Large amplitude free and forced oscillations of functionally graded beams

Mechanics of Advanced Materials and Structures

Volumn 21, Issue 4, 2014, Pages 255-262

  Hosseini, Seyedeh Marzieh ^a   Mareishi, S ^b   Kalhori, Hamed ^a   Rafiee, M ^a  

^a BU ALI SINA UNIVERSITY   (Iran)

^b IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Iran)

Author keywords

forced vibration; functionally graded beam; Galerkin procedure; multiple time scales; nonlinear oscillations

Indexed keywords

EULER BERNOULLI BEAM THEORY; FORCED VIBRATION; FREE AND FORCED VIBRATIONS; FUNCTIONALLY GRADED BEAMS; GEOMETRIC NON-LINEARITY; MULTIPLE TIME SCALE; NONLINEAR OSCILLATION; POWER LAW DISTRIBUTION;

GALERKIN METHODS;

NONLINEAR EQUATIONS;

EID: 84890662871     PISSN: 15376494     EISSN: 15376532     Source Type: Journal    
DOI: 10.1080/15376494.2012.680670     Document Type: Article

References (30)

1. B.V. Sankar, An elasticity solution for functionally graded beams, Compos. Sci. Tech., vol. 61, pp. 689-696, 2001.
2. H. Zhu and B.V. Sankar, A combined Fourier series-Galerkin method for the analysis of functionally graded beams, J. Appl. Mech. Trans. ASME, vol. 71, pp. 421-424, 2004.
3. B.V. Sankar and J.T. Tzeng, Thermal stresses in functionally graded beams, AIAA J., vol. 40, pp. 1228-1232, 2002.
4. A. Chakraborty, S. Gopalakrishnan, and J.N. Reddy, A new beam finite element for the analysis of functionally graded materials, Int. J. Mech. Sci., vol. 45, pp. 519-539, 2003.
5. K. Nirmala, P.C. Upadhyay, J. Prucz, and D. Loyns, Thermoelastic stresses in composite beams with functionally graded layer, J. Reinf. Plast. Compos., vol. 24, pp. 1965-1977, 2005.
6. H.K. Ching and S.C. Yen, Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads, Compos. Part B - Eng., vol. 36, pp. 223-240, 2005.
7. H.K. Ching and S.C. Yen, Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply, Compos. Struct., vol. 73, pp. 381-393, 2006.
8. A. Chakraborty and S. Gopalakrishnan, A spectrally formulated finite element for wave propagation analysis in functionally graded beams, Int. J. Solids Struct., vol. 40, pps. 2421-2448, 2003.
9. S.Y. Oh, L. Librescu, and O. Song, Vibration of turbomachinery rotating blades made-up of functionally graded materials and operating in a high temperature field, Acta Mech., vol. 166, pp. 69-87, 2003.
10. L. Librescu, S.Y. Oh, and O. Song, Thin-walled beams made of functionally graded materials and operating in a high temperature environment: Vibration and stability, J. Therm. Stress, vol. 28, pp. 649-712, 2005.
11. C.F. Lu and W.Q. Chen, Free vibration of orthotropic functionally graded beams with various end conditions, Struct. Eng.Mech., vol. 13, pp. 1430-1437, 2005.
12. L.F. Qian andH.K.Ching, Static and dynamic analysis of 2-D functionally graded elasticity by using meshless local Petrov-Galerkin method, J. Chinese Inst. Eng., vol. 27, pp. 491-503, 2004.
13. L. Wu, Q.S. Wang, and I. Elishakoff, Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode, J. Sound Vib., vol. 284, pp. 1190-1202, 2005.
14. M. Aydogdu and V. Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Mater. Des., vol. 28, pp. 1651-1656, 2007.
15. S. Mareishi, M. Mohammadi, and M. Rafiee, An analytical study on thermally induced vibration analysis ofFGbeams using different HSDTs. Applied Mechanics and Materials, vol. 249, pp. 784-791, 2013.
16. S. Kapuria, M. Bhattacharyya, and A.N. Kumar, Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation, Compos. Struct., vol. 82, pp. 390-402, 2008.
17. Z. Zhong and T. Yu, Analytical solution of a cantilever functionally graded beam, Compos. Sci. Technol., vol. 67, pp. 481-488, 2007.
18. J. Ying, C.F. Lu, and W.Q. Chen, Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations, Compos. Struct., vol. 84, pp. 209-219, 2008.
19. X.F. Li, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams, J. Sound Vib., vol. 318, pp. 1210-1229, 2008.
20. L.L. Ke, J. Yang, and S. Kitipornchai, An analytical study on the nonlinear vibration of functionally graded beams, Meccanica, vol. 45, pp. 743-752, 2010.
21. M. Rafiee and A. Nezamabadi, Forced oscillation of simplysupported microbeams considering nonlinear effects, Int. J. Eng. Appl. Sci., vol. 3, pp. 27-41, 2011.
22. J. Yang, Y. Chen, Y. Xiang, and X.L. Jia, Free and forced vibration of cracked inhomogeneous beams under an axial force and amoving load, J. Sound Vib., vol. 312, pp. 166-181, 2008.
23. M. Simsek and T. Kocaturk, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Compos. Struct., vol. 90, pp. 465-473, 2009.
24. Y.S. Touloukian, Thermophysical Properties of High Temperature Solid Materials, Macmillian, New York, 1967.
25. A.H. Nayfeh and D.T. Mook, Nonlinear Oscillations, John Wiley, New York, 1979.
26. A.F. El-Bassiouny, On methods for continuous systems with quadratic, cubic and quantic nonlinearities, Chaos, Solitons & Fractals, vol. 39, pp. 1308-1316, 2009.
27. M.A. Foda, On non-linear free vibrations of a beam with pinned ends, J. King Saud Univ., vol. 7, pp. 93-107, 1995.
28. A.H. Nayfeh, Perturbation Methods, Wiley, New York, 1973.
29. J.Kevorkian and J.D. Cole, Perturbation Methods in Applied Mathematics, Springer, Berlin, 1981.
30. J. Liu, D.T. Martin, K. Kadirvel, T. Nishida, L. Cattafesta, M. Sheplak, and B.P. Mann, Nonlinear model and system identification of a capacitive dual-back plate MEMS microphone, J. Sound Vib., vol. 309, pp. 276-292, 2008.