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The effect of porosity on free vibration of SPFG circular plates resting on visco-Pasternak elastic foundation based on CPT, FSDT and TSDT

  • Arshid, Ehsan (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Khorshidvand, Ahmad Reza (Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University) ;
  • Khorsandijou, S. Mahdi (Department of Mechatronics Engineering, South Tehran Branch, Islamic Azad University)
  • 투고 : 2018.12.24
  • 심사 : 2019.01.29
  • 발행 : 2019.04.10

초록

Using the classical, first order and third order shear deformation plates theories the motion equations of an undrained porous FG circular plate which is located on visco-Pasternak elastic foundation have been derived and used for free vibration analysis thereof. Strains are related to displacements by Sanders relationship. Fluid has saturated the pores whose distribution varies through the thickness according to three physically probable given functions. The equations are discretized and numerically solved by the generalized differential quadrature method. The effect of porosity, pores distribution, fluid compressibility, viscoelastic foundation and aspect ratio of the plate on its vibration has been considered.

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참고문헌

  1. Allahverdizadeh, A., Naei, M.H. and Nikkhah Bahrami, M. (2008), "Nonlinear free and forced vibration analysis of thin circular functionally graded plates", J. Sound Vibr., 310(4-5), 966-984. https://doi.org/10.1016/j.jsv.2007.08.011
  2. Amir, S. (2016), "Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory", J. Mater. Des. Appl., 233(2), 197-208.
  3. Amir, S., Bidgoli, E.M.R. and Arshid, E. (2018a), "Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT", Mech. Adv. Mater. Struct., 1-15.
  4. Amir, S., Khorasani, M. and BabaAkbar-Zarei, H. (2018b), "Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory", J. Sandw. Struct. Mater., 109963621879538.
  5. Arefi, M. and Zenkour, A.M. (2017), "Thermo-electro-magnetomechanical bending behavior of size-dependent sandwich piezomagnetic nanoplates", Mech. Res. Commun., 84, 27-42. https://doi.org/10.1016/j.mechrescom.2017.06.002
  6. Arshid, E. and Khorshidvand, A.R. (2017), "Flexural vibrations analysis of saturated porous circular plates using differential quadrature method", Iran. J. Mech. Eng. Trans. ISME, 19(1), 78-100.
  7. Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin-Wall. Struct., 125, 220-233. https://doi.org/10.1016/j.tws.2018.01.007
  8. Azimi, S. (1988), "Free vibration of circular plates with elastic edge supports using the receptance method", J. Sound Vibr., 120(1), 19-35. https://doi.org/10.1016/0022-460X(88)90332-X
  9. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517
  10. 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. https://doi.org/10.1080/15376494.2014.984088
  11. Bert, C.H.W., Jang, S.K. and Striz, A.G. (1989), "Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature", Comput. Mech., 5(2-3), 217-226. https://doi.org/10.1007/BF01046487
  12. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49(1), 1-28. https://doi.org/10.1115/1.3101882
  13. 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
  14. Brush, D.O., Almroth, B.O. and Hutchinson, J.W. (1975), "Buckling of bars, plates, and shells", J. Appl. Mech., 42, 911.
  15. Camier, C., Touze, C. and Thomas, O. (2009), "Non-linear vibrations of imperfect free-edge circular plates and shells", Eur. J. Mech.-A/Sol., 28(3), 500-515. https://doi.org/10.1016/j.euromechsol.2008.11.005
  16. Chen, C.S. (2005), "Nonlinear vibration of a shear deformable functionally graded plate", Compos. Struct., 68(3), 295-302. https://doi.org/10.1016/j.compstruct.2004.03.022
  17. Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., 108, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025
  18. Civalek, O . (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., 26(2), 171-186. https://doi.org/10.1016/j.engstruct.2003.09.005
  19. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/j.ast.2018.03.020
  20. Decha-Umphai, K. and Mei, C. (1986), "Finite element method for non-linear forced vibrations of circular plates", Int. J. Numer. Meth. Eng., 23(9), 1715-1726. https://doi.org/10.1002/nme.1620230911
  21. Detournay, E. and Cheng, A.H.D. (1993), "Fundamentals of poroelasticity", Analy. Des. Meth., 113-171.
  22. Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 99, 88-96. https://doi.org/10.1016/j.compstruct.2012.11.017
