DOI QR코드

DOI QR Code

A high-order gradient model for wave propagation analysis of porous FG nanoplates

  • Shahsavari, Davood (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Li, Li (State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology)
  • 투고 : 2018.04.25
  • 심사 : 2018.08.17
  • 발행 : 2018.10.10

초록

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

키워드

참고문헌

  1. Askes, H. and Aifantis, E.C. (2009), "Gradient elasticity and flexural wave dispersion in carbon nanotubes", Phys. Rev. B, 80(19), 195412.
  2. Azadi, V., Azadi, M., Fazelzadeh, S.A. and Azadi, E. (2014), "Active control of an fgm beam under follower force with piezoelectric sensors/actuators", Int. J. Struct. Stabil. Dyn., 14(2), 1350063. https://doi.org/10.1142/S0219455413500636
  3. Barati, M.R. (2017a), "On wave propagation in nanoporous materials", Int. J. Eng. Sci., 116, 1-11. https://doi.org/10.1016/j.ijengsci.2017.03.007
  4. Barati, M.R. (2017b), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermomechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., Int. J., 64(6), 683-693.
  5. Barati, M.R. and Zenkour, A. (2017), "A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate", Compos. Struct., 168, 885-892.
  6. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270.
  7. Bhattacharyya, M., Kapuria, S. and Kumar, A. (2007), "On the stress to strain transfer ratio and elastic deflection behavior for Al/SiC functionally graded material", Mech. Adv. Mater. Struct., 14(4), 295-302. https://doi.org/10.1080/15376490600817917
  8. Ebrahimi, F. and Dabbagh, A. (2018), "Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments", Struct. Eng. Mech., Int. J., 65(6), 645-656.
  9. Elmossouess, B., Kebdani, S., Bouiadjra, M.B. and Tounsi, A. (2017), "A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates". Struct. Eng. Mech., Int. J., 62(4), 401-415. https://doi.org/10.12989/sem.2017.62.4.401
  10. 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
  11. Farokhi, H. and Ghayesh, M.H. (2015), "Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams", Int. J. Eng. Sci., 91, 12-33.
  12. Farokhi, H., Ghayesh, M.H. and Amabili, M. (2013), "Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory", Int. J. Eng. Sci., 68, 11-23. https://doi.org/10.1016/j.ijengsci.2013.03.001
  13. Fazzolari, F.A. (2016), "Modal characteristics of P-and S-FGM plates with temperature-dependent materials in thermal environment", J. Thermal Stresses, 39(7), 854-873. https://doi.org/10.1080/01495739.2016.1189772
  14. Ghayesh, M.H. (2018a), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131. https://doi.org/10.1016/j.ijengsci.2017.11.004
  15. Ghayesh, M.H. (2018b), "Functionally graded microbeams: simultaneous presence of imperfection and viscoelasticity", Int. J. Mech. Sci., 140, 339-350. https://doi.org/10.1016/j.ijmecsci.2018.02.037
  16. Ghayesh, M.H. (2018c), "Mechanics of tapered AFG sheardeformable microbeams", Microsyste. Technol., 24(4), 1743-1754. https://doi.org/10.1007/s00542-018-3764-y
  17. Ghayesh, M.H. (2018d), "Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams", Appl. Math. Model., 59, 583-596.
  18. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013a), "Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory", Int. J. Eng. Sci., 63, 52-60. https://doi.org/10.1016/j.ijengsci.2012.12.001
  19. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013b), "Threedimensional nonlinear size-dependent behaviour of Timoshenko microbeams", Int. J. Eng. Sci., 71, 1-14.
  20. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2013c), "Nonlinear behaviour of electrically actuated MEMS resonators", Int. J. Eng. Sci., 71, 137-155. https://doi.org/10.1016/j.ijengsci.2013.05.006
  21. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2013d), "Nonlinear dynamics of a microscale beam based on the modified couple stress theory", Compos. Part B: Eng., 50, 318-324. https://doi.org/10.1016/j.compositesb.2013.02.021
  22. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2014), "In-plane and out-of-plane motion characteristics of microbeams with modal interactions", Compos. Part B: Eng., 60, 423-439. https://doi.org/10.1016/j.compositesb.2013.12.074
  23. Ghayesh, M.H., Farokhi, H. and Gholipour, A. (2017), "Oscillations of functionally graded microbeams", Int. J. Eng. Sci., 110, 35-53. https://doi.org/10.1016/j.ijengsci.2016.09.011
  24. Gholipour, A., Farokhi, H. and Ghayesh, M.H. (2015), "In-plane and out-of-plane nonlinear size-dependent dynamics of microplates", Nonlinear Dyn., 79(3), 1771-1785. https://doi.org/10.1007/s11071-014-1773-7
  25. Gupta, A. and Talha, M. (2017), "Influence of porosity on the flexural and free vibration responses of functionally graded plates in thermal environment", Int. J. Struct. Stabil. Dyn., 1850013.
