Nonlinear vibration analysis of prebuckling and postbuckling in laminated composite beams

• Autorzy: Abdollahzadeh G. , Ahmadi M.

Identyfikatory

DOI

10.1515/ace-2015-0020

Warianty tytułu

PL

Analiza drgań nieliniowych przed i po wyboczeniu laminowanych belek kompozytowych

• Języki publikacji: EN

Abstrakty

EN

In this study, we attempt to analyse free nonlinear vibrations of buckling in laminated composite beams. Two new methods are applied to obtain the analytical solution of the nonlinear governing equation of the problem. The effects of different parameters on the ratio of nonlinear to linear natural frequencies of the beams are studied. These methods give us an agreement with numerical results for the whole range of the oscillation amplitude.

PL

Niniejsze opracowanie podejmuje temat analizy swobodnych drgań nieliniowych wyboczenia laminowanych belek kompozytowych. Zastosowano dwie nowe metody w celu uzyskania rozwiązania w postaci kluczowego równania nieliniowego, opisującego ten problem. Przestudiowano wpływ różnych parametrów na stosunek częstotliwości drgań nieliniowych do drgań liniowych w odniesieniu do badanych belek. Metody te umożliwiły nam weryfikację otrzymanych wyników dla całego zakresu amplitudy oscylacji.

Słowa kluczowe

EN

nonlinear vibration; composite beam; analytical method; buckling

PL

drgania nieliniowe; belka kompozytowa; metoda analityczna; wyboczenie

• Wydawca: Komitet Inżynierii Lądowej i Wodnej PAN ; Politechnika Warszawska, Wydział Inżynierii Lądowej
• Czasopismo: Archives of Civil Engineering
• Rocznik: 2015
• Tom: Vol. 61, nr 2
• Strony: 161--178
• Opis fizyczny: Bibliogr. 32 poz., il.

Twórcy

autor

Abdollahzadeh G.

• Faculty of Civil Engineering, Babol University of Technology, Babol, Iran

autor

Ahmadi M.

• Department of Civil Engineering, Aryan Institute of Science and Technology, Babol, Iran

