[1] Drexler, K.E., Nanosystems: molecular machinery, manufacturing, and computation, John Wiley & Sons, 1992.
[2] Li, M., Tang, H.X., Roukes, M.L., Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications, Nature Nanotechnology, 2, 2007, 114–33.
[3] Cimalla, V., Niebelschütz, F., Tonisch, K., Foerster, Ch., Brueckner, K., Cimalla, I., et al., Nanoelectromechanical devices for sensing applications, Sensors and Actuators B: Chemical, 126, 2007, 24–34.
[4] Sakhaee-Pour, A., Ahmadian, M.T., Vafai, A., Applications of single-layered graphene sheets as mass sensors and atomistic dust detectors, Solid State Communications, 145, 2008, 168–72.
[5] Wang, J., Li, Z., Fan, G., Pan, H., Chen, Z., Zhang, D., Reinforcement with graphene nanosheets in aluminum matrix composites, Scripta Materialia, 66, 2012, 594–7.
[6] Iijima, S., Helical microtubules of graphitic carbon, Nature, 354, 1991, 56–63.
[7] Lu, B.P., Zhang, P.Q., Lee, H.P., Wang, C.M., Reddy, J.N., Non-local elastic plate theories, Proceedings of the Royal Society, A 463, 2007, 3225–40.
[8] Reddy, J.N., Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids, 59, 2011, 2382–99.
[9] Akgöz, B., Civalek, Ö., A size-dependent shear deformation beam model based on the strain gradient elasticity theory, International Journal of Engineering Science, 70, 2013, 1–14.
[10] Akgöz, B., Civalek, Ö., Buckling analysis of functionally graded microbeams based on the strain gradient theory, Acta Mechanica, 224, 2013, 2185–201.
[11] Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P., Experiments and theory in strain gradient elasticity, Journal of the Mechanics and Physics of Solids, 51, 2003, 1477–508.
[12] Akgöz, B., Civalek, Ö., Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory, Archive of Applied Mechanics, 82, 2012, 423-443.
[13] Ke, L.L., Wang, Y.S., Yang, J., Kitipornchai, S., Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory, Journal of Sound and Vibration, 331, 2012, 94–106.
[14] Akgöz, B., Civalek, Ö., Strain gradient elasticity, and modified couple stress models for buckling analysis of axially loaded micro-scaled beams, International Journal of Engineering Science, 49, 2011, 1268–80.
[15] Akgöz, B., Civalek, Ö., Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified couple stress theories, Journal of Computational and Theoretical Nanoscience, 8, 2011, 1821-1827.
[16] Akgöz, B., Civalek, Ö., Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory, Composite Structures, 98, 2013, 314–22.
[17] Akgöz, B., Civalek, Ö., Modeling, and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory, Meccanica, 48, 2013, 863-873.
[18] Yang, F., Chong, A.C.M., Lam, D.C.C., Tong, P., Couple stress based strain gradient theory for elasticity, International Journal of Solids Structures, 39, 2002, 2731–43.
[19] Malikan, M., Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first-order shear deformation theory, Applied Mathematical Modelling, 48, 2017, 196–207.
[20] Malikan, M., Analytical predictions for the buckling of a nanoplate subjected to non-uniform compression based on the four-variable plate theory, Journal of Applied and Computational Mechanics, 3, 2017, 218–228.
[21] Malikan, M., Buckling analysis of a micro composite plate with nano-coating based on the modified couple stress theory, Journal of Applied and Computational Mechanics, 4, 2018, 1–15.
[22] Malikan, M., Temperature influences on shear stability of a nanosize plate with piezoelectricity effect, Multidiscipline Modeling in Materials and Structures, 14, 2018, 125-142.
[23] Malikan, M., Electro-thermal buckling of elastically supported double-layered piezoelectric nanoplates affected by an external electric voltage, Multidiscipline Modeling in Materials and Structures, 15, 2019, 50-78.
[24] Eringen, A.C., Edelen, D.G.B., On nonlocal elasticity, International Journal of Engineering Science,10, 1972, 233–48.
[25] Eringen, A.C., On differential equations of nonlocal elasticity, solutions of screw dislocation, surface waves, Journal of Applied Physics, 54, 1983, 4703–10.