  26. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, M., Tounsi, A. and Mahmoud, S. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., Int. J., 25(6), 717-726.
  27. Huang, X.-L. and Shen, H.-S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solids Struct., 41(9), 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012
  28. Kapuria, S., Bhattacharyya, M. and Kumar, A. (2008), "Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation", Compos. Struct., 82(3), 390-402. https://doi.org/10.1016/j.compstruct.2007.01.019
  29. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421. https://doi.org/10.1142/S0217984916504212
  30. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25(3), 361-374.
  31. Karami, B., Janghorban, M. and Li, L. (2018a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronautica, 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  32. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110.
  33. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
  34. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  35. Karami, B., Shahsavari, D. and Janghorban, M. (2018e), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057.
  36. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018f), "Wave dispersion of mounted graphene with initial stress", Thin-Wall. Struct., 122, 102-111. https://doi.org/10.1016/j.tws.2017.10.004
  37. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2018g), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 0954406218781680.
  38. Karami, B., Shahsavari, D. and Li, L. (2018h), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 97, 317-327.
  39. Karami, B., Shahsavari, D. and Li, L. (2018i), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Thermal Stresses, 41(4), 483-499. https://doi.org/10.1080/01495739.2017.1393781
  40. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018j), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci., 0954406218756451.
  41. Klouche, F., Darcherif, L., Sekkal, M., Tounsi, A. and Mahmoud, S. (2017), "An original single variable shear deformation theory for buckling analysis of thick isotropic plates", Struct. Eng. Mech., Int. J., 63(4), 439-446.
  42. Koutsoumaris, C.C., Vogiatzis, G., Theodorou, D., Tsamasphyros, G., Simos, T.E., Kalogiratou, Z. and Monovasilis, T. (2015), "Application of bi-Helmholtz nonlocal elasticity and molecular simulations to the dynamical response of carbon nanotubes", AIP Conference Proceedings, AIP Publishing, 190011.
  43. Lam, D.C.C., Yang, F., Chong, A., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  44. Lazar, M., Maugin, G.A. and Aifantis, E.C. (2006), "On a theory of nonlocal elasticity of bi-Helmholtz type and some applications", Int. J. Solids Struct., 43(6), 1404-1421. https://doi.org/10.1016/j.ijsolstr.2005.04.027
  45. Li, L. and Hu, Y. (2016a), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011
  46. Li, L. and Hu, Y. (2016b), "Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory", Computat. Mater. Sci., 112, 282-288. https://doi.org/10.1016/j.commatsci.2015.10.044
  47. Li, J.F., Takagi, K., Ono, M., Pan, W., Watanabe, R., Almajid, A. and Taya, M. (2003), "Fabrication and evaluation of porous piezoelectric ceramics and porosity-graded piezoelectric actuators", J. Am. Ceramic Soc., 86(7), 1094-1098. https://doi.org/10.1111/j.1151-2916.2003.tb03430.x
  48. Li, Q., Iu, V. and Kou, K. (2009), "Three-dimensional vibration analysis of functionally graded material plates in thermal environment", J. Sound Vib., 324(3), 733-750. https://doi.org/10.1016/j.jsv.2009.02.036
  49. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092.
  50. Li, L., Hu, Y. and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 75, 118-124. https://doi.org/10.1016/j.physe.2015.09.028
  51. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  52. Lin, Q.-Y., Jing, G., Zhou, Y.-B., Wang, Y.-F., Meng, J., Bie, Y.-Q., Yu, D.-P. and Liao, Z.-M. (2013), "Stretch-induced stiffness enhancement of graphene grown by chemical vapor deposition", ACS Nano, 7(2), 1171-1177. https://doi.org/10.1021/nn3053999
  53. Mechab, I., Atmane, H.A., Tounsi, A. and Belhadj, H.A. (2010), "A two variable refined plate theory for the bending analysis of functionally graded plates", Acta Mech. Sinica, 26(6), 941-949. https://doi.org/10.1007/s10409-010-0372-1
  54. Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, 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. Brazil. Soc. Mech. Sci. Eng., 8(38), 2193-2211.
  55. Meftah, A., Bakora, A., Zaoui, F.Z., Tounsi, A. and Bedia, E.a.A. (2017), "A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Steel Compos. Struct., Int. J., 23(3), 317-330.
  56. Merdaci, S., Tounsi, A. and Bakora, A. (2016), "A novel four variable refined plate theory for laminated composite plates", Steel Compos. Struct., Int. J., 22(4), 713-732. https://doi.org/10.12989/scs.2016.22.4.713
