Free Vibration of, Functionally Graded Materials Cylindrical Shells on Elastic Foundation under Axial force, Lateral Pressure and Different Boundary Conditions

Document Type : Research Article

Authors

1 Aerospace Research Institute, Ministry of Science, Research and Technology, Tehran, Iran

2 Space Transportation Research Institute, Iranian Space Research Center, Tehran, Iran

3 Aerospace Engineering Department, Amirkabir University of Technology, Tehran, Iran

Abstract

Free vibration characteristics of functionally graded materials cylindrical shells surrounded by elastic medium under axial force, lateral pressure and different boundary conditions using wave propagation method are investigated in this paper. The material properties of functionally graded materials are assumed to be graded in the thickness direction according to the power law. The elastic medium is assumed as two-parameter Pasternak elastic foundation. Governing equations based on the first order shear deformation theory of Sanders-Koiter for the cylindrical shell resting on elastic foundation under mechanical loads are derived by using Hamilton’s principle. By assuming displacement field in wave propagation form, governing equations are solved. Natural frequencies of cylindrical shell under various boundary conditions are obtained and compared with the results in the literature. It is seen that using displacement field in wave propagation form, acts as an effective and reliable method and gives the acceptable results for various boundary conditions. Although it is shown that for different boundary conditions and geometry dimensions, accuracy of the wave propagation approach is different. In addition, based on the developed theory the effects of different boundary conditions, axial force, lateral pressure and elastic foundation parameters on vibration behavior of functionally graded cylindrical shell are investigated.

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[1] A.W. Leissa, Vibration of Shells, The Acoustical Society of America, 1973.
[2] K. Forsberg, Influence of boundary conditions on modal characteristics of cylindrical shells, Journal of American institute of aeronautics and astronautics, 2 (1964) 182-189.
[3] F. Shadmehri, S. Hoa, M. Hojjati, The Effect of Displacement Field on Bending, Buckling, and Vibration of Cross-Ply Circular Cylindrical Shells, Mechanics of Advanced Materials and Structures, 21(21) (2014) 14-22.
[4] C.B. Sharma, Vibration characteristics of thin circular cylinders, Journal of sound and vibration, 63 (1979) 581-592.
[5] W. Soedel, A new frequency formula for closed circular cylindrical shells for a large variety of boundary conditions, Journal of sound and vibration, 70 (1980) 309-317.
[6] K.Y. Lam, C.T. Loy, Effects of boundary conditions on frequencies of a multi-layered cylindrical shell, Journal of sound and vibration, 188(3) (1995) 363-384.
[7] A. Messina, K.P. Soldatos, Ritz-type dynamic analysis of cross-ply laminated circular cylinders subjected to different boundary conditions, Journal of Sound and Vibration, 227(4) (1999) 749-768.
[8] R. Ansari, M. Darvizeh, M. Hemmatnezhad, Vibration Analysis of FGM Cylindrical Shells Under Various Boundary Conditions, Iranian Aerospace Society, 5(3) (2008) 129-138.
[9] D.N. Paliwal, R.K. Pandey, T. Nath, Free vibration of circular cylindrical shell on Winkler and Pasternak foundation, Journal of pressure vessel and piping, 69 (1996) 79-89.
[10] D.N. Paliwal, R.K. Pandey, The free vibration of a cylindrical shell on an elastic foundation, Journal of vibration and acoustics, 120 (1998) 63-71.
[11] G.G. Sheng, X. Wang, Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium, Journal of Reinforced Plastics and Composites, 27(2) (2008) 117–134.
[12] A.G. Shah, T. Mahmood, M.N. Naeem, Z. Iqbal, S.H. Arshad, Vibrations of functionally graded cylindrical shells based on elastic foundations, Acta Mechanica, 211 (2010) 293-307.
[13] M. Mohammadimehr, M. Moradi, A. Loghman Influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based FGM cylindrical shells under combined loadings, Journal of Solid Mechanics, 6(4) (2014) 347-365.
[14] X.M. Zhang, G.R. Liu, K.Y. Lam, Vibration analysis of thin cylindrical shells using the wave propagation approach, Journal of sound and vibration, 239(3) (2001) 397-403.
[15] X.M. Zhang, G.R. Liu, K.Y. Lam, Coupled vibration analysis of fluid-filled cylindrical shells using the wave propagation approach, Applied Acoustics, 62 (2001) 229-243.
[16] L. Xuebin, Study on free vibration analysis of circular cylindrical shells using wave propagation, Journal of Sound and Vibration, 311 (2008) 667–682.
[17] S. Wang, D.J. Dawe, Buckling of composite shell structures using the spline finite strip method, Composites: Part B, 30 (1999) 351–364.
[18] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, second ed., CRC Press, Boca Raton, FL, 2004.
[19] C.W. Lim, Y.F. Ma, S. Kitipornchai, C.M. Wang, R.K.K. Yuen, Buckling of Vertical Cylindrical Shells Under Combined End Pressure and Body Force, Journal of Engineering Mechanics, 129 (2003) 876-884.
[20] H. Huang, Q. Han, N. Feng, X. Fan, Buckling of functionally graded cylindrical shells under combined loads, Mechanics of Advanced Materials and Structures, 18(5) (2011) 337-346.
[21] P.B. Goncalves, R.S.S. Ramos, Numerical Method for Vibration Analysis of Cylindrical Shells, Journal of Engineering Mechanics, (1997) 544-550.
[22] L.F.F. Gasser, Free Vibrations of thin cylindrical shells containing liquid, Federal Univ. of Rio de Janeiro, 1987.
[23] C.T. Loy, K.Y. Lam, Vibration of cylindrical shells with ring support, International Journal of Mechanical Sciences, 39(4) (1997) 455-471.
[24] M.M. Najafizadeh, M.R. Isvandzibaei, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support, Acta Mechanica, 191 (2007) 75-91.
[25] M.N. Naeem, C.B. Sharma, Prediction of natural frequencies for thin circular cylindrical shell, Journal of mechanical engineering science, 214 (2000) 1313-1328.
[26] A.G. Shah, Vibration characteristics of fluid-filled functionally graded cylindrical shells on elastic foundations, The Islamia University of Bahawalpur, Pakistan, 2011.
[27] J.M. Santiago, H.L. Wisniewski, Convergence of finite element frequency prediction for a thin walled cylinder, Computers and Structures, 32(3/4) (1989) 745–759.
[28] R.N. Arnold, G.B. Warburton, The flexural vibrations of thin cylinders, in: Proceedings of the institution of mechanical engineers A, 1953, pp. 62-80.
[29] C.T. Loy, K.Y. Lam, C. Shu, Analysis of cylindrical shells using generalized differential quadrature method, Shock and vibration, 4 (1997) 193-198.
[30] P.A.T. Gill, Vibrations of clamped-free circular cylindrical shells, Journal of Sound and Vibration, 25 (1972) 501-502.
[31] C.T. Loy, K.Y. Lam, J.N. Reddy, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences, 41 (1999) 309-324.