Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory

References

• M. R. Barati, M. H. Sadr, and A. M. Zenkour, Buckling analysis of higher order graded smart piezoelectric plates with porosities resting on elastic foundation, Int. J. Mech. Sci., vol. 117, pp. 309–320, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium, J. Braz. Soc. Mech. Sci. Eng., vol. 39, pp. 937–952, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams, Adv. Nano Res., vol. 4, no. 2, pp. 65–84, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Buckling analysis of piezoelectrically actuated smart nanoscale plates subjected to magnetic field, J. Intell. Mater. Syst. Struct., 2016. DOI: 1045389X16672569
   Web of Science ®Google Scholar
• A. C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci., vol. 10.1, pp. 1–16, 1972.
   Web of Science ®Google Scholar
• A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., vol. 54.9, pp. 4703–4710, 1983.
   Web of Science ®Google Scholar
• F. Ebrahimi, M. R. Barati, and A. Dabbagh, A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, Int. J. Eng. Sci., vol. 107, pp. 169–182, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams, Compos. Struct., vol. 159, pp. 174–182, 2017.
   Web of Science ®Google Scholar
• M. Aydogdu, A general nonlocal beam theory: Its application to nanobeam bending, buckling and vibration, Phys. E: Low-Dimen. Syst. Nanostruct., vol. 41, no. 9, pp. 1651–1655, 2009.
   Web of Science ®Google Scholar
• F. Ebrahimi and P. Nasirzadeh, A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method, J. Theor. Appl. Mech., vol. 53, no. 4, pp. 1041–1052, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and S. H. S. Hosseini, Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates, J. Therm. Stress., vol. 39, no. 5, pp. 606–625, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions, Appl. Phys. A, vol. 122, no. 10, pp. 880, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment, Appl. Phys. A, vol. 122, no. 9, pp. 792, 2016.
   Web of Science ®Google Scholar
• H. T. Thai, A nonlocal beam theory for bending, buckling, and vibration of nanobeams, Int. J. Eng. Sci., vol. 52, pp. 56–64, 2012.
   Web of Science ®Google Scholar
• M. A. Eltaher, S. A. Emam, and F. F. Mahmoud, Free vibration analysis of functionally graded size-dependent nanobeams, Appl. Math. Comput., vol. 218, no. 14, pp. 7406–7420, 2012.
   Web of Science ®Google Scholar
• M. A. Eltaher, S. A. Emam, and F. F. Mahmoud, Static and stability analysis of nonlocal functionally graded nanobeams, Compos. Struct., vol. 96, pp. 82–88, 2013.
   Web of Science ®Google Scholar
• M. Şimşek and H. H. Yurtcu, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Compos. Struct., vol. 97, pp. 378–386, 2013.
   Web of Science ®Google Scholar
• F. Ebrahimi, M. Ghadiri, E. Salari, S. A. H. Hoseini, and G. R. Shaghaghi, Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams, J. Mech. Sci. Technol., vol. 29, no. 3, pp. 1207–1215, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and E. Salari, Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams, Smart Mater. Struct., vol. 24, no. 12, pp. 125007, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and E. Salari, Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions, Compos. B Eng., vol. 78, pp. 272–290, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and E. Salari, Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method, Compos. B: Eng., vol. 79, pp. 156–169, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and E. Salari, Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment, Acta Astronaut., vol. 113, pp. 29–50, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and E. Salari, Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent FG nanobeams, Mech. Adv. Mater. Struct., vol. 23, no. 12, pp. 1379–1397, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Vibration analysis of nonlocal beams made of functionally graded material in thermal environment, Eur. Phys. J. Plus, vol. 131, no. 8, pp. 279, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams, Mech. Adv. Mater. Struct., vol. 7, no. 3, pp. 119–143, 2016.
   Google Scholar
• F. Ebrahimi and M. R. Barati, Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory, Int. J. Smart Nano Mater., pp. 1–25, 2016.
