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Original Articles

Free vibration of magneto-electro-elastic nanobeams based on modified couple stress theory in thermal environment

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Pages 601-613 | Received 10 Feb 2017, Accepted 30 Aug 2017, Published online: 26 Dec 2017

References

  • R. Rahmani, and A. Ghorbanpour, Introduction of Nanomechanics. Tehran, DC: Academic Books Publishing, 1386
  • S. Krylov, “Lyapunov exponents as a criterion for the dynamic pull-in instability of electrostatically actuated microstructures,” Int. J. Nonlinear Mech., vol. 42, no. 4, pp. 626–642, 2007. doi:10.1016/j.ijnonlinmec.2007.01.004.
  • M. Li, H. X. Tang, and M. L. Roukes, “Ultra-sensitive NEMS-based cantilevers for sensing, scanned probe and very high-frequency applications,” Nat. Nanotechnol., vol. 2, no. 2, pp. 114–120, 2007. doi:10.1038/nnano.2006.208.
  • Y. T. Beni, M. R. Abadyan, and A. Noghrehabadi, “Investigation of size effect on the pull-in instability of beam-type NEMS under van der Waals attraction,” Procedia Eng., vol. 10, pp. 1718–1723, 2011. doi:10.1016/j.proeng.2011.04.286.
  • S. C. Pradhan, and J. K. Phadikar, “Nonlocal elasticity theory for vibration of nanoplates,” J. Sound Vib., vol. 325, no. 1, pp. 206–223, 2009. doi:10.1016/j.jsv.2009.03.007.
  • P. Malekzadeh, A. R. Setoodeh, and A. A. Beni, “Small scale effect on the free vibration of orthotropic arbitrary straight-sided quadrilateral nanoplates,” Compos. Struct., vol. 93, no. 7, pp. 1631–1639, 2011. doi:10.1016/j.compstruct.2011.01.008.
  • J. Van Suchtelen, “Product properties: a new application of composite materials,” Philips Res. Rep, vol. 27, no. 1, pp. 28–37, 1972.
  • T. L. Wu, and J. H. Huang, “Closed-form solutions for the magnetoelectric coupling coefficients in fibrous composites with piezoelectric and piezomagnetic phases,” Int. J. Sol. Struct., vol. 37, no. 21, pp. 2981–3009, 2000. doi:10.1016/S0020-7683(99)00116-X.
  • S. Priya, R. Islam, S. Dong, and D. Viehland, “Recent advancements in magnetoelectric particulate and laminate composites,” J. Electroceram., vol. 19, no. 1, pp. 149–166, 2007. doi:10.1007/s10832-007-9042-5.
  • M. Avellaneda, and G. Harshé, “Magnetoelectric effect in piezoelectric/magnetostrictive multilayer (2-2) composites,” J. Int. Mat. Syst. Struct., vol. 5, no. 4, pp. 501–513, 1994. doi:10.1177/1045389X9400500406.
  • J. Chandra, V. Rao, R. Butler, and R. Damle, Multidisciplinary research in smart structures: A survey. In Proceedings of the American Control Conference, vol. 6, pp. 4167–4172. IEEE, 1995, June.
  • T. L. Daulton, K. S. Bondi, and K. F. Kelton, “Nanobeam diffraction fluctuation electron microscopy technique for structural characterization of disordered materials—Application to Al88–x Y7Fe5Tix metallic glasses,” Ultramicroscopy, vol. 110, no. 10, pp. 1279–1289, 2010. doi:10.1016/j.ultramic.2010.05.010.
  • B. Hu, Y. Ding, W. Chen, D. Kulkarni, Y. Shen, V. V. Tsukruk, and Z. L. Wang, “External-strain induced insulating phase transition in VO2 nanobeam and its application as flexible strain sensor,” Adv. Mat., vol. 22, no. 45, pp. 5134–5139, 2010. doi:10.1002/adma.201002868.
