Wave propagation of a functionally graded beam in thermal environments

- Journal title : Steel and Composite Structures
- Volume 19, Issue 6, 2015, pp.1421-1447
- Publisher : Techno-Press
- DOI : 10.12989/scs.2015.19.6.1421

Title & Authors

Wave propagation of a functionally graded beam in thermal environments

Akbas, Seref Doguscan;

Akbas, Seref Doguscan;

Abstract

In this paper, the effect of material-temperature dependent on the wave propagation of a cantilever beam composed of functionally graded material (FGM) under the effect of an impact force is investigated. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. Material properties of the beam are temperature-dependent and change in the thickness direction. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Euler-Bernoulli beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange`s equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain and frequency domain by using Newmark average acceleration method. In order to establish the accuracy of the present formulation and results, the comparison study is performed with the published results available in the literature. Good agreement is observed. In the study, the effects of material distributions and temperature rising on the wave propagation of the FGM beam are investigated in detail.

Keywords

wave propagation;temperature dependent physical properties;functionally graded materials;beam;

Language

English

Cited by

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Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory,;;;;;;

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References

1.

Ait Yahia, S., Ait Atmane, H., Ahmed Houari, M.S. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165.

2.

Akbas, S.D. (2014a), "Wave propagation analysis of edge cracked beams resting on elastic foundation", Int. J. Eng. Appl. Sci., 6(1), 40-52.

3.

Akbas, S.D. (2014b), "Wave propagation analysis of edge cracked circular beams under impact force", Plos One, 9(6), e100496.

4.

Akbas, S.D. (2015), "Wave propagation in edge cracked functionally graded beams under impact force", J. Vib. Control. DOI: 10.1177/1077546314547531

5.

Aksoy, H.G. and Senocak, E. (2009), "Wave propagation in functionally graded and layered materials", Finite Elem. Anal. Des., 45(12), 876-891.

6.

Bin, W., Jiangong, Y. and Cunfu, H. (2008), "Wave propagation in non-homogeneous magneto-electroelastic plates", J. Sound Vib., 317(1-2), 250-264.

7.

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.

8.

Bourada, M., Kaci, A., Ahmed Houari, M.S. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423.

9.

Cao, X., Shi, J. and Jin, F. (2012), "Lamb wave propagation in the functionally graded piezoelectricpiezomagnetic material plate", Acta Mechanica, 223(5), 1081-1091.

10.

Chakraborty, A. and Gopalakrishnan, S. (2004), "Wave propagation in inhomogeneous layered media: Solution of forward and inverse problems", Acta Mechanica, 169(1-4), 153-185.

11.

Chakraborty, A. and Gopalakrishnan, S. (2005), "A spectral finite element for axial-flexural-shear coupled wave propagation analysis in lengthwise graded beam", Computat. Mech., 36(1), 1-12.

12.

Chakraborty, A., Gopalakrishnan, S. and Kausel, E. (2005), "Wave propagation analysis in inhomogeneous piezo-composite layer by the thin-layer method", Int. J. Numer. Method. Eng., 64(5), 567-598.

13.

Chouvion, B., Fox, C.H.J., McWilliam, S. and Popov, A.A. (2010), "In-plane free vibration analysis of combined ring-beam structural systems by wave propagation", J. Sound Vib., 329(24), 5087-5104.

14.

Dinevay, P.S., Rangelov, T.V. and Manolis, G.D. (2007), "Elastic wave propagation in a class of cracked, functionally graded materials by BIEM", Computat. Mech., 39(3), 293-308.

15.

Du, J., Jin, X., Wang, J. and Xian, K. (2007), "Love wave propagation in functionally graded piezoelectric material layer", Ultrasonics, 46(1), 13-22.

16.

Gopalakrishnan, S. and Doyle, J.F. (1995), "Spectral super-elements for wave propagation in structures with local non-uniformities", Comput. Method. Appl. Mech. Eng., 121(1-4), 77-90.

17.

Farris, T.N. and Doyle, J.F. (1989), "Wave propagation in a split Timoshenko beam", J. Sound Vib., 130(1), 137-147.

18.

Frikha, A., Treyssede, F. and Cartraud, P. (2011), "Effect of axial load on the propagation of elastic waves in helical beams", Wave Motion, 48(1), 83-92.

19.

Islam, Z.M., Jia, P. and Lim, C.W. (2014), "Torsional wave propagation and vibration of circular nanostructures based on nonlocal elasticity theory", Int. J. Appl. Mech., 6(2), 1450011.

20.

Jiangong, Y. and Qiujuan, M. (2010), "Wave characteristics in magneto-electro-elastic functionally graded spherical curved plates", Mech. Adv. Mater. Struct., 17(4), 287-301.

21.

Kang, B., Riedel, C.H. and Tan, C.A. (2003), "Free vibration analysis of planar curved beams by wave propagation", J. Sound Vib., 260(1), 19-44.

22.

Ke, L.L., Yang, J., Kitipornchai, S. and Xiang, Y. (2009), "Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials", Mech. Adv. Mater. Struct., 16(6), 488-502.

23.

Kocaturk, T, and Akbas, S.D. (2013), "Wave propagation in a microbeam based on the modified couple stress theory", Struct. Eng. Mech., Int. J., 46(3), 417-431.

24.

Kocaturk, T., Eskin, A. and Akbas, S.D. (2011), "Wave propagation in a piecewise homegenous cantilever beam under impact force", Int. J. Phys. Sci., 6(16), 4013-4020.

25.

Krawczuk, M. (2002), "Application of Spectral beam finite element with a crack and iterative search technique to damage detection", Finite Elem. Anal. Des., 38(6), 537-548.

26.

