamics. In: Chien, W. (eds.) Proceedings of the 3rd International Conference on Nonlinear Mechanics, Shanhai, pp. 342–346

  22. Rašković, D.: Teorija oscilacija (Theory of Oscillations), Naučna knjiga, p. 503 (1965) (in Serbian)

  23. Rega G. (2004). Nonlinear vibrations of suspended cables—Part I: Modeling and analysis. ASME Appl. Mech. Rev. 57(6): 443–478

    Article  Google Scholar 

  24. Rega G. (2004). Nonlinear vibrations of suspended cables—Part II: Deterministic phenomena. ASME Appl. Mech. Rev. 57(6): 479–514

    Article  Google Scholar 

  25. Sack R.A. (1954). Transverse oscillations in travelling strings. Br. J. Appl. Phys. 5: 224–226

    Article  Google Scholar 

  26. Suweken G. and Van Horssen W.T. (2000). On the transversal vibrations of a conveyor belt. Math. J. Indones. Math. Soc. 6(5): 427–433

    Google Scholar 

  27. Suweken G. and Van Horssen W.T. (2003). On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part I: the beam-like case. J. Sound Vib. 264(118): 117–133

    Article  Google Scholar 

  28. Suweken G. and Van Horssen W.T. (2003). On the transversal vibrations of a conveyor belt with a low and time-varying velocity. Part II: the beam-like case. J. Sound Vib. 267: 1007–1027

    Article  Google Scholar 

  29. Wasfy, T.M., Leamy, M.J.: Effect of bending stiffness on the dynamic and stead-state responses of belt-drives. In: Proceedings of the ASME 2000 Design Engineering Technical Conferences, Montreal, Canada, 29 September–2 October (2002)

  30. Wickert J.A. and Mote C.D. (1989). On the energetic analysis of axially moving continua. J. Acoust. Soc. Am. 85(1): 1365–1368

    Article  Google Scholar 

  31. Wickert J.A. and Mote C.D. (1990). Classical vibrations of an axially moving continua. Trans. ASME J. Appl. Mech. 57: 738–744

    Article  MATH  Google Scholar 

  32. Wickert J.A. (1992). Nonlinear vibration of a traveling tensioned beam. Int. J. Nonlinear Mech. 273(3): 503–517

    Article  Google Scholar 

  33. Zhang, L., Zu Jean, W.: Nonlinear forcedvibrations of viscoelastic moving belts. In: Chien, W. (eds.) Proceedings of the 3rd International Conference on Nonlinear Mechanics, Shanhai, pp. 748–753 (1998)

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  1. Faculty of Mechanical Engineering, University of Niš, Mathematical Institute SANU, ul. Vojvode Tankosića 3/22, 18 000, Nis, Serbia

    Katica (Stevanović) Hedrih

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(Stevanović) Hedrih, K. Transversal forced vibrations of an axially moving sandwich belt system. Arch Appl Mech 78, 725–735 (2008). https://doi.org/10.1007/s00419-007-0187-0

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