Free vibration analysis of a rotating non-uniform functionally graded beam

- Journal title : Steel and Composite Structures
- Volume 19, Issue 5, 2015, pp.1279-1298
- Publisher : Techno-Press
- DOI : 10.12989/scs.2015.19.5.1279

Title & Authors

Free vibration analysis of a rotating non-uniform functionally graded beam

Ebrahimi, Farzad; Dashti, Samaneh;

Ebrahimi, Farzad; Dashti, Samaneh;

Abstract

In this paper, free vibration characteristics of a rotating double tapered functionally graded beam is investigated. Material properties of the beam vary continuously through thickness direction according to the power-law distribution of the volume fraction of the constituents. The governing differential equations of motion are derived using the Hamilton`s principle and solved utilizing an efficient and semi-analytical technique called the Differential Transform Method (DTM). Several important aspects such as taper ratios, rotational speed, hub radius, as well as the material volume fraction index which have impacts on natural frequencies of such beams are investigated and discussed in detail. Numerical results are tabulated in several tables and figures. In order to demonstrate the validity and accuracy of the current analysis, some of present results are compared with previous results in the literature and an excellent agreement is observed. It is showed that the natural frequencies of an FG rotating double tapered beam can be obtained with high accuracy by using DTM. It is also observed that nondimensional rotational speed, height taper ratio, power-law exponent significantly affect the natural frequencies of the FG double tapered beam while the effects of hub radius and breadth taper ratio are negligible.

Keywords

free vibration analysis;non-uniform rotating beam;functionally graded material;differential transform method;

Language

English

Cited by

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8.

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11.

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3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

References

1.

Abdel-Halim Hassan, I.H. (2002), "On solving some eigenvalue problems by using a differential transformation", Appl. Math. Comput., 127(1), 1-22.

2.

Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Model., 35(1), 412-425.

3.

Attarnejad, R. and Shahba, A. (2011), "Basic displacement functions for centrifugally stiffened tapered beams", Int. J. Numer. Method. Biomed. Eng., 27(9), 1385-1397.

4.

Attarnejad, R., Semnani, S.H. and Shahba, A. (2010), "Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams", Finite Elem. Anal. Des., 46(10), 916-929.

5.

Balkaya, M., Kaya, M.O. and Saglamer, A. (2009), "Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method", Arch. Appl. Mech., 79(2), 135-146.

6.

Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283.

7.

Benatta, M.A., Mechab, I., Tounsi, A. and Adda Bedia, E.A. (2008), "Static analysis of functionally graded short beams including warping and shear deformation effects", Comput. Mater. Sci., 44(2), 765-773.

8.

Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higherorder shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sandw. Struct. Mater., 15(6), 671-703.

9.

Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104.

10.

Bouiadjra, R.B., Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567.

11.

Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33.

12.

Bouremana, M., Houari, M.S.A., Tounsi, A., Kaci, A. and Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., Int. J., 15(5), 467-479.

13.

Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81.

14.

Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870.

15.

Ebrahimi, F., Rastgoo, A. and Atai, A.A. (2009a), "A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate", Eur. J. Mech.-A/Solids, 28(5), 962-973.

16.

Ebrahimi, F. and Rastgoo, A. (2009b), "FSDPT based study for vibration analysis of piezoelectric coupled annular FGM plate", J. Mech. Sci. Technol., 23(8), 2157-2168.

17.

Fazelzadeh, S.A. and Hosseini, M. (2007), "Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials", J. Fluid. Struct., 23(8), 1251-1264.

18.

Fazelzadeh, S.A., Malekzadeh, P., Zahedinejad, P. and Hosseini, M. (2007), "Vibration analysis of functionally graded thin-walled rotating blades under high temperature supersonic flow using the differential quadrature method", J. Sound Vib., 306(1), 333-348.

19.

Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech. (ASCE), 140(2), 374-383.

20.

Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111.

21.

Hodges, D.Y. and Rutkowski, M.Y. (1981), "Free-vibration analysis of rotating beams by a variable-order finite-element method", AIAA J., 19(11), 1459-1466.

22.

Huang, Y. and Li, X.F. (2010), "A new approach for free vibration of axially functionally graded beams with non-uniform cross-section", J. Sound Vib., 329(11), 2291-2303.

23.

Larbi, L.O., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433.

24.

Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4), 1210-1229.

25.

Li, L., Zhang, D.G. and Zhu, W.D. (2014), "Free vibration analysis of a rotating hub-functionally graded material beam system with the dynamic stiffening effect", J. Sound Vib., 333(5), 1526-1541.

26.

Mahi, A., Adda Bedia, E.A., Tounsi, A. and Mechab, I. (2010), "An analytical method for temperaturedependent free vibration analysis of functionally graded beams with general boundary conditions", Compos. Struct., 92(8), 1877-1887.

27.

Meziane, M.A.A., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318.

28.

Mohanty, S.C., Dash, R.R. and Rout, T. (2013), "Free vibration of a functionally graded rotating Timoshenko beam using FEM", Adv. Struct. Eng., 16(2), 405-418.

29.

Nachum, S. and Altus, E. (2007), "Natural frequencies and mode shapes of deterministic and stochastic non-homogeneous rods and beams", J. Sound Vib., 302(4), 903-924.

30.

O zdemir, O . and Kaya, M.O. (2006), "Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method", J. Sound Vib., 289(1), 413-420.

31.

Piovan, M.T. and Sampaio, R. (2009), "A study on the dynamics of rotating beams with functionally graded properties", J. Sound Vib., 327(1), 134-143.

32.

Pradhan, K.K. and Chakraverty, S. (2014), "Effects of different shear deformation theories on free vibration of functionally graded beams", Int. J. Mech. Sci., 82, 149-160.

33.

Rajasekaran, S. (2013), "Free vibration of centrifugally stiffened axially functionally graded tapered Timoshenko beams using differential transformation and quadrature methods", Appl. Math. Model., 37(6), 4440-4463.

34.

Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15(2), 221-245.

35.

Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials", Appl. Math. Model., 36(7), 3094-3111.

36.

Simsek, M. (2010), "Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories", Nucl. Eng. Des., 240(4), 697-705.

37.

Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747.

38.

Singh, K.V., Li, G. and Pang, S.S. (2006), "Free vibration and physical parameter identification of non-uniform composite beams", Compos. Struct., 74(1), 37-50.

39.

Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220.

40.

Zarrinzadeh, H., Attarnejad, R. and Shahba, A. (2012), "Free vibration of rotating axially functionally graded tapered beams", Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 226, 363-379.

41.

Zhou, J.K. (1986), "Differential transformation and its applications for electrical circuits", Peoples Republic of China, Huazhong University Press, Wuhan, China, pp. 1279-1289. [In Chinese]