  • Y. T. Beni, “Size-dependent analysis of piezoelectric nanobeams including electro-mechanical coupling,” Mech. Res. Commun., vol. 75, pp. 67–80, 2016. doi:10.1016/j.mechrescom.2016.05.011.
  • M. C. Ray, “Exact solutions for flexoelectric response in nanostructures,” J. Appl. Mech., vol. 81, no. 9, pp. 091002, 2014. doi:10.1115/1.4027806.
  • M. Dequesnes, S. V. Rotkin, and N. R. Aluru, “Calculation of pull-in voltages for carbon-nanotube-based nanoelectromechanical switches,” Nanotechnology, vol. 13, no. 1, pp. 120, 2002. doi:10.1088/0957-4484/13/1/325.
  • Z. Tang, Y. Xu, G. Li, and N. R. Aluru, “Physical models for coupled electromechanical analysis of silicon nanoelectromechanical systems,” J. Appl. Phys., vol. 97, no. 11, pp. 114304, 2005. doi:10.1063/1.1897483.
  • R. D. Mindlin, “Micro-structure in linear elasticity,” Arch. Ration. Mech. Anal., vol. 16, no. 1, pp. 51–78, 1964. doi:10.1007/BF00248490.
  • R. D. Mindlin, “Second gradient of strain and surface-tension in linear elasticity,” Int. J. Sol. Struct., vol. 1, no. 4, pp. 417–438, 1965. doi:10.1016/0020-7683(65)90006-5.
  • M. Şimşek, and J. N. Reddy, “Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory,” Int. J. Eng. Sci., vol. 64, pp. 37–53, 2013. doi:10.1016/j.ijengsci.2012.12.002.
  • H. Zeighampour, and Y. T. Beni, “Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory,” Physica E: Low-dimensional Systems and Nanostructures, vol. 61, pp. 28–39, 2014. doi:10.1016/j.physe.2014.03.011.
  • H. Zeighampour, and Y. T. Beni, “Analysis of conical shells in the framework of coupled stresses theory,” Int. J. Eng. Sci., vol. 81, pp. 107–122, 2014. doi:10.1016/j.ijengsci.2014.04.008.
  • P. M. Dashtaki, and Y. T. Beni, “Effects of Casimir force and thermal stresses on the buckling of electrostatic nanobridges based on couple stress theory,” Arab. J. Sci. Eng., vol. 39, no. 7, pp. 5753–5763, 2014. doi:10.1007/s13369-014-1107-6.
  • Y. T. Beni, I. Karimipöur, and M. Abadyan, “Modeling the effect of intermolecular force on the size-dependent pull-in behavior of beam-type NEMS using modified couple stress theory,” J. Mech. Sci. Technol., vol. 28, no. 9, pp. 3749–3757, 2014. doi:10.1007/s12206-014-0836-5.
  • B. Akgöz, and Ö. Civalek, “Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory,” Comp. Struct., vol. 98, pp. 314–322, 2013. doi:10.1016/j.compstruct.2012.11.020.
  • Y. T. Beni, and M. Abadyan, “Size-dependent pull-in instability of torsional nano-actuator,” Phys. Scrip., vol. 88, no. 5, pp. 055801, 2013. doi:10.1088/0031-8949/88/05/055801.
  • Y. T. Beni, and M. Abadyan, “Use of strain gradient theory for modeling the size-dependent pull-in of rotational nano-mirror in the presence of molecular force,” Int. J. Mod. Phys. B, vol. 27, no. 18, pp. 1350083, 2013. doi:10.1142/S0217979213500835.
  • H. Zeighampour, and Y. T. Beni, “Cylindrical thin-shell model based on modified strain gradient theory,” Int. J. Eng. Sci., vol. 78, pp. 27–47, 2014. doi:10.1016/j.ijengsci.2014.01.004.
  • M. K. Zeverdejani, and Y. T. Beni, “The nano scale vibration of protein microtubules based on modified strain gradient theory,” Curr. Appl. Phys., vol. 13, no. 8, pp. 1566–1576, 2013. doi:10.1016/j.cap.2013.05.019.
