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Volumn 1, Issue 1, 2014, Pages 59-92

Exact 3D solutions and finite element 2D models for free vibration analysis of plates and cylinders

Author keywords

Exact three dimensional solution; Finite element method; Free vibrations; Plates; Shells; Vibration modes

Indexed keywords

CYLINDERS (SHAPES); DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; PLATES (STRUCTURAL COMPONENTS); PLATING;

EID: 84922349406     PISSN: None     EISSN: 23537396     Source Type: Journal    
DOI: 10.2478/cls-2014-0004     Document Type: Article
Times cited : (44)

References (45)
  • 4
    • 77955301898 scopus 로고    scopus 로고
    • Importance of higher order modes and refined theories in free vibration analysis of composite plates
    • S. Brischetto and E. Carrera, Importance of higher order modes and refined theories in free vibration analysis of composite plates, Journal of Applied Mechanics, 77, 1-14, 2010.
    • Journal of Applied Mechanics , vol.77 , Issue.1-14 , pp. 2010
    • Brischetto, S.1    Carrera, E.2
  • 5
    • 84891614481 scopus 로고    scopus 로고
    • Exact elasticity solution for natural frequencies of functionally graded simply-supported structures
    • S. Brischetto, Exact elasticity solution for natural frequencies of functionally graded simply-supported structures, CMES: Computer Modeling in Engineering & Sciences, 95, 391-430, 2013.
    • (2013) CMES: Computer Modeling in Engineering & Sciences , vol.95 , pp. 391-430
    • Brischetto, S.1
  • 6
    • 84894517089 scopus 로고    scopus 로고
    • A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes
    • S. Brischetto, A continuum elastic three-dimensional model for natural frequencies of single-walled carbon nanotubes, Composites Part B: Engineering, 61, 222-228, 2014.
    • (2014) Composites Part B: Engineering , vol.61 , pp. 222-228
    • Brischetto, S.1
  • 7
    • 84894520083 scopus 로고    scopus 로고
    • Three-dimensional exact free vibration analysis of spherical, cylindrical, and flat one-layered panels
    • S. Brischetto, Three-dimensional exact free vibration analysis of spherical, cylindrical, and flat one-layered panels, Shock and Vibration, 2014, 1-29, 2014.
    • (2014) Shock and Vibration , vol.2014 , pp. 1-29
    • Brischetto, S.1
  • 8
    • 85043333835 scopus 로고    scopus 로고
    • accessed on 4th November 2014
    • MSC Nastran, Products (http://www.mscsoftware.com/product/msc-nastran, accessed on 4th November 2014).
    • MSC Nastran Products
  • 9
    • 33847394168 scopus 로고    scopus 로고
    • Analytical solution for vibration of an incompressible isotropic linear elastic rectangular plate, and frequencies missed in previous solutions
    • S. Aimmanee and R.C. Batra, Analytical solution for vibration of an incompressible isotropic linear elastic rectangular plate, and frequencies missed in previous solutions, Journal of Sound and Vibration, 302, 613-620, 2007.
    • (2007) Journal of Sound and Vibration , vol.302 , pp. 613-620
    • Aimmanee, S.1    Batra, R.C.2
  • 10
    • 0042063945 scopus 로고    scopus 로고
    • Letter to the editor: Missing frequencies in previous exact solutions of free vibrations of simply supported rectangular plates
    • R.C. Batra and S. Aimmanee, Letter to the Editor: Missing frequencies in previous exact solutions of free vibrations of simply supported rectangular plates, Journal of Sound and Vibration, 265, 887-896, 2003.
    • (2003) Journal of Sound and Vibration , vol.265 , pp. 887-896
    • Batra, R.C.1    Aimmanee, S.2
  • 11
    • 0000965178 scopus 로고
    • An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates
