Buckling and Free Vibrations of a Magneto-Electro-Elastic Sandwich Panel with Flexible Core

Subject Areas : Engineering

H Talebi Amanieh ¹ , S.A Seyed Roknizadeh ² , A Reza ³

1 - Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
2 - Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
3 - Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

Received: 2021-07-08 Accepted : 2021-09-13 Published : 2021-12-30

Keywords: Buckling, Sandwich panel, Flexible core, Out-of-plane free vibrations, Magneto-electro-elastic plate,

Abstract :

This paper presents the buckling and out-of-plane free vibration response of a sandwich panel with flexible core for the different boundary condition. In the desired configuration of the sandwich panel, the top and bottom plates are made of magneto-electro-elastic (MEE) plates. Moreover, the in-plane electric and magnetic potential fields are neglected for the derivation of the required relations. The sandwich structure is subjected to axial force in both longitudinal and transverse directions; in addition, and the top and bottom plates are exposed to electric and magnetic fields. The governing equations of motion for MEE sandwich panel with a flexible core are derived based on the first-order shear deformation theory by neglecting the displacement of the mid-plate and using the Hamilton’s principle. Furthermore, the derived partial differential equations (PDEs) are solved. According to the obtained numerical results, the core thickness, variation of electric field, variation of magnetic field and plate length are introduced as the most influential parameters on the free vibration response of the panel as well as the critical force of buckling. As one of the results, the electric potential is inversely related to the natural frequency and buckling load, so that with increasing the electric potential, the natural frequency and critical load of the structure is also increased.Moreover, the magnetic potential is directly related to the natural frequency and buckling load of the system, and increasing trends of natural frequency and critical load are observed by increasing the magnetic potential.

References:

