The effects of thickness on frequency values for rotating circular shells

Year 2016, Volume: 8 Issue: 1, 26 - 37, 03.06.2016

Kadir Mercan Çiğdem Demir Hakan Ersoy Ömer Civalek

https://doi.org/10.24107/ijeas.251257

Cited By: 5

Abstract

The aim of the present paper is to investigate effect of thickness on frequency. For this, free vibration analysis of
circular shells is made via ANSYS and numerical method. Discrete singular convolution (DSC) and differential
quadrature methods have been proposed for numerical solution of vibration problem. The formulations are based
on the Love’s first approximation shell. The performance of the present methodology is also discussed.

Keywords

Discrete singular convolution, ANSYS, free vibration, frequencies, cylindrical shells

References

• [1] Bert, C.W., Baker, J.L., and Egle, D.M., Free vibration of multilayered anisotropic cylindrical shells, Journal of composite materials, 3, 480-499, 1969.
• [2] Dong, S.B., Free vibration of laminated orthotropic cylindrical shells, Journal of Acoustical Society of America, 44, 1628-1635, 1968.
• [3] Lam, K.Y., Loy, C.T., Analysis of rotating laminated cylindrical shells by different shell theories, Journal of Sound and Vibration, 186(1), 23-35, 1995.
• [4] Hua, L., Frequency characteristics of a rotating truncated circular layered conical shell, Composite structures, 50, 59-68, 2000.
• [5] Hua, L., Lam, K.Y., Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method, International Journal of Mechanical Sciences, 40(5),443-459, 1998.
• [6] Chung, H., Free vibration analysis of circular cylindrical shells, Journal of Sound and Vibration, 74,331-350, 1981.
• [7] Dym, C.L., Some new results for the vibrations of circular cylinders, Journal of Sound and Vibration, 29,189-205, 1973.
• [8] Smith, B.L., Haft, E.E., Natural frequencies of clamped cylindrical shells, Journal of Aeronautics and Astronautics, 6, 720-721, 1968.
• [9] Liew, K.M., Ng., T.Y., Zhao, X., and Reddy, J.N., Harmonic reproducing kernel particle method for free vibration analysis of rotating cylindrical shells, Computer Methods in Applied Mechanics and Engineering, 191, 4141-4157, 2002.
• [10] Soldatos, K.P., A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels, Journal of sound and vibration, 97, 305-319, 1984.
• [11] Lam, K.Y., Loy, C.T., Influence of boundary conditions for a thin laminated rotating cylindrical shell, Composite Structures, 41, 215-228, 1998.
• [12] Love A.E.H., A Treatise on the Mathematical Theory of Elasticity, Cambridge Unviersity Press, Cambridge, 1952.
• [13] Wei G.W., Discrete singular convolution for the solution of the Fokker–Planck equations. The Journal of chemical physics, 110:8930 –8942, 1999.
• [14] Wei, G.W., Zhou Y.C., Xiang, Y., A novel approach for the analysis of highfrequency vibrations, Journal of Sound and Vibration, 257(2), 207-246, 2002.
• [15] Wei G.W., A new algorithm for solving some mechanical problems, Computer Methods in Applied Mechanics and Engineering, 190,2017-2030, 2001.
• [16] Wei, G.W., Vibration analysis by discrete singular convolution, Journal of Sound and Vibration, 244, 535-553, 2001.
• [17] Wei, G.W., Discrete singular convolution for beam analysis, Engineering Structures, 23, 1045-1053, 2001.
• [18] Wei, G.W., Zhou Y.C., Xiang, Y., Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm. International Journal for Numerical Methods in Engineering, 55,913-946, 2002.
• [19] Wei, G.W., Zhou Y.C., Xiang, Y., The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution, International Journal of Mechanical Sciences, 43,1731-1746, 2001.
• [20] Zhao, Y.B., Wei, G.W. and Xiang, Y., Discrete singular convolution for the prediction of high frequency vibration of plates, International Journal of Solids and Structures, 39, 65-88, 2002.
• [21] Zhao, Y.B., and Wei, G.W., DSC analysis of rectangular plates with non-uniform boundary conditions, Journal of Sound and Vibration, 255(2), 203-228, 2002.
• [22] Hou, Y., G. W. Wei and Y. Xiang, DSC-Ritz method for the free vibration analysis of Mindlin plates, International Journal for Numerical Methods in Engineering, 62,262– 288, 2005.
• [23] Lim, C.W., Li Z. R., and Wei, G. W., DSC-Ritz method for high-mode frequency analysis of thick shallow shells, International Journal for Numerical Methods in Engineering, 62, 205-232, 2005
• [24] Lim, C.W., Li, Z.R., Xiang, Y., Wei, G.W. and Wang, C.M., On the missing modes when using the exact frequency relationship between Kirchhoff and Mindlin plates, Advances in Vibration Engineering, 4, 221-248, 2005.
• [25] Civalek, Ö., An efficient method for free vibration analysis of rotating truncated conical shells, International Journal of Pressure Vessels and Piping, 83, 1-12, 2006.
• [26] Civalek, Ö., The determination of frequencies of laminated conical shells via the discrete singular convolution method, Journal of Mechanics of Materials and Structures, 1(1), 163-182, 2006.
• [27] Civalek, Ö., Free vibration analysis of single isotropic and laminated composite conical shells using the discrete singular convolution algorithm, Steel and Composite Structures, 6(4),353-366, 2006.
• [28] Civalek, Ö., Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method, International Journal of Mechanical Sciences, 49, 752–765, 2007.
• [29] Civalek, Ö., A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straightsided quadrilateral plates, Applied Mathematical Modelling, 33(1), 300-314, 2009.
