Linear and Nonlinear Free Vibration of a Two-Dimensional Multiferroic Composite Plate Subjected to Magneto-Electro-Thermo-Aerodynamic Loading
Subject Areas : Mechanical EngineeringS Razavi 1 , H Ghashochi Bargh 2
1 - Department of Mechanical Engineering, Tabriz Technical and Vocational College, Tabriz, Iran
2 - Imam Khomeini International University- Buein Zahra Higher Education Center of Engineering and Technology, Qazvin, Iran
Keywords: Aerodynamic loading, Magneto-electro-elastic, Nonlinear vibration, Third-order plate theory, Two-dimensional plate,
Abstract :
Vibration response of a two-dimensional magneto-electro-elastic plate is investigated in this paper. The considered multi-phase plate is rectangular and simply-supported resting on an elastic foundation. The plate is under aerodynamic pressure and subjected to temperature change. It is also assumed that the magneto-electro-elastic body is poled along the z direction and subjected to electric and magnetic potentials between the upper and lower surfaces. The nonlinear vibrational analysis of the described plate is considered as an innovation of the present paper,which had not been done before. To model this problem, third-order shear deformation theory along with Gauss’s laws for electrostatics and magnetostatics, first-order piston theory, and Galerkin and multiple times scale methods are used. After validating the presented method, effects of several parameters on the natural frequency, time history, backbone curve, and phase plane diagram of this smart composite plate are obtained. It is found that for plates with constant a/h ratio, electric and magnetic potentials have noticeable effects on the time histories, phase plane diagrams and backbone curves of the plates with smaller thicknesses. In addition, the numerical results of this research indicate that some parameters have considerable effect on the vibration behavior of presented plate. Elastic parameters of the foundation, applied electric and magnetic potentials, and environment temperature are important parameters in this analysis.
[1] Daga A., Ganesan N., Shankar K., 2009, Harmonic response of three-phase magneto-electro-elastic beam under mechanical, electrical and magnetic environment, Journal of Intelligent Material Systems and Structures 20: 1203-1220.
[2] Pan E., 2001, Exact solution for simply supported and multilayered magneto-electro-elastic plates, Journal of Applied Mechanics 68: 608-618.
[3] Pan E., Heyliger P.R., 2002, Free vibrations of simply supported and multilayered magneto-electro-elastic plates, Journal of Sound and Vibration 252: 429-442.
[4] Ebrahimi F., Jafari A., Barati M.R., 2017, Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations, Thin-Walled Structures 119: 33-46.
[5] Jiang C., Heyliger P.R., 2017, Thickness effects in the free vibration of laminated magnetoelectroelastic plates, Journal of Mechanics of Materials and Structures 12: 521-544.
[6] Vinyas M., Kattimani S.C., 2018, Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher-order shear deformation theory, Composite Structures 202: 1339-1352.
[7] Vinyas M., Sandeep A.S., Nguyen-Thoi T., Ebrahimi F., Duc D.N., 2019, A finite element–based assessment of free vibration behaviour of circular and annular magneto-electro-elastic plates using higher order shear deformation theory, Journal of Intelligent Material Systems and Structures 30: 2478-2501.
[8] Vinyas M., Nischith G., Loja M.A.R., Ebrahimi F., Duc N.D., 2019, Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory, Composite Structures 214: 132-142.
[9] Vinyas M., 2019, Vibration control of skew magneto-electro-elastic plates using active constrained layer damping, Composite Structures 208: 600-617.
[10] Zhou L., Li M., Meng G., Zhao H., 2018, An effective cell-based smoothed finite element model for the transient responses of magneto-electro-elastic structures, Journal of Intelligent Material Systems and Structures 29: 3006-3022.
[11] Shooshtari A., Razavi S., 2017, Vibration of a multiphase magneto-electro-elastic simply supported rectangular plate subjected to harmonic forces, Journal of Intelligent Material Systems and Structures 28: 451-467.
[12] Zhang X.L., Chen X.C., Yang E., Li H.F., Liu J.B., Li Y.H., 2019, Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions, Journal of Intelligent Material Systems and Structures 30: 82-99.
