Smart Structures and Systems

  • 제23권5호
  • /
  • Pages.429-447
  • /
  • 2019
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Size-dependent magneto-electro-elastic vibration analysis of FG saturated porous annular/ circular micro sandwich plates embedded with nano-composite face sheets subjected to multi-physical pre loads

  • Amir, Saeed (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arshid, Ehsan (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Arani, Mohammad Reza Ghorbanpour (Electrical Engineering Department, Amirkabir University of Technology)
  • 투고 : 2018.12.24
  • 심사 : 2019.03.14
  • 발행 : 2019.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

The present study analyzed free vibration of the three-layered micro annular/circular plate which its core and face sheets are made of saturated porous materials and FG-CNTRCs, respectively. The structure is subjected to magneto-electric fields and magneto-electro-mechanical pre loads. Mechanical properties of the porous core and also FG-CNTRC face sheets are varied through the thickness direction. Using dynamic Hamilton's principle, the motion equations based on MCS and FSD theories are derived and solved via GDQ as an efficient numerical method. Effect of different parameters such as pores distributions, porosity coefficient, pores compressibility, CNTs distribution, elastic foundation, multi-physical pre loads, small scale parameter and aspect ratio of the plate are investigated. The findings of this study can be useful for designing smart structures such as sensor and actuator.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Abdel-Rahman, E.M., Younis, M.I. and Nayfeh, A.H. (2002), "Characterization of the mechanical behavior of an electrically actuated microbeam", J. Micromech. Microeng., 12(6), 759. https://doi.org/10.1088/0960-1317/12/6/306
  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", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 1464420716670929.
  3. Amir, S., Khorasani, M. and BabaAkbar-Zarei, H. (2018a). "Buckling analysis of nanocomposite sandwich plates with piezoelectric face sheets based on flexoelectricity and first-order shear deformation theory", J. Sandw. Struct. Mater., 109963621879538.
  4. Amir, S., Bidgoli, E.M.R. and Arshid, E. (2018b), "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. https://doi.org/10.1080/15376494.2018.1487612.
  5. Arani, A.G., Haghparast, E., Maraghi, Z.K. and Amir, S. (2015), "Static stress analysis of carbon nano-tube reinforced composite (CNTRC) cylinder under non-axisymmetric thermo-mechanical loads and uniform electro-magnetic fields", Compos. Part B: Eng., 68, 136-145. https://doi.org/10.1016/j.compositesb.2014.08.036
  6. Arefi, M., Bidgoli, E.M.R. and Zenkour, A.M. (2018), "Sizedependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory", Smart Struct. Syst., 22(1), 27-40. https://doi.org/10.12989/sss.2018.22.1.027.
  7. Arshid, E., Kiani, A. and Amir, S. (2019), "Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications.
  8. Arshid, E. and Khorshidvand, A.R. (2017), "Flexural vibrations analysis of saturated porous circular plates using differential auadrature method", Iranian J. Mech. Eng. T. - ISME, 19(1), 78-100.
  9. 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.
  10. Ashrafi, B., Hubert, P. and Vengallatore, S. (2006), "Carbon nanotube-reinforced composites as structural materials for microactuators in microelectromechanical systems", Nanotechnology, 17(19), 4895. https://doi.org/10.1088/0957-4484/17/19/019
  11. Barati, M.R., Shahverdi, H. and Zenkour, A.M. (2017), "Electromechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory", Mech. Adv. Mater. Struct., 24(12), 987-998. https://doi.org/10.1080/15376494.2016.1196799.
  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. doi: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. Bui, T.Q., Do, T. Van, Ton, L.H.T., Doan, D.H., Tanaka, S., Pham, D.T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Compos.Part B: Eng., 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.