    • S. Srinivas, C.V. Joga Rao and A.K. Rao, An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates, Journal of Sound and Vibration, 12, 187-199, 1970.
    • (1970) Journal of Sound and Vibration , vol.12 , pp. 187-199
    • Srinivas, S.1    Joga Rao, C.V.2    Rao, A.K.3
  • 13
    • 0037058139 scopus 로고    scopus 로고
    • Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories
    • R.C. Batra, S. Vidoli and F. Vestroni, Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories, Journal of Sound and Vibration, 257, 63-88, 2002.
    • (2002) Journal of Sound and Vibration , vol.257 , pp. 63-88
    • Batra, R.C.1    Vidoli, S.2    Vestroni, F.3
  • 14
    • 0030837244 scopus 로고    scopus 로고
    • A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges
    • J.Q. Ye, A three-dimensional free vibration analysis of cross-ply laminated rectangular plates with clamped edges, Computer Methods in Applied Mechanics and Engineering, 140, 383-392, 1997.
    • (1997) Computer Methods in Applied Mechanics and Engineering , vol.140 , pp. 383-392
    • Ye, J.Q.1
  • 16
    • 0037084909 scopus 로고    scopus 로고
    • Three-dimensional vibration analysis of cantilevered and completely free isosceles triangular plates
    • Y.K. Cheung and D. Zhou, Three-dimensional vibration analysis of cantilevered and completely free isosceles triangular plates, International Journal of Solids and Structures, 39, 673-687, 2002.
    • (2002) International Journal of Solids and Structures , vol.39 , pp. 673-687
    • Cheung, Y.K.1    Zhou, D.2
  • 17
    • 0032690274 scopus 로고    scopus 로고
    • Three-dimensional elasticity solutions for free vibrations of circular plates: A polynomials-ritz analysis
    • K.M. Liew and B. Yang, Three-dimensional elasticity solutions for free vibrations of circular plates: a polynomials-Ritz analysis, Computer Methods in Applied Mechanics and Engineering, 175, 189-201, 1999.
    • (1999) Computer Methods in Applied Mechanics and Engineering , vol.175 , pp. 189-201
    • Liew, K.M.1    Yang, B.2
  • 18
    • 0035861785 scopus 로고    scopus 로고
    • Discrete singular convolution for the prediction of high frequency vibration of plates
    • Y.B. Zhao, G.W. Wei and Y. Xiang, Discrete singular convolution for the prediction of high frequency vibration of plates, International Journal of Solids and Structures, 39, 65-88, 2002.
    • (2002) International Journal of Solids and Structures , vol.39 , pp. 65-88
    • Zhao, Y.B.1    Wei, G.W.2    Xiang, Y.3
  • 19
    • 0037126467 scopus 로고    scopus 로고
    • A novel approach for the analysis of high-frequency vibrations
    • G.W. Wei, Y.B. Zhao and Y. Xiang, A novel approach for the analysis of high-frequency vibrations, Journal of Sound and Vibration, 257, 207-246, 2002.
    • (2002) Journal of Sound and Vibration , vol.257 , pp. 207-246
    • Wei, G.W.1    Zhao, Y.B.2    Xiang, Y.3
  • 20
    • 33746215281 scopus 로고    scopus 로고
    • Short communication free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions
    • H. Rokni Damavandi Taher, M. Omidi, A.A. Zadpoor and A.A. Nikooyan, Short Communication: Free vibration of circular and annular plates with variable thickness and different combinations of boundary conditions, Journal of Sound and Vibration, 296, 1084-1092, 2006.
    • (2006) Journal of Sound and Vibration , vol.296 , pp. 1084-1092
    • Rokni Damavandi Taher, H.1    Omidi, M.2    Zadpoor, A.A.3    Nikooyan, A.A.4
  • 21
    • 64249162358 scopus 로고    scopus 로고
    • New exact solutions for free vibrations of rectangular thin plates by symplectic dual method
    • Y. Xing and B. Liu, New exact solutions for free vibrations of rectangular thin plates by symplectic dual method, Acta Mechanica Sinica, 25, 265-270, 2009.