  23. Duc, N.D. (2014), Nonlinear Static and Dynamic Stability of Functionally Graded Plates and Shells, Vietnam National University Press.
  24. Duc, N.D. (2016), "Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy's third-order shear deformation shell theory", Eur. J. Mech., A/Sol., 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004
  25. Duc, N.D. (2018), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 20(3), 351-378. https://doi.org/10.1177/1099636216653266
  26. Duc, N.D. and Ha, N. (2011), "The bending analysis of thin composite plate under steady temperature field", J. Sci. Math.- Phys., 27(2), 77-83.
  27. Duc, N.D. and Quan, T.Q. (2015), "Nonlinear dynamic analysis of imperfect functionally graded material double curved thin shallow shells with temperature-dependent properties on elastic foundation", J. Vibr. Contr., 21(7), 1340-1362. https://doi.org/10.1177/1077546313494114
  28. Duc, N.D., Cong, P.H., Tuan, N.D., Tran, P. and Thanh, N.V. (2017), "Thermal and mechanical stability of functionally graded carbon nanotubes (FG CNT)-reinforced composite truncated conical shells surrounded by the elastic foundations", Thin-Wall. Struct., 115, 300-310. https://doi.org/10.1016/j.tws.2017.02.016
  29. Duc, N.D., Seung-Eock, K. and Chan, D.Q. (2018), "Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT", J. Therm. Stress., 41(3), 331-365. https://doi.org/10.1080/01495739.2017.1398623
  30. Duc, N., Dinh Nguyen, P. and Dinh Khoa, N. (2017), "Nonlinear dynamic analysis and vibration of eccentrically stiffened SFGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments", Thin-Wall. Struct., 117, 178-189. https://doi.org/10.1016/j.tws.2017.04.013
  31. Duc, N., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018), "Nonlinear dynamic response of functional graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Comput. Mech., 4(4), 245-259.
  32. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/SEM.2017.63.5.585
  33. Ghorbanpour Arani, A. and Kiani, F. (2018), "Nonlinear free and forced vibration analysis of microbeams resting on the nonlinear orthotropic visco-Pasternak foundation with different boundary conditions", Steel Compos. Struct., 28(2), 149-165. https://doi.org/10.12989/SCS.2018.28.2.149
  34. Ghorbanpour Arani, A., Haghparast, E. and Babaakbar Zarei, H. (2016), "Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field", Phys. B: Condens. Matt., 495, 35-49. https://doi.org/10.1016/j.physb.2016.04.039
  35. Ghorbanpour Arani, A., Haghparast, E. and Zarei, H.B. (2017b), "Vibration analysis of functionally graded nanocomposite plate moving in two directions", Steel Compos. Struct., 23(5), 529-541. https://doi.org/10.12989/scs.2017.23.5.529
  36. Ghorbanpour Arani, A., Khoddami Maraghi, Z., Khani, M. and Alinaghian, I. (2017c), "Free vibration of embedded porous plate using third-order shear deformation and poroelasticity theories", J. Eng., 1-13.
  37. Ghorbanpour Arani, A., Maraghi, Z.K. and Ferasatmanesh, M. (2017a), "Theoretical investigation on vibration frequency of sandwich plate with PFRC core and piezomagnetic face sheets under variable in-plane load", Struct. Eng. Mech., 63(1), 65-76. https://doi.org/10.12989/SEM.2017.63.1.065
  38. Hosseini-Hashemi, S. and Khorami, K. (2011), "Analysis of free vibrations of moderately thick cylindrical Shells made of functionally graded materials using differential quadrature method", Modar. Mech. Eng., 11(2), 93-106.
  39. Jabbari, M., Mojahedin, A., Khorshidvand, A.R. and Eslami, M.R. (2014), "Buckling analysis of a functionally graded thin circular plate made of saturated porous materials", J. Eng. Mech., 140(2), 287-295. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000663
  40. Khorshidvand, A.R., Jabbari, M. and Eslami, M.R. (2012), "Thermoelastic buckling analysis of functionally graded circular plates integrated with piezoelectric layers", J. Therm. Stress., 35(8), 695-717. https://doi.org/10.1080/01495739.2012.688666
  41. 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 Mech., 225(1), 179-193. https://doi.org/10.1007/s00707-013-0959-2
  42. Kolahdouzan, F., Gorbanpour Arani, A. and Abdollahian, M. (2018), "Buckling and free vibration analysis of FG-CNTRCmicro sandwich plate", Steel Compos. Struct., 26(3), 273-287. https://doi.org/10.12989/SCS.2018.26.3.273
  43. Krizhevsky, G. and Stavsky, Y. (1996), "Refined theory for vibrations and buckling of laminated isotropic annular plates", Int. J. Mech. Sci., 38(5), 539-555. https://doi.org/10.1016/0020-7403(95)00053-4
