Free Vibration Analysis of Multi-Layer Rectangular Plate with Two Magneto-Rheological Fluid Layers and a Flexible Core

Journal of Solid Mechanics

مقاله 9، دوره 12، شماره 4، اسفند 2020، صفحه 847-861   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2019.1877385.1487

نویسندگان

M Shekarzadeh¹؛ M.M Najafizadeh^{* 1}؛ P Yousefi¹؛ A. R Nezamabadi¹؛ K Khorshidi²

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

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

چکیده

In the present article, the free vibration analysis of a multi-layer rectangular plate with two magneto-rheological (MR) fluid layers and a flexible core is investigated based on exponential shear deformation theory for the first time. In exponential shear deformation theory, exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The displacement of the flexible core is modeled using Frostig’s second order model which contains a polynomial with unknown coefficients. MR fluids viscosity can be varied by changing the magnetic field intensity. Therefore, they have the capability to change the stiffness and damping of a structure. The governing equations of motion have been derived using Hamilton`s principle. The Navier technique is employed to solve derived equations.  To validate the accuracy of the derived equations, the results in a specific case are compared with available results in the literature, and a good agreement will be observed.  Then, the effect of variation of some parameters such as magnetic field intensity, core thickness to panel thickness ratio and MR layer thickness to panel thickness ratio  on natural frequency of the sandwich panel is investigated.

کلیدواژه‌ها

Vibration؛ Plate؛ Magneto-rheological؛ Flexible core؛ Exponential shear deformation theory

مراجع

[1] Nayak A., Moy S., Shenoi R., 2002, Free vibration analysis of composite sandwich plates based on Reddy's higher-order theory, Composites Part B: Engineering 33(7): 505-519.
[2] Wang J., Meng G., 2001, Magnetorheological fluid devices: principles, characteristics and applications in mechanical engineering, Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 215(3): 165-174.
[3] Weiss K.D., Carlson J.D., Nixon D.A., 1994, Viscoelastic properties of magneto-and electro-rheological fluids, Journal of Intelligent Material Systems and Structures 5(6): 772-775.
[4] Guo Y.-Q., 2017, Preparation and experimental study of magnetorheological fluids for vibration control, International Journal of Acoustics and Vibration 22(2): 194-201.
[5] Rajamohan V., Sundararaman V., Govindarajan B., 2013, Finite element vibration analysis of a magnetorheological fluid sandwich beam, Procedia Engineering 64: 603-612.
[6] Yao X., 2016, Normal force of magnetorheological fluids with foam metal under oscillatory shear modes, Journal of Magnetism and Magnetic Materials 403: 161-166.
[7] Bossis G., 2002, Magnetorheology: fluids, structures and rheology, Ferrofluids 594: 202-230.
[8] De Vicente J., Klingenberg D.J., Hidalgo-Alvarez R., 2011, Magnetorheological fluids: a review, Soft matter 7(8): 3701-3710.
[9] Dragašius E., 2012, Evaluation of the resistance force of magnetorheological fluid damper, Journal of Vibroengineering 14(1):1-6.
[10] Guo H., Liao W., 2012, A novel multifunctional rotary actuator with magnetorheological fluid, Smart Materials and Structures 21(6): 065012.
[11] Klingenberg D.J., 2001, Magnetorheology: applications and challenges, AIChE Journal 47(2): 246-249.
[12] Li W., Du H., 2003, Design and experimental evaluation of a magnetorheological brake, The International Journal of Advanced Manufacturing Technology 21(7): 508-515.
[13] Yamaguchi H., 2012, Dynamic rheological properties of viscoelastic magnetic fluids in uniform magnetic fields, Journal of Magnetism and Magnetic Materials 324(20): 3238-3244.
[14] Yeh Z.-F., Shih Y.-S., 2006, Dynamic characteristics and dynamic instability of magnetorheological material-based adaptive beams, Journal of Composite Materials 40(15): 1333-1359.
[15] 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.
[16] Mohammadi F., Sedaghati R., Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer, Smart Materials and Structures 21(7): 075035.
[17] Yeh J.-Y., 2013, Vibration analysis of sandwich rectangular plates with magnetorheological elastomer damping treatment, Smart Materials and Structures 22(3): 035010.
[18] Yeh J.-Y., 2014,Vibration characteristics analysis of orthotropic rectangular sandwich plate with magnetorheological elastomer, Procedia Engineering 79: 378-385.
[19] Hoseinzadeh M., Rezaeepazhand J., 2014,Vibration suppression of composite plates using smart electrorheological dampers, International Journal of Mechanical Sciences 84: 31-40.
[20] Eshaghi M., Sedaghati R., Rakheja S., 2016, Analytical and experimental free vibration analysis of multi-layer MR-fluid circular plates under varying magnetic flux, Composite Structures 157: 78-86.
[21] 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.
[22] Eshaghi M., Sedaghati R., Rakheja S., 2017,Vibration analysis and optimal design of multi-layer plates partially treated with the MR fluid, Mechanical Systems and Signal Processing 82: 80-102.
[23] Arani A.G. Soleymani T., 2019, Size-dependent vibration analysis of a rotating MR sandwich beam with varying cross section in supersonic airflow, International Journal of Mechanical Sciences 151: 288-299.
[24] Khorshidi K., Fallah A., 2016, Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory, International Journal of Mechanical Sciences 113: 94-104.
[25] 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.
[26] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press.
[27] Ramamoorthy M., Rajamohan V., AK J., 2016,Vibration analysis of a partially treated laminated composite magnetorheological fluid sandwich plate, Journal of Vibration and Control 22(3): 869-895.