Improved High-Order Analysis of Linear Vibrations of a Thick Sandwich Panel With an Electro-Rheological Core by Using Exponential Shear Deformation Theory

Journal of Solid Mechanics

مقاله 3، دوره 14، شماره 1، خرداد 2022، صفحه 37-56   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2020.1898465.1584

نویسندگان

M Keshavarzian¹؛ M.M Najafizadeh^{* 1}؛ K Khorshidi²؛ P Yousefi¹؛ M Alavi³

¹Department of Mechanical Engineering, Arak Branch, Islamic Azad University, Arak, Iran

²Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran

³Department of Mathematics, Arak branch, Islamic Azad University, Arak, Iran

چکیده

In this paper, the behavior of free vibrations of the thick sandwich panel with  multi-layer face sheets and an electrorheological (ER) fluid core using  Exponential Shear Deformation Theory were investigated. For the first time, Exponential shear deformation theory is used for the face sheets while the Displacement field based on the second Frostig's model is used for the core. The governing equations and the boundary conditions are derived by Hamilton’s principle. Closed form solution is achieved using the Navier method and solving the eigenvalues. Primary attention is focused on the effects of electric field magnitude, geometric aspect ratio,and ER core layer thickness on the dynamic characteristics of the sandwich plate. The rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. When an electric field is applied, the damping of the system is more effective. The effects of the natural frequencies and loss factors on the dynamic behaviorof the  sandwich plate are studied.the natural frequency of the sandwich plate increases and the modal loss factor decreases. With increasing the thickness of the ER layer, the natural frequencies of the sandwich plate are decreased. 

کلیدواژه‌ها

Sandwich plate؛ Electro-rheological materials؛ Electric field؛ Exponential shear deformation theory؛ Free vibration

