Acknowledgement
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors
References
- Amabili, M. (2008), Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York, NY, USA.
- Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457.
- Donnell, L.H. (1976), Beam, Plates and Shells, McGraw-Hill, New York, NY, USA.
- Ebrahimi, F. and Barati, M. R. (2018a), "Surface and flexoelectricity effects on size-dependent thermal stability analysis of smart piezoelectric nanoplates", Struct. Eng. Mech., 67(2), 143-153. https://doi.org/10.12989/sem.2018.67.2.143.
- Ebrahimi, F. and Heidari, E. (2018b), "Vibration characteristics of advanced nanoplates in humid-thermal environment incorporating surface elasticity effects via differential quadrature method", Struct. Eng. Mech., 68(1), 131-157. https://doi.org/10.12989/sem.2018.68.1.131.
- Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
- Fang, X.Q., Zhu, C.S., Liu, J.X. and Liu, X.L. (2018a), "Surface energy effect on free vibration of nano-sized piezoelectric double-shell structures", Physica B., 529, 41-56. https://doi.org/10.1016/j.physb.2017.10.038.
- Fang, X.Q., Zhu, C.S., Liu, J.X. and Zhao, J. (2018b), "Surface energy effect on nonlinear buckling and postbuckling behavior of functionally graded piezoelectric cylindrical nanoshells under lateral pressure", Mater. Res. Express. 5(4), 045017. https://orcid.org/0000-0003-3341-873X. https://doi.org/10.1088/2053-1591/aab914
- Fang, X.Q., Zhang, T.F., Li, B.L., Yuan, R.J. (2020). "Elastic-slip interface effect on dynamic stress around twin tunnels in soil medium subjected to blast waves", Comput. Geotech., 119, 103301, https://doi.org/10.1016/j.compgeo.2019.103301.
- Farokhi, H., Païdoussis, M.P. and Misra, A. (2018a), "Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model", J. Sound Vib., 49, 604-629. https://doi.org/10.1016/j.jsv.2017.09.003.
- Farokhi, H., Ghayesh, M. H. (2018b), "Nonlinear mechanics of electrically actuated microplates", Int. J. Eng. Sci., 123, 197-213. https://doi.org/10.1016/j.ijengsci.2017.08.017.
- Ghayesh, M. H., Farokhi, H. (2018a), "Nonlinear behaviour of electrically actuated microplate-based MEMS resonators", Mech Syst Signal Pr., 109, 220-234, https://doi.org/10.1016/j.ymssp.2017.11.043.
- Ghayesh, M. H., Farokhi, H., Amabili, M. (2013a), "Nonlinear behaviour of electrically actuated MEMS resonators", Int. J. Eng. Sci., 71, 137-155. https://doi.org/10.1016/j.ijengsci.2013.05.006.
- Ghayesh, M. H., Amabili, M., Farokhi, H. (2013b), "Three-dimensional nonlinear size-dependent behaviour of Timoshenko microbeams", Int. J. Eng. Sci., 71, 1-14. https://doi.org/10.1016/j.ijengsci.2013.04.003.
- Ghayesh, M. H., Farokhi, H., Amabili, M. (2013c), "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.
- Ghayesh, M. H. (2018), "Dynamics of functionally graded viscoelastic microbeams", Int. J. Eng. Sci., 124, 115-131. https://doi.org/10.1016/j.ijengsci.2017.11.004.
- Ghayesh, M. H. (2019a), "Mechanics of viscoelastic functionally graded microcantilevers", Eur J Mech A-Solid, 73, 492-499. https://doi.org/10.1016/j.euromechsol.2018.09.001.
- Ghayesh, M. H. (2019b), "Viscoelastic dynamics of axially FG microbeams", Int. J. Eng. Sci., 135, 75-85. https://doi.org/10.1016/j.ijengsci.2018.10.005.
- Ghorbanpour Arani, A., Kolahchi, R., Hashemian, M. (2014), "Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories", P I Mech Eng C-J Mec., 228(17), 3258-3280. https://doi.org/10.1177/0954406214527270.
- Gurtin, M.E. and Murdoch, A.I. (1975), "A continuum theory of elastic material surface", Arch. Ration. Mech. Anal., 57, 291-323. https://doi.org/10.1007/BF00261375.
- Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solids Struct. 14(6), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2.
- Hashemi Kachapi, S.H., Dardel, M., Mohamadi daniali, H. and Fathi, A. (2019a), "Pull-in instability and nonlinear vibration analysis of electrostatically piezoelectric nanoresonator with surface/interface effects", Thin Walled Struct., 143, 106210. https://doi.org/10.1016/j.tws.2019.106210.
- Hashemi Kachapi, S.H., Dardel, M., Mohamadi daniali, H. and Fathi, A. (2019b), "Nonlinear dynamics and stability analysis of piezo-visco medium nanoshell resonator with electrostatic and harmonic actuation", Appl. Math. Modell., 75, 279-309. https://doi.org/10.1016/j.apm.2019.05.035.