  • R. Ansari, R. Gholami, V. Mohammadi, and M. F. Shojaei, “Size-dependent pull-in instability of hydrostatically and electrostatically actuated circular microplates,” J. Computat. Nonlinear Dyn., vol. 8, no. 2, pp. 021015, 2013. doi:10.1115/1.4007358.
  • M. Shojaeian, Y. T. Beni, and H. Ataei, “Electromechanical buckling of functionally graded electrostatic nanobridges using strain gradient theory,” Acta Astronaut., vol. 118, pp. 62–71, 2016. doi:10.1016/j.actaastro.2015.09.015.
  • H. M. Sedighi, A. Koochi, and M. Abadyan, “Modeling the size dependent static and dynamic pull-in instability of cantilever nanoactuator based on strain gradient theory,” Int. J. Appl. Mech., vol. 6, no. 05, pp. 1450055, 2014. doi:10.1142/S1758825114500550.
  • B. Fang, Y. X. Zhen, C. P. Zhang, and Y. Tang, “Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory,” Appl. Math. Model., vol. 37, no. 3, pp. 1096–1107, 2013. doi:10.1016/j.apm.2012.03.032.
  • K. Kiani, “Vibration analysis of elastically restrained double-walled carbon nanotubes on elastic foundation subjected to axial load using nonlocal shear deformable beam theories,” Int. J. Mech. Sci., vol. 68, pp. 16–34, 2013. doi:10.1016/j.ijmecsci.2012.11.011.
  • A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. doi:10.1063/1.332803.
  • A. C. Eringen, and D. G. B. Edelen, “On nonlocal elasticity,” Int. J. Eng. Sci., vol. 10, no. 3, pp. 233–248, 1972. doi:10.1016/0020-7225(72)90039-0.
  • A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys., vol. 54, pp. 4703, 1983.
  • S. A. Emam, “A general nonlocal nonlinear model for buckling of nanobeams,” Appl. Math. Model., vol. 37, no. 10, pp. 6929–6939, 2013. doi:10.1016/j.apm.2013.01.043.
  • H. T. Thai, “A nonlocal beam theory for bending, buckling, and vibration of nanobeams,” Int. J. Eng. Sci., vol. 52, pp. 56–64, 2012. doi:10.1016/j.ijengsci.2011.11.011.
  • R. Ansari, R. Gholami, M. F. Shojaei, V. Mohammadi, and S. Sahmani, “Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory,” Com. Struct., vol. 100, pp. 385–397, 2013. doi:10.1016/j.compstruct.2012.12.048.
  • F. A. C. M. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong, “Couple stress based strain gradient theory for elasticity,” Int. J. Sol. Struct., vol. 39, no. 10, pp. 2731–2743, 2002. doi:10.1016/S0020-7683(02)00152-X.
  • S. K. Park, and X. L. Gao, “Bernoulli–Euler beam model based on a modified couple stress theory,” J. Micromech. Microeng., vol. 16, no. 11, pp. 2355, 2006. doi:10.1088/0960-1317/16/11/015.
  • H. M. Ma, X. L. Gao, and J. N. Reddy, “A microstructure-dependent Timoshenko beam model based on a modified couple stress theory,” J. Mech. Phys. Sol., vol. 56, no. 12, pp. 3379–3391, 2008. doi:10.1016/j.jmps.2008.09.007.
  • B. Akgöz, and Ö. Civalek, “Free vibration analysis of axially functionally graded tapered Bernoulli–Euler microbeams based on the modified couple stress theory,” Com. Struct., vol. 98, pp. 314–322, 2013. doi:10.1016/j.compstruct.2012.11.020.
  • M. Şimşek, “Reddy Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory”, vol. 64, pp. 37–53, 2013.
  • 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. doi:10.1088/0964-1726/21/2/025018.
