Steel and Composite Structures

  • 제20권1호
  • /
  • Pages.205-225
  • /
  • 2016
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Deflection and vibration analysis of higher-order shear deformable compositionally graded porous plate

  • Ebrahimi, Farzad (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University) ;
  • Habibi, Sajjad (Mechanical Engineering Department, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2015.03.30
  • 심사 : 2015.08.23
  • 발행 : 2016.01.20
⟨ 이전 논문 다음 논문 ⟩

초록

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

키워드

참고문헌

  1. Batra, R.C. and Jin, J. (2005), "Natural frequencies of a functionally graded anisotropic rectangular plate", J. Sound Vib., 282(1), 509-516. https://doi.org/10.1016/j.jsv.2004.03.068
  2. Biot, M.A. (1941), "General theory of three‐dimensional consolidation", J. Appl. Phys., 12(2), 155-164. https://doi.org/10.1063/1.1712886
  3. Biot, M.A. (1955), "Theory of elasticity and consolidation for a porous anisotropic solid", J. Appl. Phys., 26(2), 182-185. https://doi.org/10.1063/1.1721956
  4. Biot, M.A. (1964), "Theory of buckling of a porous slab and its thermoelastic analogy", J. Appl. Mech., 31(2), 194-198. https://doi.org/10.1115/1.3629586
  5. Biot, M.A. (1956), "Theory of propagation of elastic waves in a fluid‐saturated porous solid. Parts I and II", J. Acoust. Soc. Am., 28(2), 168-191. https://doi.org/10.1121/1.1908239
  6. Biot, M.A. and Willis, D.G. (1957), "The elastic coefficients of the Theory of Consolidation", J. Appl. Mech., 24, 594-601.
  7. Brischetto, S. (2013), "Exact elasticity solution for natural frequencies of functionally graded simply-supported structures", Comput. Model. Eng. Sci., 95(5), 391-430.
  8. Carrera, E. and Brischetto, S. (2008), "Analysis of thickness locking in classical, refined and mixed multilayered plate theories", Compos. Struct., 82(4), 549-562. https://doi.org/10.1016/j.compstruct.2007.02.002
  9. Civalek, O. (2008), "Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method", Finite Elem. Anal. Des., 44(12-13), 725-731. https://doi.org/10.1016/j.finel.2008.04.001
  10. Civalek, O. (2009), "Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method", Appl. Math. Model., 33(10), 3825-3835. https://doi.org/10.1016/j.apm.2008.12.019
  11. Civalek, O. (2013), "Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory", Compos. Part-B: Eng., 45(1), 1001-1009. https://doi.org/10.1016/j.compositesb.2012.05.018
  12. Ebrahimi, F. and Mokhtari, M. (2014), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazil. Soc. Mech. Sci. Eng., 37(4), 1-10.
  13. 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. https://doi.org/10.1080/15376494.2012.677098
  14. Ebrahimi, F. and Rastgoo, A. (2008a), "Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers", Smart Mater. Struct., 17(1), 015044. https://doi.org/10.1088/0964-1726/17/1/015044
  15. Ebrahimi, F. and Rastgoo, A. (2008b), "An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory", Thin-Wall. Struct., 46(12), 1402-1408. https://doi.org/10.1016/j.tws.2008.03.008
  16. 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. https://doi.org/10.1016/j.euromechsol.2008.12.008
  17. Ebrahimi, F., Naei, M.H. and Rastgoo, A. (2009b), "Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation", J. Mech. Sci. Technol., 23(8), 2107-2124. https://doi.org/10.1007/s12206-009-0358-8
  18. Ebrahimi, F. and Rastgoo, A. (2011), "Nonlinear vibration analysis of piezo-thermo-electrically actuated functionally graded circular plates", Arch. Appl. Mech., 81(3), 361-383. https://doi.org/10.1007/s00419-010-0415-x
  19. Fatt, I. (1959), "The Biot-Willis elastic coefficients for a sandstone", J. Appl. Mech., 26(28), 296-297.
  20. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Jorge, R.M.N. (2006), "Natural frequencies of functionally graded plates by a meshless method", Compos. Struct., 75(1), 593-600. https://doi.org/10.1016/j.compstruct.2006.04.018
  21. Ghassemi, A. and Zhang, Q. (2004), "A transient fictitious stress boundary element method for porothermoelastic media", Eng. Anal. Bound. Elem., 28(11), 1363-1373. https://doi.org/10.1016/j.enganabound.2004.05.003