   Web of Science ®Google Scholar
• H. Niknam and M. M. Aghdam, A semi analytical approach for large amplitude free vibration and buckling of nonlocal FG beams resting on elastic foundation, Compos. Struct., vol. 119, pp. 452–462, 2015.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams, Arab. J. Sci. Eng., vol. 41, no. 5, pp. 1679–1690, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams, Eur. Phys. J. Plus, vol. 131, no. 9, pp. 346, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Buckling analysis of smart size-dependent higher order magneto-electro-thermo-elastic functionally graded nanosize beams, J. Mech., vol. 33, no.1, pp. 23–33, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment, J. Vibr. Control, 2016. DOI: 1077546316646239
   PubMedGoogle Scholar
• F. Ebrahimi and M. R. Barati, Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field, Appl. Phys. A, vol. 122, no. 4, pp. 1–18, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures, Int. J. Engg. Sci., vol. 107, pp. 183–196, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams, Eur. Phys. J. Plus, vol. 131, no. 7, pp. 1–14, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory, Smart Mater. Struct., vol. 25, no. 10, pp. 105014, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments, Appl. Phys. A, vol. 122, no. 10, pp. 910, 2016.
   Web of Science ®Google Scholar
• D. C. C. Lam, F. Yang, A. C. M. Chong, J. Wang, and P. Tong, Experiments and theory in strain gradient elasticity, J. Mech. Phys. Solids, vol. 51, no. 8, pp. 1477–1508, 2003.
   Web of Science ®Google Scholar
• C. W. Lim, G. Zhang, and J. N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids, vol. 78, pp. 298–313, 2015.
   Web of Science ®Google Scholar
• L. Li and Y. Hu, Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory, Int. J. Eng. Sci., vol. 97, pp. 84–94, 2015.
   Web of Science ®Google Scholar
• L. Li, X. Li, and Y. Hu, Free vibration analysis of nonlocal strain gradient beams made of functionally graded material, Int. J. Eng. Sci., vol. 102, pp. 77–92, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Flexural wave propagation analysis of embedded S-FGM nanobeams under longitudinal magnetic field based on nonlocal strain gradient theory, Arab. J. Sci. Eng., pp. 1–12, 2016. DOI: 10.1007/s13369-016-2266-4
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory, Appl. Phys. A, vol. 122, no. 9, pp. 843, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi and M. R. Barati, Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory, J. Therm. Stress., vol. 39, no. 12, pp. 1560–1571, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi, M. R. Barati, and P. Haghi, Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams, J. Therm. Stress., pp. 1–13, 2016. DOI: 10.1080/01495739.2016.1230483
   Web of Science ®Google Scholar
• F. Ebrahimi, M. R. Barati, and A. Dabbagh, Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams, Appl. Phys. A, vol. 122, no. 11, pp. 949, 2016.
   Web of Science ®Google Scholar
• F. Ebrahimi, M. R. Barati, and P. Haghi, Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams, Eur. Phys. J. Plus, vol. 131, no. 11, pp. 383, 2016.
   Web of Science ®Google Scholar
• Y. Yue, K. Xu, and E. C. Aifantis, Strain gradient and electric field gradient effects in piezoelectric cantilever beams, J. Mech. Behav. Mater., vol. 24, no. 3–4, pp. 121–127, 2015.
   Google Scholar
• A. Assadi and B. Farshi, Size dependent vibration of curved nanobeams and rings including surface energies, Phys. E: Low-Dimen. Syst. Nanostruct., vol. 43, no. 4, pp. 975–978, 2011.
   Web of Science ®Google Scholar
• Z. Yan and L. Jiang, Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects, J. Phys. D: Appl. Phys., vol. 44, no. 36, pp. 365301, 2011.
   Web of Science ®Google Scholar
• H. Kananipour, M. Ahmadi, and H. Chavoshi, Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams, Latin Am. J. Solids Struct., vol. 11, no. 5, pp. 848–853, 2014.
   Web of Science ®Google Scholar
• A. Setoodeh, M. Derahaki, and N. Bavi, DQ thermal buckling analysis of embedded curved carbon nanotubes based on nonlocal elasticity theory, Latin Am. J. Solids Struct., vol. 12, no. 10, pp. 1901–1917, 2015.
   Web of Science ®Google Scholar
• E. Tufekci, S. A. Aya, and O. Oldac, In-plane static analysis of nonlocal curved beams with varying curvature and cross-section, Int. J. Appl. Mech., vol. 8, no. 1, pp. 1650010, 2016.
   Web of Science ®Google Scholar
• S. A. H. Hosseini and O. Rahmani, Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model, Appl. Phys. A, vol. 122, no. 3, pp. 1–11, 2016.
   Web of Science ®Google Scholar
• L. L. Ke and Y. S. Wang, Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory, Smart Mater. Struct., vol. 21, no. 2, pp. 025018, 2012.
   Web of Science ®Google Scholar