  • M. Ghadiri, and H. Safarpour, “Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory,” Appl. Phys. A, vol. 122, no. 9, pp. 833, 2016. doi:10.1007/s00339-016-0365-4.
  • Y. Tadi Beni, “Size-dependent electromechanical bending, buckling, and free vibration analysis of functionally graded piezoelectric nanobeams,” J. Intel. Mat. Sys. Struct., vol. 27, no. 16, pp. 2199–2215, 2016. doi:10.1177/1045389X15624798.
  • 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. doi:10.1016/S0022-5096(03)00053-X.
  • H. Razavi, A. F. Babadi, and Y. T. Beni, “Free vibration analysis of functionally graded piezoelectric cylindrical nanoshell based on consistent couple stress theory,” Com. Struct., vol. 160, pp. 1299–1309, 2017. doi:10.1016/j.compstruct.2016.10.056.
  • X. Liang, S. Hu, and S. Shen, “Bernoulli–Euler dielectric beam model based on strain-gradient effect,” J. Appl. Mech., vol. 80, no. 4, pp. 044502, 2013. doi:10.1115/1.4023022.
  • L. Xu, and S. Shen, “Size-dependent piezoelectricity and elasticity due to the electric field-strain gradient coupling and strain gradient elasticity,” Int. J. Appl. Mech., vol. 5, no. 02, pp. 1350015, 2013. doi:10.1142/S1758825113500154.
  • N. Ebrahimi, and Y. T. Beni, “Electro-mechanical vibration of nanoshells using consistent size-dependent piezoelectric theory,” Steel Comp. Struct., vol. 22, no. 6, pp. 1301–1336, 2016. doi:10.12989/scs.2016.22.6.1301.
  • J. H. He, “Some asymptotic methods for strongly nonlinear equations,” Int. J. Mod. Phys. B, vol. 20, no. 10, pp. 1141, 2006. doi:10.1142/S0217979206033796.
  • A. Fallah, and M. M. Aghdam, “Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation,” Comp. Part B: Eng., vol. 43, no. 3, pp. 1523–1530, 2012. doi:10.1016/j.compositesb.2011.08.041.
  • J. F. Liu, “He's variational approach for nonlinear oscillators with high nonlinearity,” Comput. Math. Appl., vol. 58, no. 11, pp. 2423–2426, 2009. doi:10.1016/j.camwa.2009.03.074.
  • W. Xia, L. Wang, and L. Yin, “Nonlinear non-classical microscale beams: static bending, postbuckling and free vibration,” Int. J. Eng. Sci., vol. 48, no. 12, pp. 2044–2053, 2010. doi:10.1016/j.ijengsci.2010.04.010.
  • L. L. Ke, and Y. S. Wang, “Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory,” Phys. E: Low-dimen. Syst. Nanostruc., vol. 63, pp. 52–61, 2014. doi:10.1016/j.physe.2014.05.002.
  • F. Ebrahimi, and E. Salari, “Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments,” Comp. Struct., vol. 128, pp. 363–380, 2015. doi:10.1016/j.compstruct.2015.03.023.
  • O. Rahmani, and O. Pedram, “Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory,” Int. J. Eng. Sci., vol. 77, pp. 55–70, 2014. doi:10.1016/j.ijengsci.2013.12.003.
  • F. Ebrahimi, and E. Salari, “Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions,” Comp. Part B: Eng., vol. 78, pp. 272–290, 2015. doi:10.1016/j.compositesb.2015.03.068.
  • M. A. Eltaher, S. A. Emam, and F. F. Mahmoud, “Free vibration analysis of functionally graded size-dependent nanobeams,” Appl. Math. Comput., vol. 218, pp. 14, pp. 7406–7420, 2012. doi:10.1016/j.amc.2011.12.090.
  • F. Ebrahimi, and E. Salari, “Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams,” Mech. Adv. Mat. Struct., vol. 23, no. 12, pp. 1379–1397, 2016. doi:10.1080/15376494.2015.1091524.

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