- Hashemi Kachapi, S.H., Dardel, M., Mohamadi daniali, H. and Fathi, A. (2019c), "Nonlinear vibration and stability analysis of double-walled piezoelectric nanoresonator with nonlinear van der Waals and electrostatic excitation". J. Vib. Control, https://doi.org/10.1177/1077546319889858.
- Hashemi Kachapi, S.H., Mohamadi daniali, H., Dardel, M. and Fathi, A. (2020a), "The effects of nonlocal and surface/interface parameters on nonlinear vibrations of piezoelectric nanoresonator", J. Intell. Mater. Syst. Struct., https://doi.org/10.1177/1045389X19898756.
- Hashemi Kachapi, S.H. (2020b), "Nonlinear vibration and stability analysis of piezo-harmo-electrostatic nanoresonator based on surface/interface and nonlocal strain gradient effects", J. Braz. Soc. Mech. Sci., 42(107), https://doi.org/10.1007/s40430-020-2173-1.
- Hashemi Kachapi, S.H. (2020c), "Vibration analysis and pull-in instability behavior in multi walled piezoelectric nano-sensor with fluid flow conveyance: influences of surface/interface energy", Beilstein J. Nanotechnol., 11, 1072-1081. https://doi.org/10.3762/bjnano.11.92.
- Rupitsch, S.J. (2019), Piezoelectric sensors and actuators: fundamentals and applications, Springer, New York, USA.
- Jalili, N. (2010), Piezoelectric-Based Vibration Control: From Macro to Micro/Nano Scale Systems, Springer, New York, NY, USA.
- Li, C., Zhang, N., Fan, X.L., Yan, J.W. and Yao, L.Q. (2019), "Impact Behaviors of Cantilevered Nano-beams Based on the Nonlocal Theory", J. Vib. Eng. Technol. 7, 533-542. https://doi.org/10.1007/s42417-019-00173-6.
- Mahmoud, F.F. and Shaat, M. (2015), "A new mindlin FG plate model incorporating microstructure and surface energy effects", Struct. Eng. Mech., 53(1), 105-130. https://doi.org/10.12989/sem.2014.53.1.105.
- Mindlin, R.D. and Tiersten, H.F. (1962), "Effects of couple-stresses in linear elasticity", Arch. Ration. Mech. Anal., 11, 415-448. https://doi.org/10.1007/BF00253946.
- Mindlin, R.D. (1965), "Second gradient of strain and surfacetension in linear elasticity", Int. J. Solids Struct., 1(4), 417-438. https://doi.org/10.1016/0020-7683(65)90006-5.
- Mindlin, R.D. and Eshel, N.N. (1968), "on first strain-gradient theories in linear elasticity", Int. J. Solids Struct., 4(1), 109-124. https://doi.org/10.1016/0020-7683(68)90036-X.
- Sarafraz, A., Sahmani, S. and Mohammadi Aghdam, M. (2019) "Nonlinear secondary resonance of nanobeams under subharmonic and superharmonic excitations including surface free energy effects", Appl. Math. Modell., 66, 195-226. https://doi.org/10.1016/j.apm.2018.09.013.
- Tzou, H. (2019), Piezoelectric Shells: Sensing, Energy Harvesting, and Distributed Control, Springer, New York, NY, USA.
- Wang, L. and Ni, Q. (2009), "A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid", Mech Res Comm., 36(7), 833-837. https://doi.org/10.1016/j.mechrescom.2009.05.003.
- Wang, W., Rong, D., Xu, C., Zhang, J., Xu, X. and Zhou, Z. (2019), "Accurate Buckling Analysis of Magnetically Affected Cantilever Nanoplates Subjected to In-plane Magnetic Fields", J. Vib. Eng. Technol., https://doi.org/10.1007/s42417-019-00106-3.
- Xiao, Q.X., Zou, J., Lee, K. Y. and Li, X.F. (2017), "Surface effects on flutter instability of nanorod under generalized follower force", Struct. Eng. Mech., 68(6), 723-730. https://doi.org/10.12989/sem.2017.64.6.723.
- Zhu, C.S., Fang, X.Q., Liu, J.X., Li, H.Y. (2017). "Surface energy effect on nonlinear free vibration behavior of orthotropic piezoelectric cylindrical nano-shells", Eur J Mech A-Solid, 66, 423-432. https://doi.org/10.1016/j.euromechsol.2017.08.001.
- Zhu, C.S., Fang, X.Q., Liu, J.X., Nie, G.; Zhang, C. (2020). "An analytical solution for nonlinear vibration control of sandwich shallow doubly-curved nanoshells with functionally graded piezoelectric nanocomposite sensors and actuators ", Mech. Based Des. Struc. https://doi.org/10.1080/15397734.2020.1779742.