Lazreg Hadji, Hassen Ait Atmane, Abdelouahed Tounsi, Ismail Mechab, Noureddine Ziane, El Abbas Adda Bedia. Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory[J]. Applied Mathematics and Mechanics, 2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010
Citation: Lazreg Hadji, Hassen Ait Atmane, Abdelouahed Tounsi, Ismail Mechab, Noureddine Ziane, El Abbas Adda Bedia. Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory[J]. Applied Mathematics and Mechanics, 2011, 32(7): 866-882. doi: 10.3879/j.issn.1000-0887.2011.07.010

Free Vibration of Functionally Graded Sandwich Plates Using Four Variable Refined Plate Theory

doi: 10.3879/j.issn.1000-0887.2011.07.010
  • Received Date: 2010-10-18
  • Rev Recd Date: 2011-04-17
  • Publish Date: 2011-07-15
  • The novelty of this paper was the use of four variable refined plate theory for freevibration analysis of functionally graded material sand wich rectangular plates. Unlike any other theories, the numbe rofunknown functions involved was only four, as a gainst five in case of other shearde formation theories. The theory presented was variationally consistent, had strong smiilarity with classical plate theory in many a spects, did not require shear correction factor, and gave rise to tran sverse shear stress variation such that the trans verse shear stresses vary parabolically a cross the thickness satisfying shear stress free surface conditions. Two commonty pes of FGM sand wich plates, namely, the sand wich with FGM face sheet and homogeneouscore and the sandwich with homogeneous faceshee tand FGM core, were considered. The equation of motion for FGM sandwich plates was obtained through Hamilton. sprinciple. The closed form solutions were obtained by using Navierte chnique, and then fundamental frequencies were found by solving the results of eigenvalue problems. The validity of the present theory was investigated by comparing some of the present results with those of the classical, the firstorder and the other higherorder theories. It can be concluded that the proposed theory is a ccurate and simple in solving the free vibration beha vior of FGM sandwich plates.
  • loading
  • [1]
    Plantema F J. Sandwich Construction: The Bending and Buckling of Sandwich Beam, Plates and Shells[M]. New York: Wiley, 1966.
    [2]
    Allen H G. Analysis and Design of Structural Sandwich Panels[M]. Oxford: Pergamon Press, 1969.
    [3]
    Whitney J M. Structural Analysis of Laminated Anisotropic Plates[M]. Lancaster, PA: Technomic, 1987.
    [4]
    Zenkert D. An Introduction to Sandwich Construction[M].London: Chameleon Press Ltd, 1995.
    [5]
    Vinson J R. The Behavior of Sandwich Structures of Isotropic and Composite Materials[M]. Lancaster: Technomic, 1999.
    [6]
    Pagano N J. Exact solutions for rectangular bidirectional composite and sandwich plates[J]. Journal of Composite Materials, 1970, 4(1): 20-34.
    [7]
    Pagano N J, Hatfield S J. Elastic behaviour of multilayered bidirectional composite[J]. AIAA Journal, 1972, 10(12): 931-933. doi: 10.2514/3.50249
    [8]
    Koizumi M. The concept of FGMS[J]. Ceramic Transactions, Functionally Gradient Materials, 1993, 34(1): 3-10.
    [9]
    Suresh S, Mortensen A. Fundamentals of Functionally Graded Materials[M]. London: IOM Communications, 1998.
    [10]
    Koizumi M. FGM activities in Japan[J]. Compos Part B, Eng, 1997, 28(1/2): 1-4. doi: 10.1016/S1359-8368(96)00016-9
    [11]
    Tanigawa Y. Some basic thermoelastic problems for nonhomogeneous structural materials[J]. Appl Mech Rev, 1995, 48(6): 287-300. doi: 10.1115/1.3005103
    [12]
    Suresh S, Mortensen A. Functionally graded metals and metal ceramic composites 2: thermomechanical behaviour[J]. Int Mater Rev, 1997, 42(3): 85-116. doi: 10.1179/095066097790093217
    [13]
    Bao G, Wang L. Multiple cracking in functionally graded ceramic/metal coatings[J]. International Journal of Solids and Structures, 1995, 32(19): 2853-2871. doi: 10.1016/0020-7683(94)00267-Z
    [14]
    Marur P R. Fracture Behaviour of Functionally Graded Materials[D]. Ph D Thesis. Alabama:Auburn University, 1999.
    [15]
    Williamson R L, Rabin B H, Drake J T. Finite element analyses of thermal residual stresses at graded ceramic-metal interfaces-part I: model description and geometrical effects[J]. Journal of Applied Physics, 1993, 74(2): 1310-1320. doi: 10.1063/1.354910
    [16]
    Drake J T, Williamson R L, Rabin B H. Finite element analysis of thermal residual stresses at graded ceramic-metal interfaces-part II: interface optimization for residual stress reduction[J]. Journal of Applied Physics, 1993, 74(2): 1321-1326. doi: 10.1063/1.354911
    [17]
    Noda N. Thermal stresses in functionally graded material[J]. Journal of Thermal Stresses, 1999, 22(4/5): 477-512. doi: 10.1080/014957399280841
    [18]
    Kesler O, Finot M, Sampath S. Determination of processing induced stresses and properties of layered and graded coatings: experimental method and results for plasma-sprayed Ni-Al2O3[J]. Acta Materialia, 1997, 45(8): 3123-3134. doi: 10.1016/S1359-6454(97)00015-3
    [19]
    Kwon P, Crimp M, Chung M J. Automating the design process and powder processing of functionally gradient materials[C]Composites and Functionally Graded Materials, Proceedings of the Symposia, 1997, 1997: 73-88.
