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Warianty tytułu
Analityczne rozwiązania problemu drgań swobodnych belek umieszczonych na sprężystym podłożu wyznaczone za pomocą iteracyjnej metody wariacyjnej
Języki publikacji
Abstrakty
Closed form expressions are obtained for the dynamic response of an elastic beam rested on a nonlinear foundation in this paper. The nonlinear governing equation is solved using the Variational Iteration Method (VIM). An iteration formulation is constructed based on the VIM and the dynamic responses are then obtained. Frequency responses are presented in a closed form and their sensitivity with respect to the initial amplitudes are investigated. A number of numerical simulations are then carried out and performance and validity of the solution procedure is evaluated in the time domain. It is proved that the VIM is quite a reliable and straightforward technique to solve the corresponding set of coupled nonlinear differential equations.
W pracy przedstawiono zamknięte formy rozwiązań opisujących odpowiedź dynamiczną elastycznej belki spoczywającej na nieliniowo sprężystym podłożu. Równanie ruchu rozwiązano przy pomocy iteracyjnej metody wariacyjnej (VIM). Sformułowanie iteracyjne skonstruowane w oparciu o tę metodę pozwoliło na wyznaczenie odpowiedzi dynamicznej belki. Charakterystyki częstościowe przedstawiono w zamkniętej formie i podkreślono ich wrażliwość na wartość amplitud początkowych. Następnie zaprezentowano wyniki kilku symulacji numerycznych w celu oszacowania wydajności i dokładności zastosowanej procedury rozwiązywania równań ruchu w dziedzinie czasu. Wykazano, że metoda VIM jest wystarczająco prosta i wiarygodna w rozwiązywaniu układu sprzężonych, nieliniowych równań różniczkowych.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
639--652
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
autor
autor
- Center of Excellence in Railway Transportation, School of Railway Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran, younesian@iust.ac.ir
Bibliografia
- 1. Ansari M., Esmailzadeh E., Younesian D., 2010, Internal-external resonance of beams on non-linear viscoelastic foundation traversed by moving load, Nonlinear Dynamics, 61, 163-182
- 2. Ansari M., Esmailzadeh E., Younesian D., 2011, Frequency analysis of finite beams on nonlinear Kelvin-Voight foundation under moving loads, Journal of Sound and Vibration, 330, 1455-1471
- 3. Askari H., KalamiYazdi M., SaadatNia Z., 2010, Frequency analysis of nonlinear oscillators with rational restoring force via He’s energy balance method and He’s variational approach, Nonlinear Science Letters A, 1, 425-430
- 4. Baghani M., Jafari-Talookolaei R.A., Salarieh H., 2011, Large amplitudes free vibrations and post-buckling analysis of unsymmetrically laminated composite beams on nonlinear elastic foundation, Applied Mathematical Modelling, 35, 130-138
- 5. Bogacz R., Czyczula W., 2008, Response of beam on visco-elastic foundation to moving distributed load, Journal of Theoretical and Applied Mechanics, 46, 763-775
- 6. Bogacz R., Frischmuth K., 2009, Vibration in sets of beams and plates induced by traveling loads, Archive of Applied Mechanics, 79, 509-516
- 7. Kargarnovin M.H., Younesian D., Thompson D.J., Jones C.J.C., 2005, Response of beams on nonlinear viscoelastic foundations to harmonic moving loads, Computers and Structures, 83, 1865-1877
- 8. He J.H., 2000, Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation, 114, 115-123
- 9. He J.H., Wu G.C., Austin F., 2010, The variational iteration method which should be followed, Nonlinear Science Letters A, 1, 1-30
- 10. Inan A., Yildirim A., 2010, Comparison between variational iteration method and homotopy perturbation method for linear and nonlinear partial differential equations with the nonhomogeneous initial conditions, Numerical Methods for Partial Differential Equations, 26, 1581-1593
- 11. Jafari-Talookolaei R.A., Salarieh H., Kargarnovin M.H., 2011, Analysis of large amplitude free vibrations of unsymmetrically laminated composite beams on a nonlinear elastic foundation, Acta Mech., 219, 6575, DOI 10.1007/s00707-010-0439-x
- 12. Malekzadeh P., Vosoughi A.R., 2009, DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges, Communications in Nonlinear Science and Numerical Simulation, 14, 906-915
- 13. Nayfeh A.H., 2000, Nonlinear Interactions, First ed. New York: John Wiley
- 14. Ozis T., Yildirim A., 2007, Study of nonlinear oscillators with u1/3 force by He’s variational iteration method, Journal of Sound and Vibration, 306, 372-376
- 15. Santee D.M., Goncalves P.B., 2006, Oscillations of a beam on a non-linear elastic foundation under periodic loads, Shock and Vibration, 13, 273-284
- 16. Senalp A.D., Arikoglu A., Ozkol I., Dogan V.Z., 2010, Dynamic response of a finite length Euler-Bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force, Journal of Mechanical Science and Technology, 24, 1957-1961
- 17. Wazwaz A.M., 2008, A study on linear and nonlinear Schrodinger equations by the variational iteration method, Chaos, Solitons and Fractals, 37, 1136-1142
- 18. Wazwaz A.M., 2009a, Partial Differential Equations and Solitary Waves Theory, First ed., New York: Springer
- 19. Wazwaz A.M., 2009b, The variational iteration method for analytic treatment for linear and nonlinear ODEs, Applied Mathematics and Computation, 212, 120-134
- 20. Wazwaz A.M., 2010, The variational iteration method for solving linear and nonlinear Volterra integral and integro-differential equations, International Journal of Computer Mathematics, 87, 1131-1141
- 21. Yihua M., Li Q., Hongzhi Z., Vibration analysis of Timoshenko beams on a nonlinear elastic foundation, Tsinghua Science and Technology, 14, 322-326
- 22. Yildirim A., 2010, Application of He’s variational iteration method to nonlinear integro-differential equations, Zeitschrift f¨ur Naturforschung – Section A Journal of Physical Sciences, 65, 418-422
- 23. Yildirim A., Ozis T., 2009, Solutions of Singular IVPs of Lane-Emden type by the variational iteration method, Nonlinear Analysis, Series A, Theory Methods and Applications, 70, 2480-2484
- 24. Younesian D., Askari H., SaadatNia Z., KalamiYazdi M., 2011, Frequency analysis of strongly nonlinear generalized Duffing oscillators using homotopy perturbation method and variational approach, Nonlinear Science Letters A, 2, 9-14
- 25. Younesian D., Kargarnovin M.H., Esmailzadeh E., 2008, Optimal passive vibration control of Timoshenko beams with arbitrary boundary conditions traversed by moving loads, Proceedings of the IMECHE, Part K: Journal of Multi-Body Dynamics, 229, 179-188
- 26. Younesian D., Kargarnovin M.H., Thompson D.J., Jones C.J.C., 2005, Parametrically excited vibration of a Timoshenko beam on random viscoelastic foundation subjected to a harmonic moving load, Nonlinear Dynamics, 45, 75-93
- 27. Zhang Y.S., 2002, Orthogonality conditions of the transverse vibration mode function for a stepped one-dimensional plate on a Winkler foundation and subjected to an in-plane force, Proceedings of the IMECHE, Part K: Journal of Multi-body Dynamics, 216, 271-273
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWM6-0029-0018