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Abstrakty
This study investigates forced nonlinear vibrations of a simply supported Euler-Bernoulli beam on a nonlinear elastic foundation with quadratic and cubic nonlinearities. Applying the homotopy analysis method (HAM) to the spatially discretized governing equation, we derive novel analytical solutions and discuss their convergence to present nonlinear frequency responses with varying contributions of the nonlinearity coefficients. A comparison with numerical solutions is conducted and nonlinear time responses and phase planes are compared to the results from linear beam theory. The study demonstrates that apart from nonlinear problems of free vibrations, HAM is equally capable of solving strongly nonlinear problems of forced vibrations.
Czasopismo
Rocznik
Tom
Strony
1219--1230
Opis fizyczny
Bibliogr. 24 poz., rys., tab.
Twórcy
autor
- Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil
autor
- Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil
autor
- Aeronautics Institute of Technology, ITA, São José dos Campos, Brazil
Bibliografia
- 1. Abbasbandy S., Shivanian E., 2011, Predictor homotopy analysis method and its application to some nonlinear problems, Communications in Nonlinear Science and Numerical Simulation, 16, 2456-2468
- 2. Abe A., 2006, On non-linear vibration analyses of continuous systems with quadratic and cubic non-linearities, International Journal of Non-Linear Mechanics, 41, 873-879
- 3. Abe A., Kobayashi Y., Yamada G., 1998a, Analysis of subharmonic resonance of moderately thick antisymmetric angle-ply laminated plates by using method of multiple scales, Journal of Sound and Vibration, 217, 467-484
- 4. Abe A., Kobayashi Y., Yamada G., 1998b, Internal resonance of rectangular laminated plates with degenerate modes, JSME International Journal, Series C, 41, 718-726
- 5. Abe A., Kobayashi Y., Yamada G., 1998c, Two-mode response of simply supported, rectangular laminated plates, International Journal of Non-Linear Mechanics, 33, 675-690
- 6. Abe A., Kobayashi Y., Yamada G., 2000, Non-linear vibration characteristics of clamped laminated shallow shells, Journal of Sound and Vibration, 234, 405-426
- 7. Hoseini S.H., Pirpodaghi T., Asghari M., Farrahi G.H., Ahmadian M.T., 2008, Nonlinear free vibration of conservative oscillators with inertia and static type cubic nonlinearities using homotopy analysis method, Journal of Sound and Vibration, 316, 263-273
- 8. Liao S.J., 1992, Proposed homotopy analysis techniques for the solution of nonlinear problems, Ph.D. Dissertation, Shanghai Jiao Tong University, Shanghai
- 9. Liao S.J., 1995, An approximate solution technique which does not depend upon small parameters: a special example, International Journal of Non-Linear Mechanics, 30, 371-380
- 10. Liao S.J., 2003, Beyond Perturbation: Introduction to Homotopy Analysis Method, Chapman & Hall/CRC Press, Boca Raton
- 11. Liao S.J., 2004, On the homotopy analysis method for nonlinear problems, Applied Mathematics and Computation, 147, 499-513
- 12. Liao S.J., 2009, Notes on the homotopy analysis method: some definitions and theorems, Communications in Nonlinear Science and Simulation, 14, 983-997
- 13. Liao S.J., 2012, Homotopy Analysis Method in Nonlinear Differential Equations, Springer Education Press, Heidelberg
- 14. Liao S.J., Cheung A.T., 1998, Application of homotopy analysis method in nonlinear oscillations, Journal of Applied Mechanics, 65, 914-922
- 15. Liao S.J., Tan Y., 2007, A general approach to obtain series solutions of nonlinear differential equations, Studies in Applied Mathematics, 119, 297-355
- 16. Mastroberardino A., 2011, Homotopy analysis method applied to electrohydrodynamic flow, Communications in Nonlinear Science and Numerical Simulation, 16, 2730-2736
- 17. Mehrizi A.A., Vazifeshenas Y., Domairry G., 2012, New analysis of natural convection boundary layer flow on a horizontal plate with variable wall temperature, Journal of Theoretical and Applied Mechanics, 50, 4, 1001-1010
- 18. Mohammadpour A., Rokni E., Fooladi M., Kimiaeifar A., 2012, Bernoulli-Euler beams under different boundary conditions with non-linear Winkler type foundation, Journal of Theoretical and Applied Mechanics, 50, 2, 339-355
- 19. Mustafa M., Hayat T., Hendi A.A., 2012, Influence of melting heat transfer in the stagnationpoint flow of a Jeffrey fluid in the presence of viscous dissipation, Journal of Applied Mechanics, 79, 2, 4501-4505
- 20. Nayfeh A.H., Mook D.T., 1979, Nonlinear Oscillations, Wiley, New York
- 21. Pirbodaghi T., Ahmadian M.T., Fesanghary M., 2009, On the homotopy analysis method for non-linear vibration of beams, Mechanics Research Communications, 36, 143-148
- 22. Ray S.S., Sahoo S., 2015, Traveling wave solutions to Riesz time-fractional Camassa-Holm equation in modeling for shallow-water waves, Journal of Computational and Nonlinear Dynamics, 10, 6, 1026-1030
- 23. Sedighi H.M., Shirazi K.H., Zare J., 2012, An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method, International Journal of Non-Linear Mechanics, 47, 777-784
- 24. Wen J., Cao Z., 2007, Sub-harmonic resonances of nonlinear oscillations with parametric excitation by means of the homotopy analysis method, Physics Letters A, 371, 427-431
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-65aa5961-e2bb-4c49-967f-feee29db3477