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Three-to-one internal resonances in a curved beam resting on an elastic foundation

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Języki publikacji
EN
Abstrakty
EN
Transverse vibrations of curved beams are investigated. Different curvatures are considered. The beam is simply supported and resting on a nonlinear elastic foundation. The method of multiple scales is used in the analysis. A three-to-one internal resonance case is studied. It is possible when one of the mode numbers is three times the other mode. Amplitude and phase modulation equations are obtained. Steady state solutions and stability are discussed. A three-to-one internal resonance is possible for all types of curvatures under the assumptions in the article.
Rocznik
Strony
667--678
Opis fizyczny
Bibliogr. 21 poz., tab., wykr.
Twórcy
autor
  • Department of Mechanical Engineering, University of Gaziantep, Gaziantep, 27310, TURKEY
autor
  • Department of Mechanical Engineering, Celal Bayar University, Manisa, 45140, TURKEY
Bibliografia
  • [1] Bi Q. and Dai H.H. (2000): Analysis of non-linear dynamics and bifurcations of a shallow arch subjected to periodic excitation with internal resonance. - Journal of Sound and Vibration, vol.233, No.4, pp.557-57l.
  • [2] Boyaci H. and Pakdemirli M. (1997): A comparison of different versions of the method of multiple scales for partial differential equations. - Journal of Sound and Vibration, vol.204, pp.595-607.
  • [3] Lacarbonara W. (1999): Direct treatment and discretizations of non-linear spatially continuous systems. - Journal of Sound and Vibration, vol.221, pp.849-866.
  • [4] Nayfeh A.H. (1981): Introduction to Perturbation Techniques. - New York: Wiley-Interscience.
  • [5] Nayfeh A.H. (1998): Reduced order models of weakly nonlinear spatially continuous systems. - Nonlinear Dynamics, vol.l6, pp.105-125.
  • [6] Nayfeh A.H. and Mook D.T. (1979): Nonlinear Oscillations. - New York: John Wiley.
  • [7] Oz H.R., Pakdernirli M., Ozkaya E. and Yilmaz M. (1998): Non-linear vibrations of a slightly curved beam resting on a non-linear elastic foundation. - Journal of Sound and Vibration, vol.212, No.2, pp.295-309.
  • [8] Pakdemirli M. (1994): A comparison of two perturbation methods for vibrations of systems with quadratic and cubic nonlinearities. - Mechanics Research Communications, vol.21, pp.203-208.
  • [9] Pakdemirli M. and Boyaci H. (1995): Comparison of direct-perturbation methods with discretization-perturbation methods for nonlinear vibrations. - Journal of Sound and Vibration, vol.186, pp.837-845.
  • [10] Pakdemirli M. and Boyaci H. (1996): Vibrations of continuous systems having arbitrary quadratic and cubic nonlinearities. - Applied Mechanics and Engineering, vol. l , pp.445-463.
  • [11] Pakdemirli M., Boyaci H. and Yilmaz M. (1997): Continuous systems with odd nonlinearities: A general solution procedure. - Mathematical and Computational Applications, vol.2, pp.85-90.
  • [12] Pakdemirli M. and Boyaci H. (1997): A generalized approach to coupled nonlinear vibrations of continuous systems. - Mathematical and Computational Applications, vol.2, pp.141-154.
  • [13] Pakdemirli M., Boyaci H. (1999): A comparison of different versions of the method of multiple scales for an arbitrary model of odd nonlinearities. - Mathematical and Computational Applications, vol.4, pp.273-282.
  • [14] Pakdemirli M. (2001a): Vibrations of continuous systems with a general operator notation suitable for perturbative calculations. - Journal of Sound and Vibration, vol.246, pp.841-851.
  • [15] Pakdemirli M. (200lb): A general solution procedure for coupled systems with arbitrary internal resonances. - Mechanics Research Communications, vol.28, pp.617 -622.
  • [16] Pakdemirli M. and Ozkaya E. (2003): Three-to-one internal resonance in a general cubic nonlinear continuous system. - Journal of Sound and Vibration, vol.268, pp.543-553.
  • [17] Rehfield L.W. (1974): Nonlinear flexural oscillations of shallow arches. - AIAA Journal, vol.l2, pp.91-93.
  • [18] Singh P.N. and Ali S.M.J. (1975): Nonlinear vibration of a moderately thick shallow clamped arch. - Journal of Sound and Vibration, vol.41, pp.275-282.
  • [19] Tien W.-M., Sri Namachchivaya N. and Bajaj A.K. (1994a): Non-linear dynamics of a shallow arch under periodic excitation-I. 1:2 internal resonance. - International Journal of Non-linear Mechanics, vol.29, pp.349-366.
  • [20] Tien W.-M., Sri Namachchivaya N. and Bajaj A.K. (l994b): Non-linear dynamics of a shallow arch under periodic excitation-II. 1 : 1 internal resonance. – International Journal of Nonlinear Mechanies, vol.29, pp.367-386.
  • [21] Yamaki N. and Mori A. (1980): Nonlinear vibrations of a clamped beam with initial deflection and initial axial displacement, Part 1: Theory. - Journal of Sound and Vibration, vol.71, pp.333-346.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ2-0015-0018
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