• [30] Civalek, Ö., Vibration Analysis of Laminated Composite Conical Shells by the Method of Discrete Singular Convolution Based on the Shear Deformation Theory, Composite Part-B: Engineering, 451001-1009, 2013.
• [31] Civalek, Ö., Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory, Journal of Composite Materials, 42(26), 2853-2867, 2008.
• [32] Civalek, Ö., Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method, Finite Elements in Analysis and Design, 44(12-13)725-731, 2008.
• [33] Civalek, Ö., Vibration analysis of conical panels using the method of discrete singular convolution, Communications in Numerical Methods in Engineering, 24, 169-181, 2008.
• [34] Civalek, Ö., Gürses, M., Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique, International Journal of Pressure Vessels and Piping, 86, 677-683, 2009.
• [35] Civalek, Ö., Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method, Applied Mathematical Modelling, 33(10), 3825-3835, 2009.
• [36] Baltacıoglu, A.K., Civalek, Ö., Akgöz, B., Demir, F., Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution. International Journal of Pressure Vessels and Piping, 88, 290-300, 2011.
• [37] Civalek, Ö., Free vibration and buckling analyses of composite plates with straightsided quadrilateral domain based on DSC approach, Finite Elements in Analysis and Design,43,1013-1022, 2007.
• [38] Civalek, Ö., Korkmaz, A.K., Demir, Ç., Discrete Singular Convolution Approach for Buckling Analysis of Rectangular Kirchhoff Plates Subjected to Compressive Loads on Two Opposite Edges, Advance in Engineering Software, 41, 557-560, 2010.
• [39] Civalek, Ö., Finite Element analysis of plates and shells, Elazığ, Fırat University,(in Turkish), Seminar Manuscript, 1998. [40] Markus, S., The mechanics of vibrations of cylindrical shells, Elsevier, New York, 1988.
• [41] Li, H., Lam, K.Y., Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method, International Journal of Mechanical Sciences, 40, 443-459, 1998.
• [42] Zhang, L. Xiang Y. , and Wei, G.W., Vibration analysis of cylindrical shells by a local adaptive differential quadrature method, International Journal Mechanics and Science, 48(10), 1126-1138, 2006.
• [43] Liew, K.M., Han, J-B., Xiao, Z.M., and Du, H., Differential quadrature method for Mindlin plates on Winkler foundations, International Journal of Mechanical Sciences 38(4), 405-421, 1996.
• [44] Bert, C.W., Wang, Z. and Striz, A.G., Differential quadrature for static and free vibration analysis of anisotropic plates, International Journal of Solids and Structures 30(13), 1737-1744, 1993.
• [45] Bert, C.W. and Malik, M., Free vibration analysis of tapered rectangular plates by differential quadrature method: a semi- analytical approach, Journal of Sound and Vibration 190(1), 41-63, 1996.
• [46] Bert, C.W. and Malik, M., Differential quadrature method in computational mechanics: a review, Applied Mechanics Review, 49(1), 1-28, 1996.
• [47] Civalek, Ö., Ülker, M., HDQ-FD Integrated Methodology For Nonlinear Static and Dynamic Response of Doubly Curved Shallow Shells, International Journal of Structural Engineering and Mechanics, 19(5), 535-550, 2005.
• [48] Civalek, Ö., Demir, Ç., Bending analysis of microtubules using nonlocal EulerBernoulli beam theory, Applied Mathematical Modelling, 35(5)2053-2067, 2011.
• [49] Civalek, Ö., Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations, International Journal of Pressure Vessels and Piping, 113, 1-9, 2014.
• [50] Civalek, Ö., Çok Serbestlik Dereceli Sistemlerin Harmonik Diferansiyel Quadrature (HDQ) Metodu ile Lineer ve Lineer Olmayan Dinamik Analizi, Dokuz Eylül Üniversitesi Fen Bilimleri Enstitüsü, 2003.
• [51] Liew, K.M., Teo T.M. and Han, J.B., Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates. International Journal for Numerical Methods in Engineering, 45, 1831-1848, 1999.
• [52] Shu C. and Richards, B.E., Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations, International Journal for Numerical Methods in Fluids, 15, 791-798, 1992.
• [53] Shu, C. and Xue, H., Explicit computations of weighting coefficients in the harmonic differential quadrature, Journal of Sound and Vibration, 204(3), 549-555, 1997
• [54] Striz, A.G., Jang, S.K. and Bert, C.W., Nonlinear bending analysis of thin circular plates by differential quadrature, Thin-Walled Structures, 6, 51-62, 1988.
• [55] Civalek, Ö., Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Engineering Structures, 26(2), 171-186, 2004.
• [56] Civalek, Ö., and Ülker, M., Free vibration analysis of elastic beams using harmonic differential quadrature (HDQ), Mathematical and Computational Applications, 9(2), 257-264, 2004.
• [57] Civalek, Ö., and Ülker, M., Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates, International Journal of Structural Engineering and Mecanics, 17(1), 1-14, 2004.
• [58] Civalek, Ö., 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(6), 470-479, 2005.
• [59] Civalek, Ö., Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ), PhD. Thesis, Fırat University, (in Turkish), Elazığ, 2004.
• [60] Mercan, K., Civalek, Ö., DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix, Composite Structures, 143, 300-309, 2016.
• [61] Demir, Ç., Mercan, K., Civalek, Ö., Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel, Composites Part B: Engineering, 94, 1-10, 2016.