  22. Hashin, Z. and Shtrikman, S. (1963), "A variational approach to the theory of the elastic behaviour of multiphase materials", J. Mech. Phys. Solid., 11(2), 127-140. https://doi.org/10.1016/0022-5096(63)90060-7
  23. Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H. and Omidi, M. (2010), "Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory", Appl. Math. Model., 34(5), 1276-1291. https://doi.org/10.1016/j.apm.2009.08.008
  24. Jabbari, M., Mojahedin, A., Khorshidvand, A.R. and Eslami, M.R. (2013a), "Buckling analysis of a functionally graded thin circular plate made of saturated porous materials", J. Eng. Mech., 140(2), 287-295.
  25. Jabbari, M., Joubaneh, E.F., Khorshidvand, A.R. and Eslami, M.R. (2013b), "Buckling analysis of porous circular plate with piezoelectric actuator layers under uniform radial compression", Int. J. Mech. Sci., 70, 50-56. https://doi.org/10.1016/j.ijmecsci.2013.01.031
  26. Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M.R. (2014a), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Therm. Stress., 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768
  27. Jabbari, M., Joubaneh, E.F. and Mojahedin, A. (2014b), "Thermal buckling analysis of porous circular plate with piezoelectric actuators based on first order shear deformation theory", Int. J. Mech. Sci., 83, 57-64. https://doi.org/10.1016/j.ijmecsci.2014.03.024
  28. Khorshidvand, A.R., Joubaneh, E.F., Jabbari, M. and Eslami, M.R. (2014), "Buckling analysis of a porous circular plate with piezoelectric sensor-actuator layers under uniform radial compression", Acta Mechanica, 225(1), 179-193. https://doi.org/10.1007/s00707-013-0959-2
  29. Leclaire, P., Horoshenkov, K.V. and Cummings, A. (2001), "Transverse vibrations of a thin rectangular porous plate saturated by a fluid", J. Sound Vib., 247(1), 1-18. https://doi.org/10.1006/jsvi.2001.3656
  30. Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin-Wall. Struct., 46(3), 333-337. https://doi.org/10.1016/j.tws.2007.06.006
  31. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  32. Ng, C.H.W., Zhao, Y.B. and Wei, G.W. (2004), "Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates", Comput. Method. Appl. Mech. Eng., 193(23-26), 2483-2506. https://doi.org/10.1016/j.cma.2004.01.013
  33. Reddy, J.N. (1984), "A refined nonlinear theory of plates with transverse shear deformation", Int. J. Solid. Struct., 20(9), 881-896. https://doi.org/10.1016/0020-7683(84)90056-8
  34. Reddy, J.N. (1993), An Introduction to the Finite Element Method, (Vol. 2, No. 2.2), McGraw-Hill, New York, NY, USA.
  35. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  36. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
  37. Reddy, J.N. and Cheng, Z.Q. (2003), "Frequency of functionally graded plates with three-dimensional asymptotic approach", J. Eng. Mech., 129(8), 896-900. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:8(896)
  38. Thai, H.T. and Choi, D.H. (2014), "Finite element formulation of a refined plate theory for laminated composite plates", J. Compos. Mater., 48(28), 3521-3538. https://doi.org/10.1177/0021998313511353
  39. Theodorakopoulos, D.D. and Beskos, D.E. (1994), "Flexural vibrations of poroelastic plates", Acta Mech., 103(1-4), 191-203. https://doi.org/10.1007/BF01180226
  40. 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. https://doi.org/10.1016/S0022-460X(03)00412-7
  41. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method", Meccanica, 50(5), 1-12. https://doi.org/10.1007/s11012-014-0082-z
  42. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009
  43. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11), 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026
  44. Zhang, B., He, Y., Liu, D., Gan, Z. and Shen, L. (2013), "A non-classical Mindlin plate finite element based on a modified couple stress theory", Eur. J. Mech. - A/Solids, 42, 63-80. https://doi.org/10.1016/j.euromechsol.2013.04.005
  45. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319(3), 918-939. https://doi.org/10.1016/j.jsv.2008.06.025

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