  16. Bui, T.Q., Nguyen, M.N. and Zhang, C. (2011), "An efficient meshfree method for vibration analysis of laminated composite plates", Comput. Mech., 48(2), 175-193. https://doi.org/10.1007/s00466-011-0591-8
  17. Chakraverty, S., Bhat, R.B. and Stiharu, I. (2001), "Free vibration of annular elliptic plates using boundary characteristic orthogonal polynomials as shape functions in the Rayleigh-Ritz method", J. Sound Vib., 241, 524-539. doi: 10.1006/jsvi.2000.3243.
  18. Chen, D., Kitipornchai, S. and Yang, J. (2016), "Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core", Thin Wall. Struct., 107, 39-48. https://doi.org/10.1016/j.tws.2016.05.025.
  19. Chen, D., Yang, J. and Kitipornchai, S. (2016), "Free and forced vibrations of shear deformable functionally graded porous beams", Int. J. Mech. Sci., 108-109, 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025
  20. 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.
  21. Detournay, E. and Cheng, A.H.D. (1995), "Fundamentals of poroelasticity", Anal. Design Methods, 1993, 113-171. https://doi.org/10.1016/B978-0-08-040615-2.50011-3.
  22. Do, T.V., Bui, T.Q., Yu, T.T., Pham, D.T. and Nguyen, C.T. (2017), "Role of material combination and new results of mechanical behavior for FG sandwich plates in thermal environment", J. Comput. Sci., 21, 164-181. https://doi.org/10.1016/j.jocs.2017.06.015.
  23. Duc, N.D., Dinh Nguyen, P. and Dinh Khoa, N. (2017), "Nonlinear dynamic analysis and vibration of eccentrically stiffened S-FGM 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.
  24. Duc, N.D, 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.
  25. 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.
  26. Duc, N.D. (2014), "Nonlinear static and dynamic stability of functionally graded plates and shells", Vietnam National University Press.
  27. 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 - Solids, 58, 10-30. https://doi.org/10.1016/j.euromechsol.2016.01.004.
  28. 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.
  29. Duc, N.D. and Quan, T.Q. (2015), "Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation", J. Vib. Control, 21(7), 1340-1362. https://doi.org/10.1177/1077546313494114
  30. Ebrahimi, F., Jafari, A. and Barati, M.R. (2017a), "Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations", Thin Wall. Struct., 119, 33-46. https://doi.org/10.1016/j.tws.2017.04.002.
  31. Ebrahimi, F., Daman, M. and Jafari, A. (2017b), "Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment", Smart Struct. Syst., 20(6), 709-728. https://doi.org/10.12989/sss.2017.20.6.709.
  32. Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on pasternak elastic foundation using higher-order shear deformation plate theories", Smart Struct. Syst., 21(1), 113-122. https://doi.org/10.12989/sss.2018.21.1.113.
  33. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803.
  34. Eringen, A.C. (2002), Nonlocal continuum field theories. Springer Science & Business Media.
  35. Ferreira, A.J.M., Fasshauer, G.E., Batra, R.C. and Rodrigues, J.D. (2008), "Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter", Compos. Struct., 86(4), 328-343. https://doi.org/10.1016/j.compstruct.2008.07.025
  36. Ferreira, A.J.M., Viola, E., Tornabene, F., Fantuzzi, N. and Zenkour, A.M. (2013), "Analysis of sandwich plates by generalized differential quadrature method", Math. Probl. Eng,, 2013, 1-12. http://dx.doi.org/10.1155/2013/964367.
  37. Ghorbanpour-Arani, A. and Zamani, M.H. (2018), "Nonlocal free vibration analysis of FG-porous shear and normal deformable sandwich nanoplate with piezoelectric face sheets resting on silica aerogel foundation", Arabian J. Sci. Eng., 43(9), 4675-4688. https://doi.org/10.1007/s13369-017-3035-8
  38. Ghorbanpour Arani, A., BabaAkbar Zarei, H. and Haghparast, E. (2018), "Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally gradedpiezoelectric nanocomposite face sheets", J. Vib. Control, 107754631774750.