[13] Mohammadimehr M., Okhravi S.V., Akhavan Alavi S.M., 2018, Free vibration analysis of magneto-electro-elastic cylindrical composite panel reinforced by various distributions of CNTs with considering open and closed circuits boundary conditions based on FSDT, Journal of Vibration and Control 24: 1551-1569.
[14] Kiani A., Sheikhkhoshkar M., Jamalpoor A., Khanzadi M., 2018, Free vibration problem of embedded magneto-electro-thermo-elastic nanoplate made of functionally graded materials via nonlocal third-order shear deformation theory, Journal of Intelligent Material Systems and Structures 29: 741-763.
[15] Farajpour M.R., Shahidi A.R., Hadi A., Farajpour A., 2018, Influence of initial edge displacement on the nonlinear vibration, electrical and magnetic instabilities of magneto-electro-elastic nanofilms, Mechanics of Advanced Materials and Structures 26: 1469-1481.
[16] Vinyas M., 2019, A higher-order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods, Composites Part B: Engineering 158: 286-301.
[17] Xue C.X., Pan E., Zhang S.Y., Chu H.J., 2011, Large deflection of a rectangular magnetoelectroelastic thin plate, Mechanics Research Communications 38: 518-523.
[18] Razavi S., Shooshtari A., 2015, Nonlinear free vibration of magneto-electro-elastic rectangular plates, Composite Structures 119: 377-384.
[19] Shooshtari A., Razavi S., 2015, Linear and nonlinear free vibration of a multilayered magneto-electro-elastic doubly-curved shell on elastic foundation, Composites Part B: Engineering 78: 95-108.
[20] Shabanpour S., Razavi S., Shooshtari A., 2019, Nonlinear vibration analysis of laminated magneto-electro-elastic rectangular plate based on third-order shear deformation theory, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 43: 211-223.
[21] Ansari R., Gholami R., Rouhi H., 2019, Geometrically nonlinear free vibration analysis of shear deformable magneto-electro-elastic plates considering thermal effects based on a novel variational approach, Thin-Walled Structures 135: 12-20.
[22] Carrera E., Zappino E., 2013, Aeroelastic analysis of pinched panels in supersonic flow changing with altitude, Journal of Spacecraft and Rockets 51: 187-199.
[23] Zhao M.H., Zhang W., 2014, Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics, Acta Mechanica 225: 1985-2004.
[24] Meijer M.C., Dala L., 2015, Zeroth-order flutter prediction for cantilevered plates in supersonic flow, Journal of Fluids and Structures 57: 196-205.
[25] Chen T., Xu M., Xie D., An X., 2017, Post-flutter response of a flexible cantilever plate in low subsonic flows, International Journal of Non-Linear Mechanics 91: 113-127.
[26] Eugeni M., Mastroddi F., Dowell E.H., 2017, Normal form analysis of a forced aeroelastic plate, Journal of Sound and Vibration 390: 141-163.
[27] Pacheco D.R.Q., Marques F.D., Ferreira A.J.M., 2018, Finite element analysis of fluttering plates reinforced by flexible beams: An energy-based approach, Journal of Sound and Vibration 435: 135-148.
[28] Raja S., Pashilkar A.A., Sreedeep R., Kamesh J.V., 2006, Flutter control of a composite plate with piezoelectric multilayered actuators, Aerospace Science and Technology 10: 435-441.
[29] Song Z.G., Li F.M., 2012, Active aeroelastic flutter analysis and vibration control of supersonic composite laminated plate, Composite Structures 94: 702-713.
[30] Makihara K., Shimose S., 2012, Supersonic flutter utilization for effective energy-harvesting based on piezoelectric switching control, Smart Materials Research 2012: 181645.
[31] Leão L.S., de Lima A.M.G., Donadon M.V., Cunha-Filho A.G., 2016, Dynamic and aeroelastic behavior of composite plates with multimode resonant shunted piezoceramics in series, Composite Structures 153: 815-824.
[32] Lu S.F., Zhang W., Song X.J., 2018, Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force, Acta Mechanica Sinica 34: 303-314.
[33] Serry M., Tuffaha A., 2018, Static stability analysis of a thin plate with a fixed trailing edge in axial subsonic flow: Possio integral equation approach, Applied Mathematical Modelling 63: 644-659.