[26] Eringen, A.C., Nonlocal continuum field theories, New York, Springer, 2002.
[27] Eringen, A.C., Nonlocal continuum mechanics based on distributions, International Journal of Engineering Science, 44, 2006, 141-7.
[28] Malikan, M., Jabbarzadeh, M., Dastjerdi, Sh., Non-linear Static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo-elasticity using nonlocal continuum, Microsystem Technologies, 23, 2017, 2973–2991.
[29] Malikan, M., Nguyen, V.B., A novel one-variable first-order shear deformation theory for biaxial buckling of a size-dependent plate based on the Eringen׳s nonlocal differential law, World Journal of Engineering, 15, 2018, 633-645.
[30] Malikan, M., On the buckling response of axially pressurized nanotubes based on a novel nonlocal beam theory, Journal of Applied and Computational Mechanics, 5, 2019, 103-112.
[31] Malikan, M., Tornabene, F., Dimitri, R., Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals, Materials Research Express, 5, 2018, 095006.
[32] Golmakani, M.E., Malikan, M., Sadraee Far, M.N., Majidi, H.R., Bending and buckling formulation of graphene sheets based on nonlocal simple first-order shear deformation theory, Materials Research Express, 5, 2018, 065010.
[33] Malikan, M., Sadraee Far, M.N., Differential quadrature method for dynamic buckling of graphene sheet coupled by a viscoelastic medium using neperian frequency based on nonlocal elasticity theory, Journal of Applied and Computational Mechanics, 4, 2018, 147-160.
[34] Sadraee Far, M.N., Golmakani, M.E., Large deflection of thermo-mechanical loaded bilayer orthotropic graphene sheet in/on polymer matrix based on nonlocal elasticity theory, Computers and Mathematics with Applications, 76, 2018, 2061-89.
[35] Ansari, R., Torabi, J., Nonlocal vibration analysis of circular double-layered graphene sheets resting on an elastic foundation subjected to thermal loading, Acta Mechanica Sinica, 32, 2016, 841-853.
[36] Dastjerdi, Sh., Akgöz, B., Yazdanparast, L., A new approach for bending analysis of bilayer conical graphene panels considering nonlinear van der Waals force, Composites Part B: Engineering, 150, 2018, 124-134.
[37] Demir, C., Civalek, Ö., Torsional and longitudinal frequency and wave response of microtubules based on the nonlocal continuum and nonlocal discrete models, Applied Mathematical Modelling, 37, 2013, 9355-9367.
[38] Pradhan, S.C., Kumar, A., Vibration analysis of orthotropic graphene sheets using nonlocal elasticity theory and differential quadrature method, Composite Structures, 93, 2011, 774-779.
[39] Prasanna, T.J., Kumar, S., Gopalakrishnan, N.S., Thermal vibration analysis of monolayer graphene embedded in elastic medium based on nonlocal continuum mechanics, Composite Structures, 100, 2013, 332-342.
[40] Numanoğlu, H.M., Akgöz, B., Civalek, Ö., On dynamic analysis of nanorods, International Journal of Engineering Science, 130, 2018, 33-50.
[41] She, G.L., Yuan, F.G., Ren, Y.R., Xiao, W.Sh., On buckling and post-buckling behavior of nanotubes, International Journal of Engineering Science, 121, 2018, 130–142.
[42] Malikan, M., Nguyen, V.B., Buckling analysis of piezo-magnetoelectric nanoplates in a hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory, Physica E: Low-dimensional Systems and Nanostructures, 102, 2018, 8-28.
[43] Malikan, M., Nguyen, V.B., Tornabene, F., Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory, Materials Research Express, 5, 2018, 075031.
[44] Malikan, M., Nguyen, V.B., Tornabene, F., Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory, Engineering Science and Technology, an International Journal, 21, 2018, 778-786.
[45] Malikan, M., Dimitri, R., Tornabene, F., Effect of Sinusoidal Corrugated Geometries on the Vibrational response of Viscoelastic Nanoplates, Applied Sciences, 8, 2018, 1432.