  39. Ghorbanpour Arani, A., Roudbari, M.A. and Amir, S. (2016), "Longitudinal magnetic field effect on wave propagation of fluid-conveyed SWCNT using Knudsen number and surface considerations", Appl. Math. Model., 40(3), 2025-2038. https://doi.org/10.1016/j.apm.2015.09.055
  40. Ghorbanpour Arani, A., Shajari, A., Amir, S. and Atabakhshian, V. (2013a), "Nonlinear fluid-induced vibration and instability of an embedded piezoelectric polymeric microtube using nonlocal elasticity theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 227(12), 2870-2885. https://doi.org/10.1177/0954406213479094
  41. Ghorbanpour Arani, A., Shirali, A., Farahani, M.N., Amir, S. and Loghman, A. (2013b), "Nonlinear vibration analysis of protein microtubules in cytosol conveying fluid based on nonlocal elasticity theory using differential quadrature method", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 227(1), 137-145. https://doi.org/10.1177/0954406212445151
  42. Ghorbanpour Arani, A. and Zamani, M.H. (2017), "Investigation of electric field effect on size-dependent bending analysis of functionally graded porous shear and normal deformable sandwich nanoplate on silica Aerogel foundation", J. Sandw. Struct. Mater., 1099636217721405.
  43. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56. https://doi.org/10.1038/354056a0
  44. Ke, L.L. and Wang, Y.S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory", Physica E: Low-Dimens. Syst. Nanostruct., 63, 52-61. https://doi.org/10.1016/j.physe.2014.05.002.
  45. Ke, L.L., Wang, Y.S., Yang, J. and Kitipornchai, S. (2014), "Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory", Acta Mechanica Sinica, 30(4), 516-525. https://doi.org/10.1007/s10409-014-0072-3
  46. Ke, L.L., Yang, J., Kitipornchai, S. and Bradford, M.A. (2012), "Bending, buckling and vibration of size-dependent functionally graded annular microplates", Compos. Struct., 94(11), 3250-3257. https://doi.org/10.1016/j.compstruct.2012.04.037.
  47. 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
  48. Kiran, M.C. and Kattimani, S.C. (2018), "Free vibration and static analysis of functionally graded skew magneto-electro-elastic plate", Smart Struct. Syst., 21(4), 493-519. https://doi.org/10.12989/sss.2018.21.4.493.
  49. 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.
  50. Lal, R. and Ahlawat, N. (2015), "Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method", Eur. J. Mech. - A- Solids, 52, 85-94. https://doi.org/10.1016/j.euromechsol.2015.02.004
  51. Leclaire, P., Horoshenkov, K.V., Swift, M.J. and Hothersall, D.C. (2001), "The vibrational response of a clamped rectangular porous plate", J. Sound Vib., 247(1), 19-31. https://doi.org/10.1006/jsvi.2000.3657.
  52. Lei, Z.X., Liew, K.M. and Yu, J.L. (2013), "Free vibration analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method in thermal environment", Compos. Struct., 106, 128-138. https://doi.org/10.1016/j.compstruct.2013.06.003.
  53. Leissa, A.W. (1969), Vibration of plates. Ohio State Univ. Columbus.
  54. 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.
  55. Liu, S., Yu, T., Bui, T.Q. and Xia, S. (2017a), "Size-dependent analysis of homogeneous and functionally graded microplates using IGA and a non-classical Kirchhoff plate theory", Compos. Struct., 172, 34-44. https://doi.org/10.1016/j.compstruct.2017.03.067.
  56. Liu, S., Yu, T. and Bui, T.Q. (2017b), "Size effects of functionally graded moderately thick microplates: A novel non-classical simple-FSDT isogeometric analysis", Eur. J. Mech. - A - Solids, 66, 446-458. https://doi.org/10.1016/j.euromechsol.2017.08.008.