    • (2009) Acta Mechanica Sinica , vol.25 , pp. 265-270
    • Xing, Y.1    Liu, B.2
  • 22
    • 2142713821 scopus 로고    scopus 로고
    • Three-dimensional exact solution for the vibration of functionally graded rectangular plates
    • S.S. Vel and R.C. Batra, Three-dimensional exact solution for the vibration of functionally graded rectangular plates, Journal of Sound and Vibration, 272, 703-730, 2004.
    • (2004) Journal of Sound and Vibration , vol.272 , pp. 703-730
    • Vel, S.S.1    Batra, R.C.2
  • 23
    • 0032215259 scopus 로고    scopus 로고
    • On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells
    • W.-Q. Chen, H.-J. Ding and R.-Q. Xu, On exact analysis of free vibrations of embedded transversely isotropic cylindrical shells, International Journal of Pressure Vessels and Piping, 75, 961-966, 1998.
    • (1998) International Journal of Pressure Vessels and Piping , vol.75 , pp. 961-966
    • Chen, W.-Q.1    Ding, H.-J.2    Xu, R.-Q.3
  • 24
    • 84868286413 scopus 로고    scopus 로고
    • Analysis of free vibration of cylindrical shells on the basis of three dimensional exact elasticity theory
    • B. Gasemzadeh, R. Azarafza, Y. Sahebi and A. Motallebi, Analysis of free vibration of cylindrical shells on the basis of three dimensional exact elasticity theory, Indian Journal of Science and Technology, 5, 3260-3262, 2012.
    • (2012) Indian Journal of Science and Technology , vol.5 , pp. 3260-3262
    • Gasemzadeh, B.1    Azarafza, R.2    Sahebi, Y.3    Motallebi, A.4
  • 25
    • 0029209197 scopus 로고
    • Exact analysis for three-dimensional free vibrations of cross-ply cylindrical and doubly-curved laminates
    • N.N. Huang, Exact analysis for three-dimensional free vibrations of cross-ply cylindrical and doubly-curved laminates, Acta Mechanica, 108, 23-34, 1995.
    • (1995) Acta Mechanica , vol.108 , pp. 23-34
    • Huang, N.N.1
  • 26
    • 84897970890 scopus 로고    scopus 로고
    • Three-dimensional free vibration analysis of a viscothermoelastic hollow sphere
    • J.N. Sharma, D.K. Sharma and S.S. Dhaliwal, Three-dimensional free vibration analysis of a viscothermoelastic hollow sphere, Open Journal of Acoustics, 2, 12-24, 2012.
    • (2012) Open Journal of Acoustics , vol.2 , pp. 12-24
    • Sharma, J.N.1    Sharma, D.K.2    Dhaliwal, S.S.3
  • 27
    • 77955246594 scopus 로고    scopus 로고
    • Three-dimensional free vibration analysis of a homogeneous transradially isotropic thermoelastic sphere
    • J.N. Sharma and N. Sharma, Three-dimensional free vibration analysis of a homogeneous transradially isotropic thermoelastic sphere, Journal of Applied Mechanics, 77, 1-9, 2010.
    • (2010) Journal of Applied Mechanics , vol.77 , pp. 1-9
    • Sharma, J.N.1    Sharma, N.2
  • 28
    • 0029345001 scopus 로고
    • Axisymmetric static and dynamic analysis of laminated hollow cylinders composed of monoclinic elastic layers
    • K.P. Soldatos and J. Ye, Axisymmetric static and dynamic analysis of laminated hollow cylinders composed of monoclinic elastic layers, Journal of Sound and Vibration, 184, 245-259, 1995.
    • (1995) Journal of Sound and Vibration , vol.184 , pp. 245-259
    • Soldatos, K.P.1    Ye, J.2
  • 30
    • 0021292354 scopus 로고
    • A higher order theory for free vibration analysis of circular cylindrical shells
    • A. Bhimaraddi, A higher order theory for free vibration analysis of circular cylindrical shells, International Journal of Solids and Structures, 20, 623-630, 1984.
    • (1984) International Journal of Solids and Structures , vol.20 , pp. 623-630
    • Bhimaraddi, A.1
  • 31
    • 84862797761 scopus 로고    scopus 로고
    • Free vibrations of cylindrical shellswith elastic-support boundary conditions