  57. Nami, M.R. and Janghorban, M. (2014), "Wave propagation in rectangular nanoplates based on strain gradient theory with one gradient parameter with considering initial stress", Modern Phys. Lett. B, 28(03), 1450021.
  58. Narendar, S. and Gopalakrishnan, S. (2012), "Scale effects on buckling analysis of orthotropic nanoplates based on nonlocal two-variable refined plate theory", Acta Mechanica, 223(2), 395-413. https://doi.org/10.1007/s00707-011-0560-5
  59. Panyatong, M., Chinnaboon, B. and Chucheepsakul, S. (2016), "Free vibration analysis of FG nanoplates embedded in elastic medium based on second-order shear deformation plate theory and nonlocal elasticity", Compos. Struct., 153, 428-441.
  60. Praveen, G. and Reddy, J. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solids Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9
  61. Rad, A.B. (2015), "Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation", Appl. Math. Computat., 256, 276-298.
  62. Reddy, J. and Chin, C. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Thermal Stresses, 21(6), 593-626. https://doi.org/10.1080/01495739808956165
  63. Sarangan, S. and Singh, B. (2016), "Higher-order closed-form solution for the analysis of laminated composite and sandwich plates based on new shear deformation theories", Compos. Struct., 138, 391-403.
  64. Sehoul, M., Benguediab, M., Bakora, A. and Tounsi, A. (2017), "Free vibrations of laminated composite plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 24(5), 603-613.
  65. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S. (2017), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., Int. J., 25(4), 389-401.
  66. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0
  67. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express, 4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89
  68. Shahsavari, D., Karami, B. and Mansouri, S. (2018a), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Solids, 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  69. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018b), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004
  70. She, G.-L., Yuan, F.-G., Ren, Y.-R. and Xiao, W.-S. (2017), "On buckling and postbuckling behavior of nanotubes", Int. J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005
  71. She, G.-L., Ren, Y.-R., Yuan, F.-G. and Xiao, W.-S. (2018), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009
  72. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA Journal, 40(1), 137-146. https://doi.org/10.2514/2.1622
  73. Shimpi, R. and Patel, H. (2006a), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030
  74. Shimpi, R. and Patel, H. (2006b), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solids Struct., 43(22-23), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007
  75. Thai, H.-T. and Kim, S.-E. (2012), "Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates", Int. J. Mech. Sci., 54(1), 269-276. https://doi.org/10.1016/j.ijmecsci.2011.11.007
  76. Touloukian, Y.S. and Ho, C. (1970), "Thermal expansion. Nonmetallic solids", Thermophysical properties of matter-The TPRC Data Series, New York: IFI/Plenum, 1970-, edited by Touloukian, YS e (series ed.); Ho, CY e (series tech. ed.).
  77. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  78. Yahia, S.A., Atmane, H.A., 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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  79. Zhu, X. and Li, L. (2017), "Closed form solution for a nonlocal strain gradient rod in tension", Int. J. Eng. Sci., 119, 16-28. https://doi.org/10.1016/j.ijengsci.2017.06.019
  80. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO 2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2
  81. Zidi, M., Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S. (2017), "A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams", Struct. Eng. Mech., Int. J., 64(2), 145-153.

피인용 문헌

  1. Elastic guided waves in fully-clamped functionally graded carbon nanotube-reinforced composite plates vol.6, pp.9, 2019, https://doi.org/10.1088/2053-1591/ab3474
  2. Using IGA and trimming approaches for vibrational analysis of L-shape graphene sheets via nonlocal elasticity theory vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.717
  3. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  4. Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches vol.34, pp.2, 2020, https://doi.org/10.12989/scs.2020.34.2.261
  5. Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation vol.38, pp.1, 2018, https://doi.org/10.12989/scs.2021.38.1.001
  6. Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches vol.40, pp.2, 2021, https://doi.org/10.12989/scs.2021.40.2.157
  7. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2018, https://doi.org/10.12989/scs.2021.40.3.355