An efficient shear deformation theory for wave propagation of functionally graded material plates

- Journal title : Structural Engineering and Mechanics
- Volume 57, Issue 5, 2016, pp.837-859
- Publisher : Techno-Press
- DOI : 10.12989/sem.2016.57.5.837

Title & Authors

An efficient shear deformation theory for wave propagation of functionally graded material plates

Boukhari, Ahmed; Atmane, Hassen Ait; Tounsi, Abdelouahed; Adda Bedia, E.A.; Mahmoud, S.R.;

Boukhari, Ahmed; Atmane, Hassen Ait; Tounsi, Abdelouahed; Adda Bedia, E.A.; Mahmoud, S.R.;

Abstract

An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton`s principle and the physical neutral surface concept. There is no stretching.bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

Keywords

wave propagation;functionally graded plate;thermal effects;efficient shear deformation theory;neutral surface position;

Language

English

Cited by

1.

Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation,;;;;

2.

A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates,;;;;

3.

Bending analysis of FGM plates using a sinusoidal shear deformation theory,;;;

4.

A refined theory with stretching effect for the flexure analysis of laminated composite plates,;;;

5.

A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates,;;;;

6.

A novel four variable refined plate theory for laminated composite plates,;;;

7.

Shear wave in a fiber-reinforced anisotropic layer overlying a pre-stressed porous half space with self-weight,;;

8.

A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate,;;;

9.

An analytical approach for buckling of functionally graded plates,;;

10.

A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations,;;;

11.

Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory,;;;

12.

Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects,;;;;

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

References

1.

Ait Amar Meziane, M., 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.

2.

Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384.

3.

Ait Atmane, H., Tounsi, A. and Bernard, F. (2016), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", International Journal of Mechanics and Materials in Design. (in Press)

4.

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

5.

Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447.

6.

Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630.

7.

Arefi, M. (2013), "Nonlinear thermoelastic analysis of thick-walled functionally graded piezoelectric cylinder", Acta. Mech., 224, 2771-2783.

8.

Arefi, M. and Rahimi, G.H. (2011), "Non linear analysis of a functionally graded square plate with two smart layers as sensor and actuator under normal pressure", Smart Struct. Syst., 8(5), 433-446.

9.

Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672.

10.

Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212.

11.

Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., 56(1), 85-106.

12.

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

13.

Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J Braz. Soc. Mech. Sci. Eng., 38, 265-275.

14.

Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081.

15.

Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42, 1386-1394.

16.

Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546.

17.

Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431.

18.

Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 29-37.

19.

Bouazza, M., Tounsi, A., Adda Bedia, E.A. and Megueni, A. (2010), "Thermoelastic stability analysis of functionally graded plates: An analytical approach", Comput. Mater. Sci., 49, 865-870.

20.

Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515.

21.

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., 14(1), 85-104.

22.

Bouguenina, O., Belakhdar, K, Tounsi, A. and Adda Bedia, E.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695.

23.

Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249.

24.

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.

25.

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

26.

Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A., (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1350082.

27.

Chattibi, F., Benrahou, K.H., Benachour, A., Nedri, K. and Tounsi, A. (2015), "Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory", Steel Compos. Struct., 19(1), 93-110.

28.

Chemi, A., Heireche, H., Zidour, M., Rakrak, K. and Bousahla, A.A. (2015), "Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity", Adv. Nano Res., 3(4), 193-206.

29.

Chen, W.Q., Wang, H.M. and Bao, R.H. (2007), "On calculating dispersion curves of waves in a functionally graded elastic plate", Compos. Struct., 81, 233-242.

30.

Curiel-Sosa, J.L., Beg, O.A. and Murillo, J.L. (2013), "Finite element analysis of structural instability using an implicit/explicit switching technique", Int. J. Comput. Meth. Eng. Sci. Mech., 14(5), 452-464.

31.

Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., 18(2), 395-408.

32.

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., 17(1), 69-81.

33.

Ebrahimi, F. and Dashti, S. (2015)," Free vibration analysis of a rotating non-uniform functionally graded beam", Steel Compos. Struct., 19(5), 1279-1298.

34.

Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49, 795-810.

35.

Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., 16(5), 507-519.

36.

Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253.

37.

Han, X. and Liu, G.R. (2002), "Effects of SH waves in a functionally graded plate", Mechanics Research Communications, 29, 327-338.

38.

Han, X., Liu, G.R., Xi, Z.C. and Lam, K.Y. (2001), "Transient responses in a functionally graded cylinder", Int. J. Solid. Struct., 38, 3021-3037.