    • H. Zhou, W. Li, B. Lv and W.L. Li, Free vibrations of cylindrical shellswith elastic-support boundary conditions, Applied Acoustics, 73, 751-756, 2012.
    • (2012) Applied Acoustics , vol.73 , pp. 751-756
    • Zhou, H.1    Li, W.2    Lv, B.3    Li, W.L.4
  • 32
    • 84858338185 scopus 로고    scopus 로고
    • Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory
    • S.M.R. Khalili, A. Davar and K.M. Fard, Free vibration analysis of homogeneous isotropic circular cylindrical shells based on a new three-dimensional refined higher-order theory, International Journal of Mechanical Sciences, 56, 1-25, 2012.
    • (2012) International Journal of Mechanical Sciences , vol.56 , pp. 1-25
    • Khalili, S.M.R.1    Davar, A.2    Fard, K.M.3
  • 33
    • 77953356042 scopus 로고    scopus 로고
    • Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells
    • S.S. Vel, Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells, Composite Structures, 92, 2712-2727, 2010.
    • (2010) Composite Structures , vol.92 , pp. 2712-2727
    • Vel, S.S.1
  • 34
    • 0001624739 scopus 로고    scopus 로고
    • Vibration of thick cylindrical shells on the basis of three-dimensional theory of elasticity
    • C.T. Loy and K.Y. Lam, Vibration of thick cylindrical shells on the basis of three-dimensional theory of elasticity, Journal of Sound and Vibration, 226, 719-737, 1999.
    • (1999) Journal of Sound and Vibration , vol.226 , pp. 719-737
    • Loy, C.T.1    Lam, K.Y.2
  • 35
    • 78649634000 scopus 로고    scopus 로고
    • Three-dimensional exact solutions for free vibrations of simply supportedmagneto-electroelastic cylindrical panels
    • Y.Wang, R. Xu, H. Ding and J. Chen, Three-dimensional exact solutions for free vibrations of simply supportedmagneto-electroelastic cylindrical panels, International Journal of Engineering Science, 48, 1778-1796, 2010.
    • (2010) International Journal of Engineering Science , vol.48 , pp. 1778-1796
    • Wang, Y.1    Xu, R.2    Ding, H.3    Chen, J.4
  • 36
    • 33646797081 scopus 로고    scopus 로고
    • Exact vibration frequencies of segmented axisymmetric shells
    • E. Efraim and M. Eisenberger, Exact vibration frequencies of segmented axisymmetric shells, Thin-Walled Structures, 44, 281-289, 2006.
    • (2006) Thin-Walled Structures , vol.44 , pp. 281-289
    • Efraim, E.1    Eisenberger, M.2
  • 37
    • 0034051244 scopus 로고    scopus 로고
    • Three-dimensional vibrations of thick spherical shell segments with variable thickness
    • J.-H. Kanga and A.W. Leissa, Three-dimensional vibrations of thick spherical shell segments with variable thickness, International Journal of Solids and Structures, 37, 4811-4823, 2000.
    • (2000) International Journal of Solids and Structures , vol.37 , pp. 4811-4823
    • Kanga, J.-H.1    Leissa, A.W.2
  • 38
    • 0036819575 scopus 로고    scopus 로고
    • Three-dimensional vibration analysis of spherical shell panels subjected to different boundary conditions
    • K.M. Liew, L.X. Peng and T.Y. Ng, Three-dimensional vibration analysis of spherical shell panels subjected to different boundary conditions, International Journal of Mechanical Sciences, 44, 2103-2117, 2002.
    • (2002) International Journal of Mechanical Sciences , vol.44 , pp. 2103-2117
    • Liew, K.M.1    Peng, L.X.2    Ng, T.Y.3
  • 45
    • 0037354371 scopus 로고    scopus 로고
    • Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later
    • C. Molery and C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Review, 45, 1-46, 2003.
    • (2003) SIAM Review , vol.45 , pp. 1-46
    • Molery, C.1    Van Loan, C.2


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