  57. Liu, S., Yu, T., Lich, L. Van, Yin, S. and Bui, T.Q. (2019), "Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis", Comput. Struct., 212, 173-187. https://doi.org/10.1016/j.compstruc.2018.10.009.
  58. Liu, S., Yu, T., Van Lich, L., Yin, S. and Bui, T.Q. (2018), "Size effect on cracked functional composite micro-plates by an XIGA-based effective approach", Meccanica, 53(10), 2637-2658. https://doi.org/10.1007/s11012-018-0848-9
  59. Loghman, A. and Cheraghbak, A. (2018), "Agglomeration effects on electro-magneto-thermo elastic behavior of nano-composite piezoelectric cylinder", Polymer Compos., 39(5), 1594-1603. https://doi.org/10.1002/pc.24104.
  60. Loghman, A., Ghorbanpour Arani, A. and Mosallaie Barzoki, A. (2017), "Nonlinear stability of non-axisymmetric functionally graded reinforced nano composite microplates", Comput. Concrete, 19(6), 677-687. https://doi.org/10.12989/cac.2017.19.6.677.
  61. Malekzadeh, P. and Zarei, A.R. (2014), "Free vibration of quadrilateral laminated plates with carbon nanotube reinforced composite layers", Thin Wall. Struct., 82, 221-232. https://doi.org/10.1016/j.tws.2014.04.016.
  62. Mechab, I., Mechab, B., Benaissa, S., Serier, B. andBouiadjra, B. B. (2016), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Braz. Soc. Mech. Sci. Eng., 38(8), 2193-2211. https://doi.org/10.1007/s40430-015-0482-6
  63. Mehar, K., Panda, S.K., Bui, T.Q. and Mahapatra, T.R. (2017), "Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM", J. Therm. Stresses, 40(7), 899-916. https://doi.org/10.1080/01495739.2017.1318689.
  64. Meirovitch, L. (1997), Principles and techniques of vibrations (Vol. 1). Prentice Hall New Jersey.
  65. Mirzaei, M. and Kiani, Y. (2016), "Free vibration of functionally graded carbon nanotube reinforced composite cylindrical panels", Compos. Struct., 142, 45-56. https://doi.org/10.1016/j.compstruct.2015.12.071.
  66. Mohammadzadeh-Keleshteri, M., Asadi, H. and Aghdam, M.M. (2017), "Geometrical nonlinear free vibration responses of FGCNT reinforced composite annular sector plates integrated with piezoelectric layers", Compos. Struct., 171, 100-112. https://doi.org/10.1016/j.compstruct.2017.01.048.
  67. Pham, T. Van and Duc, N.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.
  68. 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.
  69. Reddy, J.N. and Berry, J. (2012), "Nonlinear theories of axisymmetric bending of functionally graded circular plates with modified couple stress", Compos. Struct., 94(12), 3664-3668. https://doi.org/10.1016/j.compstruct.2012.04.019.
  70. Reddy, J.N. and Khdeir, A. (1989), "Buckling and vibration of laminated composite plates using various plate theories", AIAA J., 27(12), 1808-1817. https://doi.org/10.2514/3.10338.
  71. Reddy, J., Wang, C. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally graded circular and annular plates", Eur. J. Mech. -A - Solids, 18(2), 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4.
  72. Rezaei, A.S. and Saidi, A.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos.Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125.
  73. Shafiei, N. and Kazemi, M. (2017), "Buckling analysis on the bidimensional functionally graded porous tapered nano-/microscale beams", Aerosp. Sci. Technol., 66, 1-11. https://doi.org/10.1016/j.ast.2017.02.019.
  74. Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M. (2017), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Method. Appl. M., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.
  75. Shahverdi, H. and Barati, M.R. (2017), "Vibration analysis of porous functionally graded nanoplates", Int. J. Eng. Science, 120, 82-99. https://doi.org/10.1016/j.ijengsci.2017.06.008.