39.

Han, X., Liu, G.R. and Lam, K.Y. (2002), "Transient waves in plates of functionally graded materials", Int. J. Numer. Meth. Eng., 52, 851-865.

40.

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

41.

Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709.

42.

Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Meth., 11(5), 135007.

43.

Kim, Y.W. (2005), "Temperature dependent vibration analysis of functionally graded rectangular plates", J. Sound Vib., 284(3-5), 531-549.

44.

Kim, S.E., Thai, H.T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89, 197-205.

45.

Kirkland, B. and Uy, B. (2015), "Behaviour and design of composite beams subjected to flexure and axial load", Steel Compos. Struct., 19(3), 615-633.

46.

Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28, 1-4.

47.

Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442.

48.

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, 2489-2508.

49.

Mansouri, M.H. and Shariyat, M. (2014), "Thermal buckling predictions of three types of high-order theories for the heterogeneous orthotropic plates, using the new version of DQM", Compos. Struct., 113(1), 40-55.

50.

Mansouri, M.H. and Shariyat, M. (2015), "Biaxial thermo-mechanical buckling of orthotropic auxetic FGM plates with temperature and moisture dependent material properties on elastic foundations", Compos. Part B, 83, 88-104.

51.

Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82, 499-512.

52.

Mechab, I., Ait Atmane, H., Tounsi, A., Belhadj, H.A. and Adda Bedia, E.A. (2010), "A two variable refined plate theory for the bending analysis of functionally graded plates", Acta Mech Sin, 26, 941-949.

53.

Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809.

54.

Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 91-120.

55.

Ould Larbi, L., 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. Bas. Des. Struct. Mach., 41, 421-433.

56.

Ozturk, H. (2015), "Vibration analysis of a pre-stressed laminated composite curved beam", Steel Compos. Struct., 19(3), 635-659.

57.

Park, J.S. and Kim, J.H. (2006), "Thermal postbuckling and vibration analyses of functionally graded plates", J. Sound Vib., 289(1-2), 77-93.

58.

Pradhan, K.K. and Chakraverty, S. (2015), "Free vibration of functionally graded thin elliptic plates with various edge supports", Struct. Eng. Mech., 53(2), 337-354.

59.

Rashidi, M.M., Shooshtari, A. and Beg, O.A. (2012), "Homotopy perturbation study of nonlinear vibration of Von K?rm?n rectangular plates", Compu. Struct., 106-107, 46-55.

60.

Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684.

61.

Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A/Solid., 20, 841-855.

62.

Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, Wiley, New York.

63.

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

64.

Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., 17(3), 321-338.

65.

Sallai, B., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Analytical solution for bending analysis of functionally graded beam", Steel Compos. Struct., 19(4), 829-841.

66.

Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D.L.A. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Tech., 25(9), 2195-2209.

68.

Shimpi, R.P. and Patel, H.G. (2006a), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct, 43(22), 6783-6799.

69.

Shimpi, R.P. and Patel, H.G. (2006b), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999.

70.

Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87.

71.

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

72.

Sun, D. and Luo, S.N. (2011b), "Wave propagation of functionally graded material plates in thermal environments", Ultrasonics, 51, 940-952.

73.

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, 444-462.

74.

Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, IOM Communications Ltd., London.

75.

Tagrara, S.H., Benachour, A., Bachir Bouiadjra, M. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277.

76.

Tebboune, W., Benrahou, K.H., Houari, M.S.A. and Tounsi, A. (2015), "Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory", Steel Compos. Struct., 18(2), 443-465.

77.

Touloukian, T.S. (1967), Thermophysical Properties of High Temperature Solid Materials, McMillan, New York.

78.

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

79.

Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013b), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11.

80.

Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272, 703-730.

81.

Yang, J. and Shen, H.S. (2002), "Vibration characteristics and transient response of shear deformable functionally graded plates in thermal environments", J. Sound Vib., 255, 579-602.

82.

Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach", Meccanica, 48, 2019-2035.

83.

Yahoobi, H. and Feraidoon, A. (2010), "Influence of neutral surface position on deflection of functionally graded beam under uniformly distributed load", World Appl. Sci. J., 10(3), 337-341.

84.

Yaghoobi, H., Valipour, M.S., Fereidoon, A. and Khoshnevisrad, P. (2014), "Analytical study on post-buckling and nonlinear free vibration analysis of FG beams resting on nonlinear elastic foundation under thermo-mechanical loading using VIM", Steel Compos. Struct., 17(5), 753-776.

85.

Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710.

86.

Zenkour, AM. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84.