    [20]
    Reddy J N. Analysis of functionally graded plates[J]. International Journal for Numerical Methods in Engineering, 2000, 47(1/3): 663-684. doi: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
    [21]
    Cheng Z Q, Batra R C. Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates[J]. Journal of Sound and Vibration, 2000, 229(4): 879-895. doi: 10.1006/jsvi.1999.2525
    [22]
    Loy C T, Lam K Y, Reddy J N. Vibration of functionally graded cylindrical shells[J]. International Journal of Mechanical Sciences, 1999, 41(3): 309-324. doi: 10.1016/S0020-7403(98)00054-X
    [23]
    Praveen G V, Reddy J N. Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates[J]. International Journal of Solids and Structures, 1998, 35(33): 4457-4476. doi: 10.1016/S0020-7683(97)00253-9
    [24]
    Venkataraman S, Sankar B V. Analysis of sandwich beams with functionally graded core [C] Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA-2001-1281, Seattle, 16-19 April, 2001.
    [25]
    Anderson T A. A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere[J]. Composite Structures, 2003, 60(3): 265-274. doi: 10.1016/S0263-8223(03)00013-8
    [26]
    Pan E, Han F. Exact solution for functionally graded and layered magneto-electro-elastic plates[J]. International Journal of Engineering Science, 2005, 43(3/4): 321-339. doi: 10.1016/j.ijengsci.2004.09.006
    [27]
    Das M, Barut A, Madenci E, Ambur D R. A triangular plate element for thermo-elastic analysis of sandwich panels with a functionally graded core[J]. International Journal for Numerical Method in Engineering, 2006, 68(9): 940-966. doi: 10.1002/nme.1724
    [28]
    Shen H S. Postbuckling of FGM plates with piezoelectric actuators under thermo-electro-mechanical loadings[J]. International Journal of Solids and Structures, 2005, 42(23): 6101-6121. doi: 10.1016/j.ijsolstr.2005.03.042
    [29]
    Noda N. Thermal stress in functionally graded materials[C]Third International Congress on Thermal Stresses. Thermal Stresses 1999, Cracow, Poland, 13-17 June 1999.
    [30]
    Li Q, Iu V P, Kou K P. Three-dimensional vibration analysis of functionally graded material sandwich plates[J]. Journal of Sound and Vibration, 2008, 311(1/2): 498-515. doi: 10.1016/j.jsv.2007.09.018
    [31]
    Shimpi R P. Refined plate theory and its variants[J]. AIAA J, 2002, 40(1): 137-146. doi: 10.2514/2.1622
    [32]
    Shimpi R P, Patel H G. A two variable refined plate theory for orthotropic plate analysis[J]. International Journal of Solids and Structures, 2006, 43(22): 6783-6799. doi: 10.1016/j.ijsolstr.2006.02.007
    [33]
    Shimpi R P, Patel H G. Free vibrations of plate using two variable refined plate theory[J]. Journal of Sound and Vibration, 2006, 296(4/5): 979-999. doi: 10.1016/j.jsv.2006.03.030
    [34]
    Lee K H, Senthilnathan N R, Lim S P, Chow S T. A simple higher-order non-linear shear deformation plate theory[J]. Int J Non-Linear Mechanics, 1989, 24(2): 127-137. doi: 10.1016/0020-7462(89)90004-8
    [35]
    Mechab I, Ait Atmane H, Tounsi A, Belhadj H A, Adda bedia E A. A two variable refined plate theory for bending of functionally graded plates[J]. Acta Mechanica Sinica, 2010, 26(6): 941. doi: 10.1007/s10409-010-0372-1
    [36]
    Delale F, Erdogan F. The crack problem for a nonhomogeneous plane[J]. Journal of Applied Mechanics, 1983, 50(3): 609-614. doi: 10.1115/1.3167098
    [37]
    Reddy J N. Energy and Variational Methods in Applied Mechanics[M]. New York: John Wiley and Sons, 1984.
    [38]
    Leissa A W, Narita Y. Vibration studies for simply supported symmetrically laminated rectangular plates[J]. Compos Struct, 1989, 12(2): 113-132. doi: 10.1016/0263-8223(89)90085-8
    [39]
    Baharlou B, Leissa A W. Vibration and buckling of generally laminated composite plates with arbitrary edge conditions[J]. Int J Mech Sci, 1987, 29(8): 545-555. doi: 10.1016/0020-7403(87)90026-9
    [40]
    Qatu M S. Free vibration of laminated composite rectangular plates[J]. Int J Solids Struct, 1991, 28(8): 941-954. doi: 10.1016/0020-7683(91)90122-V
    [41]
    Messina A, Soldatos K P. Influence of edge boundary conditions on the free vibrations of cross-ply laminated circular panels[J]. J Acoust Soc Am, 1999, 106(5): 2608-2626. doi: 10.1121/1.428126
    [42]
    Bhat R B. Natural frequencies of rectangular plates using characteristics orthogonal polynomials in Rayleigh-Ritz method[J]. J Sound and Vib, 1985, 102(4): 493-499. doi: 10.1016/S0022-460X(85)80109-7
    [43]
    Dickinson S M, Blasio X. On the use of orthogonal polynomials in the Rayleigh-Ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates[J]. J Sound Vib, 1986, 108(1): 51-62. doi: 10.1016/S0022-460X(86)80310-8
    [44]
    Narita Y. Combinations for the free-vibration behaviors of anisotropic rectangular plates under general edge conditions[J]. J Appl Mech, 2000, 67(3): 568-573. doi: 10.1115/1.1311959
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1677) PDF downloads(909) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return