  76. Sidhoum, I.A., Boutchicha, D., Benyoucef, S. and Tounsi, A. (2018), "A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates", Smart Struc. Syst., 22(3), 303-314. https://doi.org/10.12989/gae.2017.12.1.009
  77. Shu, C. (2012), Differential quadrature and its application in engineering. Springer Science & Business Media.
  78. Theodorakopoulos, D.D. and Beskos, D.E. (1994), "Flexural vibrations of poroelastic plates", Acta Mechanica, 103(1-4), 191-203. https://doi.org/10.1007/BF01180226
  79. Tohidi, H., Hosseini-Hashemi, S.H. and Maghsoudpour, A. (2018), "Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory", Smart Struct. Syst., 22(5), 527-546. https://doi.org/10.12989/sss.2018.22.5.527.
  80. Wang, Z.X. and Shen, H.S. (2012), "Nonlinear vibration and bending of sandwich plates with nanotube-reinforced composite face sheets", Compos. Part B: Eng., 43(2), 411-421. https://doi.org/10.1016/j.compositesb.2011.04.040.
  81. Wu, T., Wang, Y. and Liu, G. (2002), "Free vibration analysis of circular plates using generalized differential quadrature rule", Comput. Method. Appl. M., 191(46), 5365-5380. https://doi.org/10.1016/S0045-7825(02)00463-2.
  82. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. andHouari, M. S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015.
  83. Yu, T., Hu, H., Zhang, J. and Bui, T.Q. (2019a), "Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory", Thin Wall. Struct., 138, 1-14. https://doi.org/10.1016/j.tws.2018.12.006
  84. Yu, T., Zhang, J., Hu, H. and Bui, T.Q. (2019b), "A novel sizedependent quasi-3D isogeometric beam model for twodirectional FG microbeams analysis", Compos. Struct., 211, 76-88. https://doi.org/10.1016/j.compstruct.2018.12.014.
  85. Zhou, D., Au, F.T.K., Cheung, Y.K. and Lo, S.H. (2003), "Threedimensional vibration analysis of circular and annular plates via the Chebyshev-Ritz method", Int. J. Solids Struct., 40(12), 3089-3105. https://doi.org/10.1016/S0020-7683(03)00114-8.
  86. Zhou, Z.H., Wong, K.W., Xu, X.S. and Leung, A.Y.T. (2011), "Natural vibration of circular and annular thin plates by Hamiltonian approach", J. Sound Vib., 330(5), 1005-1017. https://doi.org/10.1016/j.jsv.2010.09.015.
  87. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010.

피인용 문헌

  1. Free Vibration Response of FG Porous Sandwich Micro-Beam with Flexoelectric Face-Sheets Resting on Modified Silica Aerogel Foundation vol.11, pp.9, 2019, https://doi.org/10.1142/s175882511950087x
  2. Axisymmetric free vibration and stress analyses of saturated porous annular plates using generalized differential quadrature method vol.25, pp.21, 2019, https://doi.org/10.1177/1077546319871132
  3. Quasi-3D tangential shear deformation theory for size-dependent free vibration analysis of three-layered FG porous micro rectangular plate integrated by nano-composite faces in hygrothermal environmen vol.43, pp.2, 2019, https://doi.org/10.1080/01495739.2019.1660601
  4. Vibration analysis of magnetorheological fluid circular sandwich plates with magnetostrictive facesheets exposed to monotonic magnetic field located on visco-Pasternak substrate vol.26, pp.17, 2019, https://doi.org/10.1177/1077546319899203
  5. Analytical solution for analyzing initial curvature effect on vibrational behavior of PM beams integrated with FGP layers based on trigonometric theories vol.10, pp.3, 2019, https://doi.org/10.12989/anr.2021.10.3.235
  6. Vibration characteristics of microplates with GNPs-reinforced epoxy core bonded to piezoelectric-reinforced CNTs patches vol.11, pp.2, 2019, https://doi.org/10.12989/anr.2021.11.2.115