  44. Lal, R. and Ahlawat, N. (2015), "Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method", Eur. J. Mech.-A/Sol., 52, 85-94.
  45. Leclaire, P., Horoshenlov, K.V. and Cummings, A. (2001), "Transverse vibrations of a thin rectangular porous plate saturated by a fluid", J. Sound Vibr., 247(1), 1-18. https://doi.org/10.1006/jsvi.2001.3656
  46. Leissa, A.W. (1969), Vibration of Plates, OHIO State Univ Columbus.
  47. Liew, K.M., Han, J.B. and Xiao, Z.M. (1996), "Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility", Int. J. Sol. Struct., 33(18), 2647-2658. https://doi.org/10.1016/0020-7683(95)00174-3
  48. Liew, K.M., Han, J.B., Xiao, Z.M. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundations", Int. J. Mech. Sci., 38(4), 405-421. https://doi.org/10.1016/0020-7403(95)00062-3
  49. Loghman, A. and Cheraghbak, A. (2018), "Agglomeration effects on electro-magneto-thermo elastic behavior of nano-composite piezoelectric cylinder", Polym. Compos., 39(5), 1594-1603. https://doi.org/10.1002/pc.24104
  50. Ma, L.S. and Wang, T.J. (2003a), "Axisymmetric post-buckling of a functionally graded circular plate subjected to uniformly distributed radial compression", Mater. Sci. For., 423-424, 719-724. https://doi.org/10.4028/www.scientific.net/msf.423-425.719
  51. Ma, L.S. and Wang, T.J. (2003b), "Nonlinear bending and postbuckling of a functionally graded circular plate under mechanical and thermal loadings", Int. J. Sol. Struc., 40(13-14), 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5
  52. Ma, L.S. and Wang, T.J. (2004), "Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory", Int. J. Sol. Struct., 41(1), 85-101. https://doi.org/10.1016/j.ijsolstr.2003.09.008
  53. 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
  54. Mohammadimehr, M., Zarei, H.B., Parakandeh, A. and Arani, A. G. (2017), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., 64(3), 361-379. https://doi.org/10.12989/SEM.2017.64.3.361
  55. Ozdemir, Y.I. (2018), "Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation", Struct. Eng. Mech., 65(3), 213-222. https://doi.org/10.12989/SEM.2018.65.3.213
  56. Pham, T.V. and Nguyen, D.D. (2016), "Nonlinear stability analysis of imperfect three-phase sandwich laminated polymer nanocomposite panels resting on elastic foundations in thermal environments", VNU J. Sci.: Math. Phys., 32(1), 20-36.
  57. Quan, T.Q., Tran, P., Tuan, N.D. and Duc, N.D. (2015), "Nonlinear dynamic analysis and vibration of shear deformable eccentrically stiffened S-FGM cylindrical panels with metalceramic-metal layers resting on elastic foundations", Compos. Struct., 126, 16-33. https://doi.org/10.1016/j.compstruct.2015.02.056
  58. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells, CRC Press.
  59. Reddy, J.N., Wang, C.M. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally graded circular and annular plates", Eur. J. Mec.-A/Sol., 18(2), 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4
  60. Shu, C. and Richards, B.E. (1992), "Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations", Int. J. Numer. Meth. Flu., 15(7), 791-798. https://doi.org/10.1002/fld.1650150704
  61. 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
  62. Wang, Q., Quek, S.T., Sun, C.T. and Liu, X. (2001), "Analysis of piezoelectric coupled circular plate", Smart Mater. Struct., 10(2), 229. https://doi.org/10.1088/0964-1726/10/2/308
  63. Wang, X. (2008), "Changes in the natural frequency of a ferromagnetic rod in a magnetic field due to magnetoelastic interaction", Appl. Math. Mech., 29(8), 1023-1032. https://doi.org/10.1007/s10483-008-0806-x
  64. Wang, Y., Xu, R. and Ding, H. (2009), "Free axisymmetric vibration of FGM circular plates", Appl. Math. Mech., 30(9), 1077-1082. https://doi.org/10.1007/s10483-009-0901-x
  65. Wu, T., Wang, Y. and Liu, G. (2002), "Free vibration analysis of circular plates using generalized differential quadrature rule", Comput. Meth. Appl. Mech. Eng., 191(46), 5365-5380. https://doi.org/10.1016/S0045-7825(02)00463-2
  66. Yahiaoui, M., Tounsi, A., Fahsi, B., Bouiadjra, R.B. and Benyoucef, S. (2018), "The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams", Struct. Eng. Mech., 68(1), 53-66. https://doi.org/10.12989/sem.2018.68.1.053
  67. Zenkour, A.M. (2018), "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147
  68. Zong, Z., Zhang, Y. and Zhang, Y. (2009), Advanced Differential Quadrature Methods (18), Chapman and Hall/CRC.

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