과제정보
The authors would like to thank the referees for their valuable comments. Also, they would like to thank the Iranian Nanotechnology Development Committee for their financial support and the University of Kashan for supporting this work by Grant No. 891238/19.
참고문헌
- Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Computat. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
- Akbas, S.D. (2018), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.
- Akbas, S.D. (2020), "Modal analysis of viscoelastic nanorods under an axially harmonic load", Adv. Nano Res., Int. J., 8(4), 277-282. https://doi.org/10.12989/anr.2020.8.4.277.
- Analooei, H.R., Azhari, M., Heidarpour, A., Ng, T.Y. and Lin, R.M. (2013), "Elastic buckling and vibration analyses of orthotropic Nano plates using nonlocal continuum mechanics and spline finite strip method", Appl. Math. Model., 37(10-11), 6703-6717. https://doi.org/10.1016/j.commatsci.2012.06.031.
- Anirudh, B., Ganapathi, M., Anant, C. and Polit, O. (2019), "A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: Bending, vibration and buckling", Compos. Struct., 222, 110899. https://doi.org/10.1016/j.compstruct.2019.110899.
- Ansari, R. and Sahmani, S. (2011), "Surface stress effects on the free vibration behavior of nanoplates", Int. J. Eng. Sci., 49(11), 1204-1215. https://doi.org/10.1016/j.ijengsci.2011.06.005.
- Arefi, M., Kiani, M. and Rabczuk, T., (2019) "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part B-Eng., 168, 320-333. https://doi.org/10.1016/j.compositesb.2019.02.057.
- Bessaim, A., Ahmed Houari, M.S., Abdelmoumen Anis, B., Kaci, A., Tounsi, A. and Adda Bedia, E.A. (2018), "Buckling analysis of embedded nanosize FG beams based on a refined hyperbolic shear deformation theory", J. Appl. Computat. Mech., 4(3), 140-146. https://doi.org/10.22055/JACM.2017.22996.1146.
- Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic Buckling and Static Bending of Shear Deformable Functionally Graded Porous Beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
- Chen, D., Kitipornchai, S. and Yang, J. (2017) "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
- Chen, X.C., Chen, L., Huang, S., Li, M. and Li, X. (2021), "Nonlinear forced vibration of in-plane bi-directional functionally graded materials rectangular plate with global and localized geometrical imperfections", Appl. Math. Model., 93, 443-466. https://doi.org/10.1016/j.apm.2020.12.033.
- Chikr, C., Kaci, A., Yeghnem, R. and Tounsi, A. (2019), "A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates", Struct. Eng. Mech., Int. J., 72(5), 653-673. https://doi.org/10.12989/sem.2019.72.5.653.
- Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach", Compos. Part B-Eng., 160, 661-676. https://doi.org/10.1016/j.compositesb.2018.12.020.
- Ebrahimi, F., Nouraei, M., Dabbagh, A. and Civalek, O. (2019), "Buckling analysis of graphene oxide powder-reinforced nanocomposite beams subjected to non-uniform magnetic field", Struct. Eng. Mech., Int. J., 71(4), 351-361. https://doi.org/10.12989/sem.2019.71.4.351.
- Gao, Y., Xiao, W.S. and Zhu, H. (2019), "Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method", Struct. Eng. Mech., Int. J., 69(2), 205-219. https://doi.org/10.12989/sem.2019.69.2.205.
- Halpin, J.C. and Tsai, S.W. (1967), "Environmental Factors in Composite Materials Design", U.S. Air Force Technical Report AFML TR, 67423.
- Hosseini-Hashemi, S., Bedroud, M. and Nazemnezhad, R. (2013), "An exact analytical solution for free vibration of functionally graded circular/annular Mindlin nanoplates via nonlocal elasticity", Compos. Struct., 103, 108-118. https://doi.org/10.1016/j.compstruct.2013.02.022.
- Jabbari, M., Mojahedin, A., Khorshidvand. A.R. and Eslami, M.R. (2013). "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.
- Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M.R. (2014), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Therm. Stresses, 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768.
- Jabbari, M. and Rezaei, M. (2016), "Mechanical Buckling of FG Saturated Porous Rectangular Plate with Piezoelectric Actuators", Iran. J. Mech. Eng., 17 (2), 45-65.
- Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., Int. J., 7(1), 51-61. https://doi.org/10.12989/anr.2019.7.1.051.
- Kim, J., Kamil Zur, K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/j.compstruct.2018.11.023.
- Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010.
- Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021.
- Li, X. (2021), "Parametric resonances of rotating composite laminated nonlinear cylindrical shells under periodic axial loads and hydrothermal environment", Compos. Struct., 255, 112887. https://doi.org/10.1016/j.compstruct.2020.112887.
- Liu, L. and Huang, Z. (2014), "A note on Mori-Tanaka's method", Acta Mech. Solida Sin., 27(3), 234-244. https://doi.org/10.1016/S0894-9166(14)60033-1.
- Magnucka-Blandzi, E. (2008), "Axisymmetrical deflection and buckling of circular porous-cellular plate", Thin Wall. Struct., 46, 333-337. https://doi.org/10.1016/j.tws.2007.06.006.
