Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells

被引:95
|
作者
Vel, Senthil S. [1 ]
机构
[1] Univ Maine, Dept Mech Engn, Orono, ME 04469 USA
关键词
Functionally graded material; Natural frequencies of inhomogeneous shells; Three-dimensional analytical solution; Asymptotic expansion homogenization; Graded fiber orientation; THICK RECTANGULAR-PLATES; MULTIOBJECTIVE OPTIMIZATION; NATURAL FREQUENCIES; COMPOSITE-MATERIALS; ELEMENT; DEFORMATION;
D O I
10.1016/j.compstruct.2010.03.012
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
An exact elasticity solution is presented for the free and forced vibration of functionally graded cylindrical shells. The functionally graded shells have simply supported edges and arbitrary material gradation in the radial direction. The three-dimensional linear elastodynamics equations, simplified to the case of generalized plane strain deformation in the axial direction, are solved using suitable displacement functions that identically satisfy the boundary conditions. The resulting system of coupled ordinary differential equations with variable coefficients are solved analytically using the power series method. The analytical solution is applicable to shallow as well as deep shells of arbitrary thickness. The formulation assumes that the shell is made of a cylindrically orthotropic material but it is equally applicable to the special case of isotropic materials. Results are presented for two-constituent isotropic and fiber-reinforced composite materials. The homogenized elastic stiffnesses of isotropic materials are estimated using the self-consistent scheme. In the case of fiber-reinforced materials, the effective properties are obtained using either the Mori-Tanaka or asymptotic expansion homogenization (AEH) methods. The fiber-reinforced composite material studied in the present work consists of silicon-carbide fibers embedded in titanium matrix with the fiber volume fraction and fiber orientation graded in the radial direction. The natural frequencies, mode shapes, displacements and stresses are presented for different material gradations and shell geometries. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2712 / 2727
页数:16
相关论文
共 50 条
  • [1] EXACT ELASTICITY SOLUTION FOR LAMINATED ANISOTROPIC CYLINDRICAL-SHELLS
    BHASKAR, K
    VARADAN, TK
    [J]. JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1993, 60 (01): : 41 - 47
  • [2] Vibration of functionally graded cylindrical shells
    Loy, CT
    Lam, KY
    Reddy, JN
    [J]. INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 1999, 41 (03) : 309 - 324
  • [3] Vibration of functionally graded cylindrical shells with ring support
    Rahimi, G. H.
    Ansari, R.
    Hemmatnezhad, M.
    [J]. SCIENTIA IRANICA, 2011, 18 (06) : 1313 - 1320
  • [4] Vibration frequencies of functionally graded cylindrical and conical shells
    Eisenberger, M.
    Efraim, E.
    [J]. Structural Dynamics - EURODYN 2005, Vols 1-3, 2005, : 1149 - 1154
  • [5] Thermoelastic and vibration analysis of functionally graded cylindrical shells
    Zhao, X.
    Lee, Y. Y.
    Liew, K. M.
    [J]. INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 2009, 51 (9-10) : 694 - 707
  • [6] An Exact Elasticity Solution for Monoclinic Functionally Graded Beams
    İsa Çömez
    Umit N. Aribas
    Akif Kutlu
    Mehmet H. Omurtag
    [J]. Arabian Journal for Science and Engineering, 2021, 46 : 5135 - 5155
  • [7] An Exact Elasticity Solution for Monoclinic Functionally Graded Beams
    Comez, Isa
    Aribas, Umit N.
    Kutlu, Akif
    Omurtag, Mehmet H.
    [J]. ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING, 2021, 46 (05) : 5135 - 5155
  • [8] Nonlinear forced vibration of functionally graded cylindrical thin shells
    Du, Changcheng
    Li, Yinghui
    Jin, Xuesong
    [J]. THIN-WALLED STRUCTURES, 2014, 78 : 26 - 36
  • [9] An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells
    Pelletier, JL
    Vel, SS
    [J]. INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 2006, 43 (05) : 1131 - 1158
  • [10] Mode interaction in nonlinear vibration of functionally graded cylindrical shells
    Du, Chang-Cheng
    Li, Ying-Hui
    [J]. Zhendong Gongcheng Xuebao/Journal of Vibration Engineering, 2013, 26 (05): : 647 - 653