Bibliografia

• 1. M. I. Qaisi, Application of the harmonic balance principle to the nonlinear free vibration of beams, Appl. Acoust. 40 (1993) 141–51.
• 2. Q. Guo, H. Zhong, Nonlinear vibration analysis of beams by a spline-based differential quadrature method. J. Sound. Vib. 269 (2004) 413–20.
• 3. W. C. Xie, H. P. Lee, S. P. Lin, Normal modes of a nonlinear clamped–clamped beam. J. Sound. Vib. 250(2) (2002) 339–49.
• 4. A. H. Nayfeh, S. A. Nayfeh, Nonlinear normal modes of a continuous system with quadratic nonlinearities. J. Vib. Acoust. Trans. ASME. 117(2) (1995) 199–205.
• 5. G. R. Bhashyam, G. Prathap, Galerkin finite element method for nonlinear beam vibrations. J. Sound. Vib. 72 (1980) 91–203.
• 6. E. N. M. Carlos, E. S. S. Ma’rio, G. P. B. Odulpho, Nonlinear normal modes of a simply supported beam: continuous system and finite element models. Comput. Struct. 82 (2004) 2683–91.
• 7. L. Azrar, R. Benamar, R. G. White, A semi-analytical approach to the nonlinear dynamic response problem of S–S and C–C beams at large vibration amplitudes Part I: general theory and application to the single mode approach to free and forced vibration analysis. J. Sound. Vib. 224 (1999) 183–207.
• 8. R. K. Gupta, B. G. Jagadish, G. R. Janardhan, G. Rao, Relatively simple finite element formulation for the large amplitude free vibrations of uniform beams. Finite. Elem. Anal. Des. 2009;45:624–31.
• 9. R. K. Kapania, S. Raciti, Nonlinear vibrations of unsymmetrically laminated beams. AIAA. J. 27 (1989) 201–10.
• 10. G. Singh, G. Rao, N. G. R. Iyengar, Analysis of the nonlinear vibrations of unsymmetrically laminated composite beams. AIAA. J. 29(10) (1991) 1727–35.
• 11. M. Ganapathi, B. P. Patel, J. Saravanan, M. Touratier, Application of spline element for large-amplitude free vibrations. Composites. Part. B. 29 (1998) 1–8.
• 12. P. Malekzadeh, A. R. Vosoughi, DQM Large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges. Commun. Nonlinear. Sci. Numer. Simulat. 14 (2009) 906–15.
• 13. M. Kisa, Free vibration analysis of a cantilever composite beam with multiple cracks. Compos. Sci. Technol. 64(9) (2004) 1391-1402
• 14. M. Arvin, M. Sadighi, A. R. Ohadi, A numerical study of free and forced vibration of composite sandwich beam with viscoelastic core. Compos. Struct. 92(4) (2010) 996-1008.
• 15. C. Lee, H. Zhuo, C. Hsu, Lateral vibration of a composite stepped beam consisted of SMA helical spring based on equivalent Euler–Bernoulli beam theory, J. Sound. Vib. 324 (2009) 179-193.
• 16. H. J. He, Homotopy Perturbation technique. Comput. Method. Appl. M. 178 (1999) 257–262.
• 17. M. Bayat, I. Pakar, A. Emadi, Vibration of electrostatically actuated microbeam by means of homotopy perturbation method. Struct. Eng. mech. 48(6) (2013) 823-831.
• 18. J. H. He, Preliminary report on the energy balance for nonlinear oscillations. Mech. Res. Commun. 29 (2002) 107–111.
• 19. J. H. He, Max–min approach to nonlinear oscillators. Int. J. Non. Sci. Num. 9(2) (2008a) 207–210.
• 20. J. H. He, An improved amplitude–frequency formulation for nonlinear oscillators. Int. J. Non. Sci. Num. 9(2) (2008b) 211–212.
• 21. Pakar, M. Bayat, Vibration analysis of high nonlinear oscillators using accurate approximate methods. Struct. Eng. Mech. 46(1) (2013) 137-151.
• 22. H. He, Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B. 20(10) (2006) 1141–1199.
• 23. H. He, Variational Approach for nonlinear oscillators. Chaos. Soliton. Fract. 34 (2007) 1430–1439.
• 24. J. H. He, Hamiltonian Approach to nonlinear oscillators. Phys. Lett. A. 374 (2010a) 2312–2314.
• 25. Ahmadi, G. Hashemi, A. Asghari, Application of iteration perturbation method and Hamiltonian approach for nonlinear vibration of Euler-Bernoulli beams, Lat. Am. J. Solids. Struct, 11(6) (2014) 1049–1062.
• 26. Bayat, I. Pakar, Accurate analytical solution for nonlinear free vibration of beams. Struct. Eng. Mech. 43(3), 2012, 337-347.
• 27. J. H. He, G. C. Wu, F. Austin, The variational iteration method which should be followed. Nonlinear. Sci. Lett. A. 1(1) (2010b), 1–30.
• 28. S. A. Emam, A. H. Nayfeh, Postbuckling and free vibration of composite beams. Compos. Struct. (2009) 88:636–42.
• 29. W. Hyer, Stress Analysis of Fiber-Reinforced Composite Materials. (McGraw- Hill; 1998).
• 30. S. A. Emam, Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling. Compos. Struct. 100 (2013) 186-194.
• 31. L. Ke, J. Yang, S. Kitipornchai, An analytical study on the nonlinear vibration of functionally graded beams. Meccanica. 45(6) (2010) 743-752.
• 32. S. S. Ganji, S. Karimpour, D. D. Ganji, Z. Z. Ganji, Periodic solution for strongly nonlinear vibration systems by energy balance method, Acta Appl. Math. 106(1) (2009) 79-92.