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ISSN Печать: 2152-2057
ISSN Онлайн: 2152-2073
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ELECTROMAGNETIC RESPONSE OF LAYERED MAGNETO-ELECTRO-ELASTIC THIN RECTANGULAR PLATE UNDER MODERATELY LARGE DEFLECTION
Краткое описание
The analytical solution of a layered thin magneto-electro-elastic rectangular plate is presented. The governing equation is based on classical laminate plate theory and von Karman's stress function; capturing the effects of moderately large deflection. Electromagnetic fields are determined in terms of mechanical unknowns by solving Maxwell's equations of electrostatics and magnetostatics. The condensation of the electric and magnetic state into plate kinematics, coupled with a stress function definition, derives the governing nonlinear partial differential equation of motion. Solution for both simply supported and clamped transverse boundary conditions is obtained using the Galerkin method, which reduces the system into an ordinary differential equation of cubic and quadratic nonlinearity. Numerical results of the laminated plate with constituent piezoelectric BaTiO3 and piezomagnetic CoFe2O4 is produced utilizing electromagnetic boundary and continuity conditions. The effect of transverse elastic boundary condition on through the thickness variation of electric and magnetic potential under linear and moderately large deflection is produced.
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Alaimo, A., Benedetti, I., and Milazzo, A., A Finite Element Formulation for Large Deflection of Multi-layered Magneto-Electro-Elastic Plates, Compos. Struct., vol. 107, pp. 643-653, 2014.
-
Alaimo, A., Milazzo, A., and Orlando, C., A Four-Node MITC Finite Element for Magneto-Electro-Elastic Multilayered Plates, Compos. Struct., vol. 129, pp. 120-133, 2013.
-
Carrera, E. and Nali, P., Multilayered Plate Elements for the Analysis of Multifield Problems, Finite Elem. Anal. Des., vol. 46, no. 9, pp. 732-742, 2010.
-
Chandra, R. and Raju, B., Large Amplitude Flexural Vibration of Cross Ply Laminated Composite Plates, Fib. Sci. Technol., vol. 8, no. 4, pp. 243-263, 1975.
-
Chia, C.Y., Geometrically Nonlinear Behavior of Composite Plates: A Review, Appl. Mech. Rev., vol. 41, no. 12, pp. 439-451, 1988.
-
El-Gamel, M. and Mohsen, A., Sinc-Galerkin Solution to the Clamped Plate Eigenvalue Problem, SeMA J, vol. 74, no. 2, pp. 165-180, 2017.
-
Guru, B.S. and Hiziroglu, H., Electromagnetic Field Theory Fundamentals, Cambridge, UK: Cambridge University Press, 2004.
-
Lage, R.G., Soares, C.M., Soares, C.M., and Reddy, J., Layerwise Partial Mixed Finite Element Analysis of Magneto-Electro-Elastic Plates, Comput. Struct., vol. 82, nos. 17-19, pp. 1293-1301, 2004.
-
Liu, M.F., An Exact Deformation Analysis for the Magneto-Electro-Elastic Fiber-Reinforced Thin Plate, Appl. Math. Modell., vol. 35, no. 5, pp. 2443-2461, 2011.
-
Liu, M.F. and Chang, T.P., Closed Form Expression for the Vibration Problem of a Transversely Isotropic Magneto-Electro-Elastic Plate, J. Appl. Mech. Trans. ASME, vol. 77, no. 2, pp. 024502-1-024502-8, 2010.
-
Milazzo, A., An Equivalent Single-Layer Model for Magnetoelectroelastic Multilayered Plate Dynamics, Compos. Struct., vol. 94, no. 6, pp. 2078-2086, 2012.
-
Milazzo, A., Large Deflection of Magneto-Electro-Elastic Laminated Plates, Appl. Math. Modell., vol. 38, pp. 1737-1752, 2014.
-
Milazzo, A. and Orlando, C., A Beam Finite Element for Magneto-Electro-Elastic Multilayered Composite Structures, Compos. Struct., vol. 94, no. 12, pp. 3710-3721, 2012a.