[34] Song Z.G., Yang T.Z., Li F.M., Carrera E., Hagedorn P., 2018, A method of panel flutter suppression and elimination for aeroelastic structures in supersonic airflow, Journal of Vibration and Acoustics 140: 064501.
[35] Kelkar A., Deshpande P., Vogel J., 2016, Energy recovery concepts in actively controlled lco instabilities caused by free-play induced aeroelastic flutter, Proceedings of the First International Symposium on Flutter and its Application.
[36] de Sousa V.C., Silva T.M.P., Junior C.D.M., 2017, Aeroelastic flutter enhancement by exploiting the combined use of shape memory alloys and nonlinear piezoelectric circuits, Journal of Sound and Vibration 407: 46-62.
[37] de Sousa V.C., Junior C.D.M., Elahinia M.H., 2018, Effect of constitutive model parameters on the aeroelastic behavior of an airfoil with shape memory alloy springs, Journal of Vibration and Control 24: 1065-1085.
[38] de Sousa V.C., Junior C.D.M., Elahinia M., 2017, Aeroelastic behavior of a typical section with shape memory alloy springs: Modeling nonhomogeneous distribution of state variables, Applied Mathematical Modelling 52: 404-416.
[39] Rafiee M., Mohammadi M., Sobhani Aragh B., Yaghoobi H., 2013, Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells, Part I: Theory and analytical solutions, Composite Structures 103: 179-187.
[40] Rafiee M., Mohammadi M., Sobhani Aragh B., Yaghoobi H., 2013, Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells Part II: Numerical results, Composite Structures 103: 188-196.
[41] Arefi M., Ashraf M. Zenkour., 2017, Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers, Acta Mechanica 228: 475-493.
[42] Arefi M., Ashraf M. Zenkour., 2017, Thermo-electro-mechanical bending behavior of sandwich nanoplate integrated with piezoelectric face-sheets based on trigonometric plate theory, Composite Structures 162: 108-122.
[43] Ashraf M. Zenkour., Arefi M., 2017, Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation, Journal of Thermal Stresses 40: 167-184.
[44] Arefi M., Ashraf M. Zenkour., 2019, Effect of thermo-magneto-electro-mechanical fields on the bending behaviors of a three-layered nanoplate based on sinusoidal shear-deformation plate theory, Journal of Sandwich Structures & Materials 21: 639-669.
[45] Arefi M., Ashraf M. Zenkour., 2016, Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets, Smart Materials and Structures 25: 115040.
[46] Arefi M., Zamani M.H., Kiani M., 2018, Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation, Journal of Intelligent Material Systems and Structures 29: 774-786.
[47] Arefi M., Soltan Arani A.H., 2018, Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments, Mechanics Based Design of Structures and Machines 46: 669-692.
[48] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Boca Raton, CRC Press.
[49] Li Y.S., Cai Z.Y., Shi S.Y., 2014, Buckling and free vibration of magnetoelectroelastic nano plate based on nonlocal theory, Composite Structures 111: 552-529.
[50] Chia C.Y., 1980, Nonlinear Analysis of Plates, McGraw-Hill.
[51] Shiau L.C., Lu L.T., 1992, Nonlinear flutter of two-dimensional simply supported symmetric composite laminated plates, Journal of Aircraft 29: 140-145.
[52] Nayfeh A.H., Dean TMook., 1995, Nonlinear Oscillation, John Wiley & Sons.
[53] Shooshtari A., Razavi S., 2014, Nonlinear free and forced vibrations of anti-symmetric angle-ply hybrid laminated rectangular plates, Journal of Composite Materials 48: 1091-1111.
[54] Ramirez F., Heyliger P.R., Pan E., 2006, Free vibration response of two-dimensional magneto-electro-elastic laminated plates, Journal of Sound and Vibration 292: 626-644.
[55] Young W.C., Budynas R.G., 2001, Roark’s Formulas for Stress and Strain, McGraw-Hill.
[56] Ansari R., Gholami R., 2016, Nonlocal free vibration in the pre- and post-buckled states of magneto-electro-thermo elastic rectangular Nano plates with various edge conditions, Smart Materials and Structures 25: 095033-095050.