[1] Plantema F., 1966, Sandwich Construction, New York, John Wiley and Sons.
[2] Allen H.G., 2013, Analysis and Design of Structural Sandwich Panels: The Commonwealth and International Library: Structures and Solid Body Mechanics Division, Elsevier.
[3] Rais-Rohani M., Marcellier P.,1999, Buckling and vibration analysis of composite sandwich plates with elastic rotational edge restraints,AIAA Journal 37(5): 579-587.
[4] Frostig Y., Thomsen O.T., 2004, High-order free vibration of sandwich panels with a flexible core, International Journal of Solids and Structures 41(5-6): 1697-1724.
[5] Frostig Y., 1998, Buckling of sandwich panels with a flexible core—high-order theory, International Journal of Solids and Structures 35(3-4): 183-204.
[6] Schwarts-Givli H., Rabinovitch O., Frostig Y., 2007, Free vibrations of delaminated unidirectional sandwich panels with a transversely flexible core—a modified Galerkin approach, Journal of Sound and Vibration 301(1-2): 253-277.
[7] Schwarts-Givli H., Rabinovitch O., Frostig Y., 2008, Free vibration of delaminated unidirectional sandwich panels with a transversely flexible core and general boundary conditions—A high-order approach, Journal of Sandwich Structures & Materials 10(2): 99-131.
[8] Frostig Y., Thomsen O.T., 2009, On the free vibration of sandwich panels with a transversely flexible and temperature-dependent core material–Part I: Mathematical formulation,Composites Science and Technology 69(6): 856-862.
[9] Frostig Y., Thomsen O.T., 2009, On the free vibration of sandwich panels with a transversely flexible and temperature dependent core material–part II: numerical study,Composites Science and Technology 69(6): 863-869.
[10] Araújo A.L., Carvalho V.S., Mota Soares C.M., Belinha J., Ferreira A.J.M., 2016, Vibration analysis of laminated soft core sandwich plates with piezoelectric sensors and actuators,Composite Structures 151: 91-98.
[11] Malekzadeh Fard K., Payganeh G., Kardan M., 2013, Dynamic response of sandwich panels with flexible cores and elastic foundation subjected to low-velocity impact ,Amirkabir Journal of Science & Research (Mechanical Engineering) 45(2): 27-42.
[12] Malekzadeh Fard K., Malek M.H., 2017, Free vibration and buckling analysis of sandwich panels with flexible cores using an improved higher order theory, Journal of Solid Mechanics 9(1): 39-53.
[13] Daikh A.A., Drai A., Bensaid I., Houari M.S.A., Tounsi A., 2020, On vibration of functionally graded sandwich nanoplates in the thermal environment, Journal of Sandwich Structures & Materials doi.org/10.1177/1099636220909790.
[14] Jam J., Eftari B., Taghavian S., 2010, A new improved high‐order theory for analysis of free vibration of sandwich panels, Polymer Composites 31(12): 2042-2048.
[15] Mohammadimehr M., Mostafavifar M., 2016, Free vibration analysis of sandwich plate with a transversely flexible core and FG-CNTs reinforced nanocomposite face sheets subjected to magnetic field and temperature-dependent material properties using SGT,Composites Part B: Engineering 94: 253-270.
[16] Kumar P., Srinivasa C., 2018, On buckling and free vibration studies of sandwich plates and cylindrical shells: a review, Journal of Thermoplastic Composite Materials 33: 673-724.
[17] Pan E., Heyliger P.R., 2002, Free vibrations of simply supported and multilayered magneto-electro-elastic plates, Journal of Sound and Vibration 252(3): 429-442.
[18] Buchanan G.R., 2004, Layered versus multiphase magneto-electro-elastic composites, Composites Part B: Engineering 35(5): 413-420.
[19] Chen W.Q., Lee K.Y., Ding H.J., 2005, On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates, Journal of Sound and Vibration 279: 237-251.
[20] 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(3-5): 626-644.
[21] Liu M.-F., Chang T.-P., 2010, Closed form expression for the vibration problem of a transversely isotropic magneto-electro-elastic plate ,Journal of Applied Mechanics 77(2): 024502.
[22] Davì G., Milazzo A., 2011, A regular variational boundary model for free vibrations of magneto-electro-elastic structures, Engineering Analysis with Boundary Elements 35(3): 303-312.
[23] Milazzo A., Orlando C., 2012, An equivalent single-layer approach for free vibration analysis of smart laminated thick composite plates,Smart Materials and Structures 21(7): 075031.
[24] Chang T.P., 2013, On the natural frequency of transversely isotropic magneto-electro-elastic plates in contact with fluid, Applied Mathematical Modelling 37(4): 2503-2515.
[25] Chang T.P., 2013, Deterministic and random vibration analysis of fluid-contacting transversely isotropic magneto-electro-elastic plates,Computers & Fluids 84: 247-254.
[26] Chen J.Y., Heyliger P.R., Pan E., 2014, Free vibration of three-dimensional multilayered magneto-electro-elastic plates under combined clamped/free boundary conditions, Journal of Sound and Vibration 333(17): 4017-4029.
[27] Kattimani S.C., Ray M.C., 2014, Smart damping of geometrically nonlinear vibrations of magneto-electro-elastic plates,Composite Structures 114: 51-63.
[28] Ke L.-L., Wang Y.-S., Yang J., Kitipornchai S., 2014, Free vibration of size-dependent magneto-electro-elastic nanoplates based on the nonlocal theory,Acta Mechanica Sinica 30(4): 516-525.
[29] Li Y., Zhang J., 2014, Free vibration analysis of magnetoelectroelastic plate resting on a Pasternak foundation,Smart Materials and Structures 23(2): 025002.
[30] Li Y.S., 2014, Buckling analysis of magnetoelectroelastic plate resting on Pasternak elastic foundation, Mechanics Research Communications 56: 104-114.
[31] Karimi M., Farajpour M.R., Rafieian S., Milani A.S., Khayyam H., 2020, Surface energy layers investigation of intelligent magnetoelectrothermoelastic nanoplates through a vibration analysis, The European Physical Journal Plus 135(6): 488.
[32] Karimi M., Shahidi A.R., 2019, A general comparison the surface layer degree on the out-of-phase and in-phase vibration behavior of a skew double-layer magneto–electro–thermo-elastic nanoplate, Applied Physics A 125(2): 106.
[33] Karimi M., Shahidi A.R., 2019, Comparing magnitudes of surface energy stress in synchronous and asynchronous bending/buckling analysis of slanting double-layer METE nanoplates, Applied Physics A 125(2): 154.
[34] Barati M.R., Shahverdi H., Zenkour A.M., 2017, Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory, Mechanics of Advanced Materials and Structures 24(12): 987-998.
[35] Thai H.-T., Choi D.-H., 2012, A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation,Composites Part B: Engineering 43(5): 2335-2347.
[36] Yang C., Jin G., Ye X., Liu Z., 2016, A modified Fourier–Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials, International Journal of Mechanical Sciences 106: 1-18.