[46] Malikan, M., Nguyen, V.B., Dimitri, R., Tornabene, F., Dynamic modeling of non-cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory, Materials Research Express, 6, 2019, 075041.
[47] Malikan, M., Dimitri, R., Tornabene, F., Transient response of oscillated carbon nanotubes with internal and external damping, Composites Part B Engineering, 158, 2019, 198-205.
[48] She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B., Xiao, W.Sh., Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory, Composite Structures, 203, 2018, 614–23.
[49] Shen, L., Shen, H.S., Zhang, C.L., Nonlocal plate model for nonlinear vibration of single-layer graphene sheets in thermal environments, Computational Materials Science, 48, 2010, 680–5.
[50] Pradhan, S.C., Kumar, A., Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Materials Science, 50, 2010, 239–45.
[51] Akgöz, B., Civalek, Ö., Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory, Materials and Design, 42, 2012, 164–71.
[52] Mohammadi, M., Ghayour, M., Farajpour, A., Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composites Part B: Engineering, 45, 2013, 32–42.
[53] Asemi, S.R., Farajpour, A., Decoupling the nonlocal elasticity equations for thermo-mechanical vibration of circular graphene sheets including surface effects, Physica E, 60, 2014, 80–90.
[54] Ansari, R., Mohammadi, V., Shojaei, M.F., Gholami, R., Sahmani, S., Surface stress effect on the post-buckling and free vibrations of axisymmetric circular Mindlin nanoplates subject to various edge supports Composite Structures, 112, 2014, 358–67.
[55] Pradhan, S.C., Murmu, T., Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory, Physica E, 42, 2010, 1293–301.
[56] Malekzadeh, P., Setoodeh, A.R., Alibeygi, A., Small scale effect on the thermal buckling of orthotropic arbitrary straight-sided quadrilateral nanoplates embedded in an elastic medium, Composite Structures, 93, 2011, 2083–9.
[57] Karamooz Ravari, M.R., Shahidi, A.R., Axisymmetric buckling of the circular annular nanoplates using finite difference method, Meccanica, 48, 2013, 135–144.
[58] Bedroud, M., Hosseini-Hashemi, S., Nazemnezhad, R., Buckling of circular/annular Mindlin nanoplates via nonlocal elasticity, Acta Mechanica, 224, 2013, 2663–76.
[59] Farajpour, A., Mohammadi, M., Shahidi, A.R., Mahzoon, M., Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model, Physica E, 43, 2011, 1820–5.
[60] Golmakani, M.E., Rezatalab, J., Nonuniform biaxial buckling of orthotropic nanoplates embedded in an elastic medium based on nonlocal Mindlin plate theory, Composite Structures, 119, 2015, 238–250.
[61] Farajpour, A., Dehghany, M., Shahidi, A.R., Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment, Composites Part B: Engineering, 50, 2013, 333–43.
[62] Golmakani, M.E., Vahabi, H., Nonlocal buckling analysis of functionally graded annular nanoplates in an elastic medium with various boundary conditions, Microsystem Technologies, 23, 2017, 3613-3628.
[63] Golmakani, M.E., Rezatalab, J., Nonlinear bending analysis of orthotropic nanoscale plates in an elastic matrix based on nonlocal continuum mechanics, Composite Structures, 111, 2014, 85–97.
[64] Golmakani, M.E., Sadraee Far, M.N., Nonlinear thermo-elastic bending behavior of graphene sheets embedded in an elastic medium based on nonlocal elasticity theory, Computers and Mathematics with Applications, 72, 2016, 785–805.
[65] Sobhy, M., Thermomechanical bending and free vibration of single-layered graphene sheets embedded in an elastic medium, Physica E, 56, 2014, 400–9.
[66] Sedighi, H. M., Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory, Acta Astronautica, 95, 2014, 111-123.
[67] Sedighi, H. M., Koochi, A., Daneshmand, F., Abadyan, M., Non-linear dynamic instability of a double-sided nano-bridge considering centrifugal force and rarefied gas flow, International Journal of Non-Linear Mechanics, 77, 2015, 96-106.
[68] Sedighi, H. M., Bozorgmehri, A., Dynamic instability analysis of doubly clamped cylindrical nanowires in the presence of Casimir attraction and surface effects using modified couple stress theory, Acta Mechanica, 227(6), 2016, 227-1575.
