Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations

- Journal title : Earthquakes and Structures
- Volume 10, Issue 6, 2016, pp.1429-1449
- Publisher : Techno-Press
- DOI : 10.12989/eas.2016.10.6.1429

Title & Authors

Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations

Benferhat, Rabia; Daouadji, Tahar Hassaine; Mansour, Mohamed Said; Hadji, Lazreg;

Benferhat, Rabia; Daouadji, Tahar Hassaine; Mansour, Mohamed Said; Hadji, Lazreg;

Abstract

The effect of porosity on bending and free vibration behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper. The modified rule of mixture covering porosity phases is used to describe and approximate material properties of the FGM plates with porosity phases. The effect due to transverse shear is included by using a new refined shear deformation theory. The number of unknown functions involved in the present theory is only four as against five or more in case of other shear deformation theories. The Poisson ratio is held constant. Based on the sinusoidal shear deformation theory, the position of neutral surface is determined and the equation of motion for FG rectangular plates resting on elastic foundation based on neutral surface is obtained through the minimum total potential energy and Hamilton`s principle. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for both isotropic and functionally graded material (FGM). The effect of porosity volume fraction on Al/Al2O3 and Ti-6Al-4V/Aluminum oxide plates are presented in graphical forms. The roles played by the constituent volume fraction index, the foundation stiffness parameters and the geometry of the plate is also studied.

Keywords

porosity coefficient;FGM plate;bending and free vibration behavior;elastic foundation;

Language

English

Cited by

1.

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

References

1.

Ait Atmane, H., Tounsi, A. and Bernard, F. (2015a), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater., 1-14.

2.

Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015b), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-385.

3.

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.

4.

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.

5.

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

6.

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.

7.

Brischetto, S. and Carrera, E. (2010), "Advanced mixed theories for bending analysis of functionally graded plates", Comput. Struct., 88(23-24), 1474-1483.

8.

Brischetto, S. (2013), "Exact elasticity solution for natural frequencies of functionally graded simplysupported structures", Comput. Model. Eng. Sci., 95(5), 391-430.

9.

Bodaghi, M. and Saidi, A.R. (2011), "Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation", Arch. Appl. Mech., 81(6), 765-780.

10.

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.

11.

Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2010), "Refined and advanced models for multilayered plates and shells embedding functionally graded material layers", Mech. Adv. Mater. Struct., 17(8), 603-621.

12.

Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos Part B: Eng., 42(2), 123-133.

13.

Dozio, L. (2014), "Exact free vibration analysis of Levy FGM plates with higher-order shear and normal deformation theories", Compos. Struct., 111(1), 415-425.

14.

Efraim, E. and Eisenberger, M. (2007), "Exact vibration analysis of variable thickness thick annular isotropic and FGM plates", J. Sound Vib., 299(4), 720-738.

15.

Fallah, A., Aghdam, M.M. and Kargarnovin, M.H. (2013), "Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method", Arch. Appl. Mech., 83(2), 177-191.

16.

Fazzolari, F.A. and Carrera, E. (2014), "Coupled thermoelastic effect in free vibration analysis of anisotropic multilayered plates and FGM plates by using a variable-kinematics Ritz formulation", Eur. J. Mech. A/Solid., 44, 157-174.

17.

Hadji, L. and Adda Bedia, E.A. (2015a), "Influence of the porosities on the free vibration of FGM beams", Wind Struct., 21(3), 273-287.

18.

Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015b), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., 9(3), 361-372

19.

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

20.

Hasani Baferani, A., Saidi, A.R. and Ehteshami, H. (2011), "Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation", Compos. Struct., 93(7), 1842-1853.

21.

Hirai, T. (1996), "Functional gradient materials", Proc. Ceramics-Part 2 in Mater. Sci. Technol., 17B, 293-341.

22.

Huang, Z.Y., Lu, C.F. and Chen, W.Q. (2008), "Benchmark solutions for functionally graded thick plates resting on Winkler-Pasternak elastic foundations", Compos. Struct., 85(2), 95-104.

23.

Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22.

24.

Hosseini-Hashemi, S., Fadaee, M. and Taher, H.R.D. (2011b), "Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory", Appl. Math. Model., 35(2), 708-727.

25.

Gan, B.S., Trinh, T.H., Le, T.H. and Nguyen, D.K. (2015), "Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads", Struct. Eng. Mech., 53(5), 981-995.

26.

Kitipornchai, S., Yang, J. and Liew, K.M. (2004), "Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections", Int. J. Solid. Struct., 41(9-10), 2235-2257.

27.

Lam, K.Y., Wang, C.M. and He, X.Q. (2002), "Canonical exact solutions for Levy-plates on two parameter foundation using Green's functions", Eng. Struct., 22(4), 364-378.

28.

Meksi, A., Benyoucef, S., Houari, M.S.A and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240.

29.

Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B: Eng., 44(1), 657-674.

30.

Nguyen, D.D. and Pham, H.C. (2013), "Nonlinear postbuckling of symmetric S-FGM plates resting on elastic foundations using higher order shear deformation plate theory in thermal environments", Compos. Struct., 100, 566-574.

31.

Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu I Arkhitekture Moscow USSR, 1-56. (in Russian)

32.

Pindera, M.J., Arnold, S.M., Aboudi, J. and Hui, D. (1994), "Use of composite in functionnaly graded materials", Compos. Eng., 4(1), 1-145.

33.

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

34.

Prakash, T., Singha, M.K. and Ganapathi, M. (2009), "Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates", Comput. Mech., 43(3), 341-350.

35.

Qian, L.F., Batra, R.C. and Chen, L.M. (2004), "Static and dynamic deformations of thick functionally graded elastic plates by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method", Composites: Part B., 35(6), 685-697.

36.

Srinivas, S., Joga Rao, C.V. and Rao, A.K. (1970), "An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates", J. Sound. Vib., 12(2), 187-199.

37.

Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011.

38.

Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Technol., 71(16), 1850-1858.

39.

Thai, H.T. and Choi, D.H. (2012), "A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation", Composites: Part B., 43(5), 2335-2347.

40.

Thai, H.T. and Choi, D.H. (2014), "Zeroth-order shear deformation theory for functionally graded plates resting on elastic foundation", Int. J. Mech. Sci., 78, 35-43.

41.

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", Aero. Sci. Technol., 24(1), 209-220.

42.

Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272(3), 703-730.

43.

Wattanasakulpong, N., Gangadhara Prusty, B., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190.

44.

Wattanasakulponga, N. and Ungbhakornb, V. (2014), "Linear and non linear vibration analysis of elastically restrained ends FGM beams with porosities", Aero. Sci. Technol., 32(1), 111-120.

45.

Zenkour, A.M., Mashat, D.S. and Elsiba, K.A. (2009), "Bending analysis of functionally graded plates in the context of different theories of thermoelasticity", Math. Prob. Eng., 962351.

46.

Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mater. Sci., 44(2), 716-720.