-
Milazzo, A. and Orlando, C., An Equivalent Single-Layer Approach for Free Vibration Analysis of Smart Laminated Thick Composite Plates, Smart Mater. Struct., vol. 21, no. 7, pp. 075031-1-075031-18, 2012b.
-
Pan, E., Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates, J. Appl. Mech. Trans. ASME, vol. 68, no. 4, pp. 608-618, 2001.
-
Pan, E. and Han, F., Exact Solution for Functionally Graded and Layered Magneto-Electro-Elastic Plates, Int. J. Eng. Sci., vol. 43, nos. 3-4, pp. 321-339, 2005.
-
Pan, E. and Heyliger, P., Free Vibration of Simply Supported and Multilayered Magneto-Electro-Elastic Plates, J. Sound Vib., vol. 252, no. 3, pp. 429-442, 2002.
-
Pan, E. and Heyliger, P., Exact Solutions for Magneto-Electro-Elastic Laminates in Cylindrical Bending, Int. J. Solids Struct., vol. 40, no. 24, pp. 6859-6876, 2003.
-
Phoenix, S., Satsangi, S., and Singh, B., Layer-Wise Modelling of Magneto-Electro-Elastic Plates, J. Sound Vib., vol. 324, nos. 3-5, pp. 798-815, 2009.
-
Razavi, S. and Shooshtari, A., Nonlinear Free Vibration of Magneto-Electro-Elastic Rectangular Plates, Compos. Struct., vol. 119, pp. 377-384, 2015.
-
Reddy, J., Mechanics of Laminated Composite Plates and Shells. Theory and Analysis, Boca Raton, FL: CRC Press, 2004.
-
Shabanpour, S., Razavi, S., and Shooshtari, A., Nonlinear Vibration Analysis of Laminated Magneto-Electro-Elastic Rectangular Plate Based on Third-Order Shear Deformation Theory, Iran J. Sci. Technol. Trans. Mech. Eng., vol. 43, no. 3, pp. 211-223, 2019.?.
-
Shooshtari, A. and Razavi, S., Large Amplitude Free Vibration of Symmetrically Laminated Magneto-Electro-Elastic Rectangular Plates on Pasternak Type Foundation, Mech. Res. Commun., vol. 69, pp. 103-113, 2015a.
-
Shooshtari, A. and Razavi, S., Linear and Nonlinear Free Vibration of a Multilayered Magneto-Electro-Elastic Doubly-Curved Shell on Elastic Foundation, Compos. Part B., vol. 78, pp. 95-108, 2015b.
-
Timoshenko, S. and Woinowsky-Krieger, S., Theory of Plates and Shells, New York: McGraw Hill, 1959.
-
Wang, J., Chen, L., and Fang, S., State Vector Approach to Analysis of Multilayered Magneto-Electro-Elastic Plates, Int. J. Solids Struct., vol. 40, no. 7, pp. 1669-1680, 2003.
-
Wang, X. and Shen, Y.P., The General Solution of Three-Dimensional Problems in Magnetoelectroelastic Media, Int. J. Eng. Sci., vol. 40, no. 10, pp. 1069-1080, 2002.
-
Wang, X.M. and Shen, Y.P., The Conservation Laws and Path-Independent Integrals with an Application for Linear Electro-Magneto-Elastic Media, Int. J. Solids Struct., vol. 33, no. 6, pp. 865-878, 1996.
-
Xue, C., Pan, E., Zhang, S., and Chu, H., Large Deflection of a Rectangular Magnetoelectroelastic Thin Plate, Mech. Res. Commun., vol. 38, no. 7, pp. 518-523, 2011.
-
Yifeng, Z., Lei, C., Yu, W., Xiaopin, Z., and Liangliang, Z., Asymptotical Construction of a Reissner-Like Model for Multilayer Functionally Graded Magneto-Electro-Elastic Plates, Compos. Struct., vol. 96, pp. 786-798, 2013.