Abstract
In this paper, size-dependent effect of an embedded magneto-electro-elastic (MEE) nanoshell subjected to thermo-electro-magnetic loadings on free vibration behavior is investigated. Also, the surrounding elastic medium has been considered as the model of Winkler characterized by the spring. The size-dependent MEE nanoshell is investigated on the basis of the modified couple stress theory. Taking attention to the first-order shear deformation theory (FSDT), the modeled nanoshell and its equations of motion are derived using principle of minimum potential energy. The accuracy of the presented model is validated with some cases in the literature. Finally, using the Navier-type method, an analytical solution of governing equations for vibration behavior of simply supported MEE cylindrical nanoshell under combined loadings is presented and the effects of material length scale parameter, temperature changes, external electric potential, external magnetic potential, circumferential wave numbers, constant of spring, shear correction factor and length-to-radius ratio of the nanoshell on natural frequency are identified. Since there has been no research about size-dependent analysis MEE cylindrical nanoshell under combined loadings based on FSDT, numerical results are presented to be served as benchmarks for future analysis of MEE nanoshells using the modified couple stress theory.
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References
J. Van den Boomgaard et al., An in situ grown eutectic magnetoelectric composite material. J. Mater. Sci. 9(10), 1705–1709 (1974)
Y. Wang et al., Multiferroic magnetoelectric composite nanostructures. NPG Asia Mater. 2(2), 61–68 (2010)
H. Zheng et al., Multiferroic BaTiO3–CoFe2O4 nanostructures. Science 303(5658), 661–663 (2004)
L. Martin et al., Multiferroics and magnetoelectrics: thin films and nanostructures. J. Phys.: Condens. Matter 20(43), 434220 (2008)
G.S. Lotey, N. Verma, Magnetoelectric coupling in multiferroic BiFeO3 nanowires. Chem. Phys. Lett. 579, 78–84 (2013)
H. Béa et al., Spintronics with multiferroics. J. Phys.: Condens. Matter 20(43), 434221 (2008)
A.Q. Jiang et al., A resistive memory in semiconducting BiFeO3 thin-film capacitors. Adv. Mater. 23(10), 1277–1281 (2011)
A. Annigeri, N. Ganesan, S. Swarnamani, Free vibrations of clamped–clamped magneto-electro-elastic cylindrical shells. J. Sound Vib. 292(1), 300–314 (2006)
R.K. Bhangale, N. Ganesan, Free vibration studies of simply supported non-homogeneous functionally graded magneto-electro-elastic finite cylindrical shells. J. Sound Vib. 288(1), 412–422 (2005)
J. Reddy, C. Chin, Thermomechanical analysis of functionally graded cylinders and plates. J. Therm. Stress. 21(6), 593–626 (1998)
H. Haddadpour, S. Mahmoudkhani, H. Navazi, Free vibration analysis of functionally graded cylindrical shells including thermal effects. Thin-Walled Struct. 45(6), 591–599 (2007)
M.J. Mescher et al., Novel MEMS microshell transducer arrays for high-resolution underwater acoustic imaging applications. in Sensors, 2002. Proceedings of IEEE (IEEE, 2002)
P. Soltani, J. Saberian, R. Bahramian, Nonlinear vibration analysis of single-walled carbon nanotube with shell model based on the nonlocal elasticity theory. J. Comput. Nonlinear Dyn. 11(1), 011002 (2016)
R.A. Toupin, Elastic materials with couple-stresses. Arch. Ration. Mech. Anal. 11(1), 385–414 (1962)
W. Koiter, Couple stresses in the theory of elasticity. Proc. Koninklijke Nederl. Akaad. van Wetensch 67 (1964)
R.D. Mindlin, Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16(1), 51–78 (1964)
M. Asghari et al., Investigation of the size effects in Timoshenko beams based on the couple stress theory. Arch. Appl. Mech. 81(7), 863–874 (2011)
F. Yang et al., Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)
Y.T. Beni, F. Mehralian, H. Razavi, Free vibration analysis of size-dependent shear deformable functionally graded cylindrical shell on the basis of modified couple stress theory. Compos. Struct. 120, 65–78 (2015)
M.A. Khorshidi, M. Shariati, Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory. J. Braz. Soc. Mech. Sci. Eng. 15, 1–13 (2015)
E.M. Miandoab et al., Polysilicon nano-beam model based on modified couple stress and Eringen’s nonlocal elasticity theories. Phys. E: Low-Dimens. Syst. Nanostruct. 63, 223–228 (2014)
A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, vol. 1 (Cambridge University Press, Cambridge, 2013)
L.H. Donnell, A new theory for the buckling of thin cylinders under axial compression and bending. Trans. Asme 56(11), 795–806 (1934)
J.L. Sanders Jr., An improved first-approximation theory for thin shells (NASA TR-R24). US Government Printing Office, Washington, DC (1959)
A.W. Leissa, Vibration of Shells, Scientific and Technical Information Office. NASA Report No. SP-288 (1973)
E. Reissner, The effect of transverse shear deformation on the bending of elastic plates. Trans. ASME 12, 69–77 (1945)
R.D. Mindlin, Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. Trans. ASME 18, 31–38 (1951)
G. Sheng, X. Wang, Thermoelastic vibration and buckling analysis of functionally graded piezoelectric cylindrical shells. Appl. Math. Model. 34(9), 2630–2643 (2010)
M. Mohammadimehr, M. Moradi, A. Loghman, Influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based FGM cylindrical shells under combined loadings. J. Solid Mech. 6(4), 347–365 (2014)
L. Ke, Y. Wang, J. Reddy, Thermo-electro-mechanical vibration of size-dependent piezoelectric cylindrical nanoshells under various boundary conditions. Compos. Struct. 116, 626–636 (2014)
L.-L. Ke et al., The size-dependent vibration of embedded magneto-electro-elastic cylindrical nanoshells. Smart Mater. Struct. 23(12), 125036 (2014)
Y. Li, P. Ma, W. Wang, Bending, buckling, and free vibration of magnetoelectroelastic nanobeam based on nonlocal theory. J. Intell. Mater. Syst. Struct. 27(9), 1139–1149 (2016)
A.C. Eringen, Nonlocal continuum field theories (Springer Science & Business Media, Berlin, 2002)
Q. Wang, On buckling of column structures with a pair of piezoelectric layers. Eng. Struct. 24(2), 199–205 (2002)
T.R. Tauchert, Energy Principles in Structural Mechanics (McGraw-Hill Companies, New York, 1974)
R. Ansari, R. Gholami, H. Rouhi, Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories. Compos. Part B: Eng. 43(8), 2985–2989 (2012)
C. Loy, K. Lam, C. Shu, Analysis of cylindrical shells using generalized differential quadrature. Shock Vib. 4(3), 193–198 (1997)
J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (CRC Press, Boca Raton, 2004)
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Ghadiri, M., Safarpour, H. Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory. Appl. Phys. A 122, 833 (2016). https://doi.org/10.1007/s00339-016-0365-4
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DOI: https://doi.org/10.1007/s00339-016-0365-4