Free vibration analysis of circular sandwich plates with clamped FG face sheets
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک
یونس محمدی
1
,
کیوان حسینی صفری
2
,
محسن رحمانی
3
1 - استادیار، دانشکده صنایع و مکانیک، دانشگاه آزاد اسلامی، قزوین، ایران.
2 - استادیار، دانشکده صنایع و مکانیک، دانشگاه آزاد اسلامی، قزوین، ایران.
3 - دانشجوی دکتری، دانشکده صنایع و مکانیک، دانشگاه آزاد اسلامی، قزوین، ایران.
الکلمات المفتاحية: Free vibration, Functionally graded material, Circular Sandwich Plate, Temperature Dependent Properties, Clamped Support,
ملخص المقالة :
Free vibration of sandwich plates with temperature dependent functionally graded (FG) face sheets in various thermal environments is investigated. The material properties of FG face sheets are assumed to be temperature-dependent and vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. Also, the material properties of the core are assumed to be temperature dependent. The governing equations of motion in polar system and in free natural vibration are derived using Hamilton’s principle and Galerkin method is used to solve the equations and obtain the natural frequency. In-plane stresses of the core that usually are ignored in the vibration characteristics of the sandwich structures are considered in this formulation. The results obtained by Galerkin method for symmetric circular sandwich plate with fixed support is compared with finite element method that obtained by ABAQUS and good agreement is found. The results show that varying the power-law index and temperature have important effects on natural frequency.
[1] Shen Shen, H., Rong Li, S., Post-buckling of sandwich plates with FGM face sheets and temperature-dependent properties, Compos. Part B 39, 2008, pp.332-344.
[2] Reddy, J.N., Thermo Mechanical Behavior of Functionally Graded Materials .Texas. 1998.
[3] Zhao, J., Li, Y., Ai, X., Analysis of transient thermal stress in sandwich plate with functionally graded coatings. Thin Solid Films No. 516, 2008, pp.7581-7587.
[4] Reddy JN., Analysis of functionally graded plates, Int J Numer Meth Eng, No.47, 2000, pp.663–684.
[5] A. Alibeiglooa, K.M. Liew, Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity. Composite Structures, Vol.113, 2014, pp. 23–30.
[6] F.Tornabene, E. Viola, N. Fantuzzi, General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels. Composite Structures, Vol.104, 2013, pp. 94–117.
[7] M. B. Dehkordi, S.M.R. Khalili, E. Carrera, Non-linear transient dynamic analysis of sandwich plate with composite face-sheets embedded with shape memory alloy wires and flexible core- based on the mixed LW (layer-wise)/ESL(equivalent single layer) models. Composites Part B: Engineering, Vol.87, 2016, pp. 59–74.
[8] Cheng ZQ, Batra RC., Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates,"J Sound Vib, No.229, 2000, pp.879–895.
[9] Loy CT, Lam KY, Reddy JN., Vibration of functionally graded cylindrical shells, Int J Mech Sci, N0.41, 1999, pp.309–324.
[10] Mantari JL., Granados EV., Guedes Soares C., Vibrational analysis of advanced composite plates resting on elastic foundation, Compos Part B – Eng, No.66, 2014, pp.407–419.
[11] H. A. Sherif., Free flexural vibrations of clamped circular sandwich plates, Journal of Sound and Vibration, Vol.3, No.157, 1992, pp.531-537.
[12] T. Prakash, M. Ganapathi, Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method, Composites-Part B, No.37, 2006, pp. 642–649.
[13] G.J. Nie, Z. Zhong., Semi-analytical solution for three-dimensional vibration of functionally graded circular plates, Comput. Methods Appl. Mech. Engrg, No.196, 2007, pp.4901–4910.
[14] Liu, C.F., Lee, Y.T., Finite element analysis of three-dimensional vibrations of thick circular and annular plates. J. Sound Vib. Vol. 233, 2000, pp. 63–80.
[15] Zhao, D., Au, F.T.K., Cheung, Y.K., Lo, S.H., Three-dimensional vibration analysis of circular and annular plates via the Chebyshev-Ritz method. Int. J. Solids Struct. Vol. 40, 2003, pp. 3089–3105.
[16] Wu, T.Y., Liu, G.R., Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule. Int. J. Solids Struct. Vol.38, 2001, pp. 7967–7980.
[17] Wu, T.Y., Wang, Y.Y., Liu, G.R., Free vibration analysis of circular plates using generalized differential quadrature rule. Comput. Methods Appl. Mech. Eng. Vol. 191, 2002, pp.5365–5380.
[18] G. C. Kung, Y.H. Pao, Nonlinear flexural vibrations of a clamped circular plate, J. Appl. Mech Vol. 39, No.4, 1972, pp.1050-1054.
[19] Ghaheri, A. and Nosier, A., Nonlinear forced vibrations of thin circular functionally graded plates,” In Persian, Journal of Science and Technology of Composite, Vol. 1, No. 2, 2015, pp. 1-10.
[20] Ming Liu, Yuansheng Cheng, Jun Liu., High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexible core, Composites-Part B, No.72, 2015, pp.97–107.
[21] Shu Xuefeng, Zhang Xiaoqing, Zhang Jinxiang, Thermoelastic free vibration of clampe circular plate, Appl Math Mech, Vol. 21, No.6, 2000, pp. 715-724.
[22] Frostig, Y., Thomsen, O.T., On the free vibration of sandwich panels with a transversely flexible and temperature-dependent core material e, part I: mathematical formulation. J. Compos. Sci. Technol, No.69, 2009, pp.856-862.
[23] Frostig, Y., Thomsen, O.T., Non-linear thermal response of sandwich panels with a flexible core and temperature dependent mechanical properties." Compos. Part B: Eng (special issue, Rajapakse YDS.ONR), Vol.1, No.39, 2008, pp.165-184.
[24] S.M.R. Khalili, Y. Mohammadi, Free vibration analysis of sandwich plates with functionally graded face sheets and temperature-dependent material properties: A new approach, European Journal of Mechanics A/Solids, No.35, 2012, pp.61-74.
[25] Reddy, J.N., Energy Principles and Variational Methods in Applied Mechanics, Wiley & Sons, New York, 1984.
[26] Reddy, J.N., Thermo Mechanical Behavior of Functionally Graded Materials, Texas, 1998.
[27] Y. Kiani, M. R. Eslami., Instability of heated circular FGM plates on a partial Winkler-type foundation, Acta Mech, No.224, 2013, pp.1045–1060.
[28] Young-Wann Kim, Temperature dependent vibration analysis of functionally graded rectangular plates, Journal of Sound and Vibration, No. 284 , 2005, pp.531–549.
[29] M. Es’haghi n, Sh.HosseiniHashemi, M. Fadaee., Vibration analysis of piezoelectric FGM sensors using an accurate method, International Journal of Mechanical Sciences, No.53, 2005, pp.585–594.
[30] M.M. Najafzadeh, M.R. Eslami, Buckling analysis of circular plates of functionally graded materials under uniform radial compression, International Journal of Mechanical Sciences, No.44, 2002, pp.2479–2493.