[69] Ouakad, H. M., Sedighi, H. M., Younis, M. I., One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches, Journal of Computational and Nonlinear Dynamics, 12(5), 2017, 051025.
[70] Koochi, A., Sedighi, H. M., Abadyan, M. R., Modeling the size-dependent pull-in instability of beam-type NEMS using strain gradient theory, Latin American Journal of Solids and Structures, 11, 2014, 1679-7825.
[71] Dastjerdi, Sh., Jabbarzadeh, M., Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler-Pasternak elastic foundation based on nonlocal continuum mechanics, Composites Part B: Engineering, 87, 2016, 161–75.
[72] Xu, Y.-M., Shen, H.-S., Zhang, C.-L., Nonlocal plate model for nonlinear bending of bilayer graphene sheets subjected to transverse loads in thermal environments, Composite Structures, 98, 2013, 294–302.
[73] Pradhan, S.C., Phadikar, J.K., Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A, 373, 2009, 1062–9.
[74] Ansari, R., Rajabiehfard, R., Arash, B., Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets, Computational Materials Science, 49, 2010, 831–8.
[75] Jomehzadeh, E., Saidi, A.R., A study on large amplitude vibration of multilayered graphene sheets, Computational Materials Science, 50, 2011, 1043–51.
[76] Pouresmaeeli, S., Fazelzadeh, S.A., Ghavanloo, E., Exact solution for nonlocal vibration of double orthotropic nanoplates embedded in elastic medium, Composites Part B: Engineering, 43, 2012, 3384–90.
[77] Anjomshoa, A., Shahidi, A.R., Hassani, B., Jomehzadeh, E., Finite element buckling analysis of multilayered graphene sheets on elastic substrate based on nonlocal elasticity theory, Applied Mathematical Modeling, 38, 2014, 5934–55.
[78] Murmu, T., Sienz, J., Adhikari, S., Arnold, C., Nonlocal buckling of double-nanoplate-systems under biaxial compression, Composites Part B: Engineering, 44, 2014, 84–94.
[79] Radic, N., Jeremic, D., Trifkovic, S., Milutinovic, M., Buckling analysis of double-orthotropic nanoplates embedded in Pasternak elastic medium using nonlocal elasticity theory, Composites Part B: Engineering, 61, 2014, 162–71.
[80] Golmakani, M.E., Sadraee Far, M.N., Buckling analysis of biaxially compressed double‑layered graphene sheets with various boundary conditions based on nonlocal elasticity theory, Microsystem Technologies, 23(6), 2017, 2145-2165.
[81] Asemi, S.R., Farajpour, A., Borghei, M., Hassani, A.H., Thermal effects on the stability of circular graphene sheet via nonlocal continuum mechanics, Latin American Journal of Solids and Structures, 11, 2014, 704–24.
[82] Bellman, R.E., Casti, J., Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, 34, 1971, 235–8.
[83] Bellman, R.E., Kashef, B.G., Casti, J., Differential Quadrature: A Technique for the Rapid Solution of Nonlinear Partial Differential Equation, Journal of Computational Physics, 10, 2018, 40–52.
[84] Mahinzare, M., Ranjbarpur, H., Ghadiri, M., Free vibration analysis of a rotary smart two directional functionally graded piezoelectric material in axial symmetry circular nanoplate, Mechanical Systems, and Signal Processing,100, 2018, 188-207.
[85] Mahinzare, M., Jannat Alipour, M., Sadatsakkak, S. A., Ghadiri, M., A nonlocal strain gradient theory for dynamic modeling of a rotary Thermo piezoelectrically actuated nano FG circular plate, Mechanical Systems and Signal Processing, 115, 2019, 323-337.
[86] Watson, D. W., Karageorghis, A., Chen, C. S., The radial basis function-differential quadrature method for elliptic problems in annular domains, Journal of Computational and Applied Mathematics, 363, 2020, 53-76.
[87] Lal, R., Saini, R., Vibration analysis of FGM circular plates under non-linear temperature variation using generalized differential quadrature rule, Applied Acoustics,158, 2020, 107027.