Semi-Analytical Solution for Free Vibration Analysis of Thick Laminated Curved Panels with Power-Law Distribution FG Layers and Finite Length Via Two-Dimensional GDQ Method

Journal of Solid Mechanics

مقاله 8، دوره 8، شماره 2، شهریور 2016، صفحه 334-347   

نوع مقاله: Research Paper

نویسندگان

V Tahouneh¹؛ M.H Naei^{* 2}

¹Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University

²School of Mechanical Engineering, College of Engineering, University of Tehran

چکیده

This paper deals with free vibration analysis of thick Laminated curved panels with finite length, based on the three-dimensional elasticity theory. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. The material properties vary continuously through the layers thickness according to a three-parameter power-low distribution. It is assumed that the inner surfaces of the FG sheets are metal rich while the outer surfaces of the layers can be metal rich, ceramic rich or made of a mixture of two constituents. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG panels are investigated. The obtained results show that the outer FGM Layers have significant effects on the vibration behavior of cylindrical panels. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated curved panels.

کلیدواژه‌ها

Semi-analytical solution؛ FG laminated structures؛ Finite length curved panels؛ Vibration analysis؛ Three-parameter power-low distribution

مراجع

[1] Abrate S., 1998, Impact on Composite Structures, Cambridge UK, Cambridge University Press.
[2] Viola E., Tornabene F., 2009, Free vibrations of three-parameter functionally graded parabolic panels of revolution, Mechanics Research Communications 36: 587-594.
[3] Anderson T.A., 2003, 3D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere, Composite Structure 60: 265-274.
[4] Kashtalyan M., Menshykova M., 2009, Three-dimensional elasticity solution for sandwich panels with a functionally graded core, Composite Structure 87: 36-43.
[5] Li Q., Iu V.P., Kou K.P., 2008, Three-dimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration 311(1-2): 498-515.
[6] Zenkour A.M., 2005, A comprehensive analysis of functionally graded sandwich plates. Part 1-deflection and stresses, International Journal of Solid Structure 42: 5224-5242.
[7] Zenkour A.M., 2005, A comprehensive analysis of functionally graded sandwich plates : Part 1- Deflection and stresses, International Journal of Solid Structure 42: 5243-5258.
[8] Kamarian S., Yas M.H., Pourasghar A., 2013, Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations, Sandwich Structure and Material 15: 292-308.
[9] Loy C.T., Lam K.Y., Reddy J.N., 1999, Vibration of functionally graded cylindrical shells, International Journal of Mechanical science 41: 309-324.
[10] Pradhan S.C., Loy C.T., Lam K.Y., Reddy J.N., 2000, Vibration characteristic of functionally graded cylindrical shells under various boundary conditions, Applied Acoustic 61: 119-129.
[11] Patel B.P., Gupta S.S., Loknath M.S.B., Kadu C.P., 2005, Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory, Composite Structure 69: 259-270.
[12] Pradyumna S., Bandyopadhyay J.N., 2008, Free vibration analysis of functionally graded panels using higher-order finite-element formulation, Journal of Sound and Vibration 318: 176-192.
[13] Yang J., Shen S.H., 2003, Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels, Journal of Sound and Vibration 261: 871-893.
[14] Gang S.W., Lam K.Y., Reddy J.N., 1999, The elastic response of functionally graded cylindrical shells to low-velocity, International Journal of Impact Engineering 22: 397-417.
[15] Shakeri M., Akhlaghi M., Hosseini S.M., 2006, Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder, Composite Structure 76: 174-181.
[16] Chen W.Q., Bian Z.G., Ding H.U., 2004, Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells, International Journal of Mechanical Science 46: 159-171.
[17] Tornabene F., 2009, Free vibration analysis of functionally graded conical cylindrical shell and annular plate structures with a four-parameter power-law distribution, Computer Methods Applied Mechanical Engineering 198: 2911-2935.
[18] Sobhani Aragh B., Yas M.H., 2010, Static and free vibration analyses of continuously graded fiber-reinforced cylindrical shells using generalized power-law distribution, Acta Mechanica 215: 155-173.
[19] Sobhani Aragh B., Yas M.H., 2010, Three dimensional free vibration of functionally graded fiber orientation and volume fraction of cylindrical panels, Material Design 31: 4543-4552.
[20] Paliwal D.N., Kanagasabapathy H., Gupta K.M., 1995, The large deflection of an orthotropic cylindrical shell on a Pasternak foundation, Composite Structure 31: 31-37.
[21] Paliwal D.N., Pandey R.K., Nath T., 1996, Free vibration of circular cylindrical shell on Winkler and Pasternak foundation, International Journal of Pressure Vessels and Piping 69: 79-89.
[22] Yang R., Kameda H., Takada S., 1998, Shell model FEM analysis of buried pipelines under seismic loading, Bulletin of the Disaster Prevention Research Institute 38: 115-146.
[23] Cai J.B., Chen W.Q., Ye G.R, Ding H.J., 2000, On natural frequencies of a transversely isotropic cylindrical panel on a kerr foundation, Journal of Sound and Vibration 232: 997-1004.
[24] Gunawan H., TjMikami T., Kanie S., Sato M., 2006, Free vibration characteristics of cylindrical shells partially buried in elastic foundations, Journal of Sound and Vibration 290: 785-793.
[25] Farid M., Zahedinejad P., Malekzadeh P., 2010, Three dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two parameter elastic foundation using a hybrid semi-analytic, differential quadrature method, Material Design 31: 2-13.
[26] Matsunaga H., 2008, Free vibration and stability of functionally graded shallow shells according to a 2-D higher-order deformation theory, Composite Structure 84: 132-146.
[27] Civalek Ö., 2005, Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ-FD methods, International Journal of Pressure Vessels and Piping 82: 470-479.
[28] Yas M.H., Tahouneh V., 2012, 3-D free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM), Acta Mechanica 223: 43-62.
[29] Tahouneh V., Yas M.H., 2012, 3-D free vibration analysis of thick functionally graded annular sector plates on Pasternak elastic foundation via 2-D differential quadrature method, Acta Mechanica 223: 1879-1897.
[30] Tahouneh V., Yas M.H., Tourang H., Kabirian M., 2013, Semi-analytical solution for three-dimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges, Meccanica 48: 1313-1336.
[31] Tahouneh V., Yas M.H., 2013, Influence of equivalent continuum model based on the eshelby-mori-tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates, Polymer Composites 35(8):1644-1661.
[32] Tahouneh V., Naei M.H., 2013, A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation, Meccanica 49(1):91-109.
[33] Tahouneh V., 2014, Free vibration analysis of thick CGFR annular sector plates resting on elastic foundations, Structural Engineering and Mechanics 50 (6): 773-796.
[34] Shu C., 2000, Differential Quadrature and Its Application in Engineering, Springer, Berlin.
[35] Shu C., Richards B.E., 1992, Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations , International Journal for Numerical Methods in Fluids 15: 791-798.