- Magnucki, K., Malinowski, M. and Kasprzak, J. (2006) "Bending and Buckling of a Rectangular Porous Plate", Steel Compos. Struct., Int. J., 6(4), 319-333. https://doi.org/10.12989/scs.2014.16.3.325.
- Malekzadeh, P., Setoodeh, A.R. and Beni, A.A. (2011), "Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium", Compos. Struct., 93, 2083-2089. https://doi.org/10.1016/j.compstruct.2011.02.013.
- Mehrabi, M., Mohammadimehr, M. and Mousavinejad, F.S. (2021), "2D magneto-mechanical vibration analysis of a micro composite Timoshenko beam resting on orthotropic medium", Smart Struct. Syst., Int. J., 27(1), 1-18. http://dx.doi.org/10.12989/sss.2021.27.1.001.
- Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., Int. J., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
- Mohammadimehr, M., Afshari, H., Salemi, M., Torabi, K. and Mehrabi, M. (2019), "Free vibration and buckling analyses of functionally graded annular thin sector plate in-plane loads using GDQM", Struct. Eng. Mech., Int. J., 71(5), 525-544. https://doi.org/10.12989/sem.2019.71.5.525.
- Mohammadimehr, M., Mehrabi, M. and Mousavinejad, F.S. (2020), "Magneto-mechanical vibration analysis of single-/three-layered micro-Timoshenko porous beam and graphene platelet as reinforcement based on modified strain gradient theory and differential quadrature method", J. Vib. Contr., 1077546320949083. https://doi.org/10.1177/1077546320949083.
- Murmu, T., McCarthy, M.A. and Adhikari, S. (2013), "In-plane Magnetic Field Affected Transverse Vibration of Embedded Singlelayer Graphene Sheets using Equivalent Nonlocal Elasticity Approach", Compos. Struct., 96, 57-63. https://doi.org/10.1016/j.compstruct.2012.09.005.
- Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Computat. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031.
- Nejadi, M.M. and Mohammadimehr, M. (2020), "Buckling analysis of nano composite sandwich Euler-Bernoulli beam considering porosity distribution on elastic foundation using DQM", Adv. Nano Res., Int. J., 8(1), 59-68. https://doi.org/10.12989/anr.2020.8.1.059.
- Nejadi, M.M., Mohammadimehr, M. and Mehrabi, M. (2021), "Free vibration and stability analysis of sandwich pipe by considering porosity and graphene platelet effects on conveying fluid flow", Alexandria Eng. J., 60(1), 1945-1954. https://doi.org/10.1016/j.aej.2020.11.042.
- Noroozi, R., Barati, A., Kazemi, A., Norouzi, S. and Hadi, A. (2020), "Torsional vibration analysis of bi-directional FG nanocone with arbitrary cross-section based on nonlocal strain gradient elasticity", Adv. Nano Res., Int. J., 8(1), 13-24. https://doi.org/10.12989/anr.2020.8.1.013.
- Polit, O., Anant, C., Anirudh, B. and Ganapathi, M. (2019), "Functionally graded Graphene reinforced porous nanocomposite curved beams: Bending and elastic stability using a higher-order model with thickness stretch effect", Compos. Part B-Eng., 166, 310-327. https://doi.org/10.1016/j.compositesb.2018.11.074.
- Radic, N. (2018), "On buckling of porous double-layered FG nanoplates in the Pasternak elastic foundation based on nonlocal strain gradient elasticity", Compos. Part B-Eng., 153, 456-479. https://doi.org/10.1016/j.compositesb.2018.09.014.
- Shahsavari, D., Karami, B. and Mansouri, S. (2018), "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-Solid., 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004.
- Shariati, A., Barati, M.R., Ebrahimi, F., Singhal, A. and Toghroli, A. (2020), "Investigating vibrational behavior of graphene sheets under linearly varying in-plane bending load based on the nonlocal strain gradient theory", Adv. Nano Res., Int. J., 8(4), 265-276. https://doi.org/10.12989/anr.2020.8.4.265.
- 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.
- She, G.L., Yuan, F.G. and Ren, Y.R. (2018), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002.
- She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
- Sobhy, M. and Zenkour, A.M. (2019), "Porosity and inhomogeneity effects on the buckling and vibration of doubleFGM nanoplates via a quasi-3D refined theory", Compos. Struct., 220, 289-303. https://doi.org/10.1016/j.compstruct.2019.03.096.
- Taborda, C.S., Bernardo, L. and Gama, J. (2018), "Effective torsional strength of axially restricted RC beams", Struct. Eng. Mech., Int. J., 67(5), 465-479. https://doi.org/10.12989/sem.2018.67.5.465.
- Tang, H., Li, L. and Hu, Y. (2018), "Buckling analysis of twodirectionally porous beam", Aerosp. Sci. Technol., 78, 471-479. https://doi.org/10.1016/j.ast.2018.04.045.
- Tang, H., Li, L. and Hu, Y. (2019), "Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams", Appl. Math. Model., 66, 527-547. https://doi.org/10.1016/j.apm.2018.09.027.
- Timoshenko, S. and Young, D.H. (1995), Vibration Problems in Engineering, VanNostrand Company, New York, U.S.A.