Krawczuk, M., Palacz, M. and Ostachowicz, W. (2002), "The dynamic analysis of a cracked Timoshenko beam by the spectral element method", J. Sound Vib., 264(5), 1139-1153.

27.

Kumar, D.S., Mahapatra, D.R. and Gopalakrishnan, S. (2004), "A spectral finite element for wave propagation and structural diagnostic analysis of composite beam with transverse crack", Finite Elem. Anal. Des., 40(13-14), 1729-1751.

28.

Lee, S.Y. and Yeen, W.F. (1990), "Free coupled longitudinal and flexural waves of a periodically supported beam", J. Sound Vib., 142(2), 203-211.

29.

Li, X.Y., Wang, Z.K. and Huang, S.H. (2004), "Love waves in functionally graded piezoelectric materials", Int. J. Solid. Struct., 41(26), 7309-7328.

30.

Liu, Y. and Lu, F. (2012), "Dynamic stability of a beam on an elastic foundation including stress wave effects", Int. J. Appl. Mech., 4(2), 1250017.

31.

Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508.

32.

Molaei Najafabadi, M., Ahmadian, M.T. and Taati, E. (2014), "Effect of thermal wave propagation on thermoelastic behavior of functionally graded materials in a slab symmetrically surface heated using analytical modeling", Compos. Part B: Engineering, 60, 413-422.

33.

Newmark, N.M. (1959), "A method of computation for structural dynamics", ASCE Eng. Mech. Div., 85(3), 67-94.

34.

Ostachowicz, W., Krawczuk, M., Cartmell, M. and Gilchrist, M. (2004), "Wave propagation in delaminated beam", Comput. Struct., 82(6), 475-483.

35.

Palacz, M. and Krawczuk, M. (2002), "Analysis of longitudinal wave propagation in a cracked rod by the spectral element method", Comput. Struct., 80(24), 1809-1816.

36.

Palacz, M., Krawczuk, M. and Ostachowicz, W. (2005a), "The spectral finite element model for analysis of flexural-shear coupled wave propagation, Part 1: Laminated multilayer composite beam", Compos. Struct., 68(1), 37-44.

37.

Palacz, M., Krawczuk, M. and Ostachowicz, W. (2005b), "The spectral finite element model for analysis of flexural-shear coupled wave propagation. Part 2: Delaminated multilayer composite beam", Compos. Struct., 68(1), 45-51.

38.

Park, J. (2008), "Identification of damage in beam structures using flexural wave propagation characteristics", J. Sound Vib., 318(4-5), 820-829.

39.

Reddy, J.N. and Chin, C.D. (1998), "Thermoelastical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626.

40.

Safari-Kahnaki, A., Hosseini, S.M. and Tahani, M. (2011), "Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical method", Int. J. Mech. Mater. Des., 7(3), 167-184.

41.

Shariyat, M., Khaghani, M. and Lavasani, S.M.H. (2010), "Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick FGM cylinders with temperature-dependent material properties", Eur. J. Mech., A/Solids, 29(3), 378-391.

42.

Shen, H.S. and Wang, Z.X. (2012), "Assessment of Voigt and Mori-Tanaka models for vibration analysis of functionally graded plates", Compos. Struct., 94(7), 2197-2208.

43.

Sridhar, R., Chakraborty, A. and Gopalakrishnan, S. (2007), "Wave propagation analysis in anisotropic and inhomogeneous uncracked and cracked structures using pseudospectral finite element method", Int. J. Solid. Struct., 43(16), 4997-5031.

44.

Sun, D. and Luo, S.-N. (2011a), "Wave propagation and transient response of a FGM plate under a point impact load based on higher-order shear deformation theory", Compos. Struct., 93(5), 1474-1484.

45.

Sun, D. and Luo, S.-N. (2011b), "Wave propagation and transient response of functionally graded material circular plates under a point impact load", Compos. Part B: Engineering, 42(4), 657-665.

46.

Sun, D. and Luo, S.-N. (2011c), "The wave propagation and dynamic response of rectangular functionally graded material plates with completed clamped supports under impulse load", Eur. J. Mech., A/Solids 30(3), 396-408.

47.

Sun, D. and Luo, S.-N. (2011d), "Wave propagation of functionally graded material plates in thermal environments", Ultrasonics, 51(8), 940-995.

48.

Sun, D. and Luo, S.-N. (2012), "Wave propagation and transient response of a functionally graded material plate under a point impact load in thermal environments", Appl. Math. Model., 36(1), 444-462.

49.

Teh, K.K. and Huang, C.C. (1981), "Wave propagation in generally orthotropic beams", Fibre Sci. Technol., 14(4), 301-310.

50.

Tian, J., Li, Z. and Su, X. (2003), "Crack detection in beams by wavelet analysis of transient flexural waves", J. Sound Vib., 261(4), 715-727.

51.

Touloukian, Y.S. (1967), Thermophysical Properties of High Temperature Solid Materials, Macmillan, New York, NY, USA.

52.

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.

53.

Usuki, T. and Maki, A. (2003), "Behavior of beams under transverse impact according to higher-order beam theory", Int. J. Solid. Struct., 40(13-14), 3737-3785.

54.

Vinod, K.G., Gopalakrishnan, S. and Ganguli, R. (2007), "Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite element", International Int. J. Solid. Struct., 44(18-19), 5875-5893.

55.

Watanabe, Y. and Sugimoto, N. (2005), "Flexural wave propagation in a spatially periodic structure of articulated beams", Wave Motion, 42(2), 155-167.

56.

Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83(1), 48-60.

57.

Yokoyama, T. and Kishida, K. (1982), "Finite element analysis of flexural wave propagation in elastic beams", Technol. Reports of the Osaka University, 32(1642), 103-112.