مراجع

1. Yalcintas M., Dai H., 1999, Magnetorheological and electrorheological materials in adaptive structures and their performance comparison, Smart Materials and Structures 8(5): 560-573.
2.  Hasheminejad S.M., Maleki M., 2009, Free vibration and forced harmonic  response of an electrorheological fluid-filled sandwich plate, Smart Materials and Structures 18(5): 16.
3.  Coulter J.P., 1993, Engineering application of electrorheological materials, Journal of Intelligent Materials Systems and Structures 4(2): 248-259.
4.  Coulter J.P., Duclos T.G., 1989, Applications of electrorheological materials in vibration control electrorheological fluids, 2nd International Conference on Electro-Rheological Fluids ed Carlson J. D., Sprecher  A. F., Conrad H., (Lancaster, PA: Technomic).
5.  Coulter J.P., Duclos T.G., Acker D.U., 1989, The usage of electrorheological materials in viscoelastic layer damping applications , WRDC-TR-89-3116 1: CAA-1.
6.  Yalcintas M., Coulter J.P., 1995, Analytical modeling of electrorheological material based adaptive beams, Journal of Intelligent Material Systems and Structures 6(4): 488-497.
7.  Yalcintas M., Coulter J.P., 1995, Electrorheological material based adaptive beams subjected to various boundary conditions, Journal of Intelligent Material Systems and Structures 6(5): 700-717.
8.  Yeh J.Y., Chen W., Wang C.C., 2004, Vibration of a sandwich plate with a constrained layer and electrorheological fluid core, Composite Structures 65(2): 251-258.
9.  Yeh J.Y., Chen W., Wang C.C., 2007, Finite element dynamic analysis of orthotropic sandwich plates with an electrorheological fluid core layer, Composite Structures 78(3): 368-376.
10.  Yeh J.Y., Chen W., Wang C.C., 2006, Dynamic stability analysis of a rectangular orthotropic sandwich plate with an ER fluid core, Composite Structures 72(1): 33-41.
11.  Yeh J.Y., 2007, Vibration analyses of the annular plate with ER fluid damping treatment, Finite Elements in Analysis and Design 43(11): 965-974.
12.  Yeh J.Y., Chen J.Y., Lin C.T., Liu C.Y., 2009, Damping and vibration analysis of polar orthotropic annular plates with ER treatment, Journal of Sound and Vibration 325(1): 1-13.
13.  Yeh J.Y., 2011, Free vibration analysis of rotating polar orthotropic annular plate with ER damping treatment, Composites Part B: Engineering 42(4): 781-788.
14.  Frostig Y., Thomsen O.T., 2004, Higher-order free vibration of sandwich panels with a flexible core, International Journal of Solids and Structures 41(5): 1697-1724.
15.  Malekzadeh K., Khalili M.R., Mittal R.K., 2005, Local and global damped vibrations of plates with a viscoelastic soft flexible core: an improved high-order approach, Journal of Sandwich Structures and Materials 7: 431-456.
16.  Reddy J.N., 1984, A simple higher-order theory for laminated composite plates, Journal of Applied Mechanics 51(4): 745-752.
17.  Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, CRC Press, New york.
18.  Ghugal Y.M., Sayyad A.S., 2011, Free vibration of thick orthotropic plates using trigonometric shear deformation theory, Latin American Journal of Solids and Structures 8(3): 229-243.
19.  Belarbi M.O, Tati A., 2016, Bending analysis of composite sandwich plates with laminated face sheets: new finite element formulation, Journal of Solid Mechanics 8(2): 280-299.
20.  Khorshidi K., Asgari T., Fallah A., 2015, Free vibrations analysis of functionally graded rectangular nano-plates based on nonlocal exponential shear deformation theory, Mechanics of Advanced Composite Structures‎ 2(2): 79-93.
21.  Bahrami M.R., Hatami A., 2016, Free and forced transverse vibration analysis of moderately thick orthotropic plates using spectral finite element method, Journal of Solid Mechanics 8(4): 895-915.
22.  Mozaffari A., Karami M., Azarnia A.H., 2013, The effects of embedded SMA wires on free vibrations of shape memory sandwich-composite panel, Aerospace Mechanics Journal 44(2): 29-40.
23.  Ghajar R., Malekzadeh K., Gholami M., 2015, Dynamic response analysis of doubly curved composite shells subjected to low velocity impact using two models of complete and improved spring-mass, Aerospace Mechanics Journal ‎10(4): 1-12.
24.  Khorshidi K., Siahpush A., Fallah A., 2107, Electro-mechanical free vibrations analysis of composite rectangular piezoelectric nanoplate using modified shear deformation theories, Journal of Science and Technology of Composites 4(2): 151-160.
25.  Ghorbanpour Arani , Emdad M., Ashrafi  H., Mohammadimehr M., Niknejad S., Ghorbanpour Arani A.A., Hosseinpour  A., 2019, Analysis of viscoelastic functionally graded sandwich plates with CNT reinforced composite face sheets on viscoelastic foundation, Journal of Solid Mechanics 11(4): 690-706.
26.  Carlson J.D., Coulter J.P., Duclos T.G.,1990, Electrorheological Fluid Composite Structures, 4,23,057 US Patent .
27.  Don D.L., 1993, An Investigation of Electrorheological Material Adaptive Structures, Master’s Thesis, Lehigh University.
28.  Malekzadefard k., Malek-Mohammadi, 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.
29.  Sun Q., Zhou J.X., Zhang L., 2003, An adaptive beam model and dynamic characteristics of magnetorheological materials, Journal of Sound and Vibration 261(3): 465-481.
30.  Harland N.R., Mace B.R., Jones R.W., 2001, Adaptive-passive control of vibration transmission in beams using electro/magnetorheological fluid filled inserts, IEEE Transactions on Control Systems Technology 9(2): 209-220.
31.  Ramkumar K., Ganesan N., 2009, Vibration and damping of composite sandwich box column with viscoelastic/electrorheological fluid core and performance comparison, Materials and Design 30(8): 2981-2994.
32.  Rajamohan V., Sedaghati R., Rakheja S., 2010, Vibration analysis of a multi-layer beam containing magnetorheological fluid, Smart Materialsand Structures 19(1): 1-12.
33.  Rajamohan V., Rakheja S., Sedaghati R., 2010, Vibration analysis of a partially treated multi-layer beam with magnetorheological fluid, Journal of Sound and Vibration 329(17): 3451-3469.
34.  Rajamohan V., Sedaghati R., Rakheja S., 2010, Optimum design of a multilayer beam partially treated with magnetorheological fluid, Smart Materialsand Structures 19(6): 58-73.
35.  Payganeh G., Malekzadeh K., Malek-Mohammadi H., 2016, Free vibration of sandwich panels with smart magneto-rheological layers and flexible cores, Journal of Solid Mechanics 8(1): 12-30.
36.  Malekzadeh k., Livani M., Ashenai Ghasemi F., 2014, Improved high order free vibration analysis of thick double curved sandwich panels with transversely flexible cores, Latin American Journal of Solids and Structures 11(12):2284-2307.
37.  Reddy J.N.,1987, A refined nonlinear theory of plates with transverse shear deformation, Journal of Solids and Structures 20(9): 881-896.
38.  Vinson J.R., 1986, Optimum design of composite honeycomb sandwich panels subject to uniaxial compression, AIAA Journal 24(10): 1690-1696.
39.  Sanders J.R., Lyell J.,1959, An Improved First Approximation Theory for Thin Shells, NASA THR24.
40.  Lall A.K., Asnani N.,T., Nakra B.C., 1987, Vibration and damping analysis of rectangular plate with partially covered constrained viscoelastic layer, Journal of Vibration, Acoustics, Stress, and Reliability in Design 109(3): 241-247.