Volume 3, Issue 3-1, June 2015, Page: 32-40
On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer
Zermina Gull Bhutta, Department of Mathematics, University of Sargodha, Women Sub-Campus, Faisalabad, Pakistan
M. N. Naeem, Department of Mathematics, Government College University, Faisalabad, Pakistan
M. Imran, Department of Mathematics, Government College University, Faisalabad, Pakistan
Received: May 31, 2015;       Accepted: Jun. 1, 2015;       Published: Jun. 15, 2015
DOI: 10.11648/j.ajam.s.2015030301.16      View  4799      Downloads  95
In the current analysis vibration characteristics of a cylindrical shell composed of three layers are examined. Vibration of cylindrical shells is accomplished for their involvement in various areas of engineering and technology. Shell vibration behavior depends upon on different geometrical material parameters and material parameters. They provide the maximum stability of a physical system. There is graduation distribution of constituent materials in functionally graded materials and is controlled by polynomial, exponential and trigonometric volume exponent fraction laws. In the present study a cylindrical shell is composed of three layers whereas the middle layer consists of functionally graded material and the extreme layer are of isotropic nature. Material composition of the FG layer is governed by polynomial, exponential and trigonometric volume fraction exponent laws. Impact of these laws is examined on shell vibration frequencies for different physical parameters. Love’s thin shell theory is adopted for shell motion equations. The vibration of cylindrical shells with FGM will be expressed by using the Raleigh-Ritz technique in this method. Three volume fraction laws are used to define the middle layer of tri-layer cylindrical shells. The Rayleigh-Ritz technique is applied to form the shell frequency equation which is solved by MATLAB software. The validity and accuracy of this method is investigated for a number of comparisons of numerical results.
Component, Formatting, Style, Styling, Insert
To cite this article
Zermina Gull Bhutta, M. N. Naeem, M. Imran, On Vibration of Three-Layered Cylindrical Shell with Functionally Graded Middle Layer, American Journal of Applied Mathematics. Special Issue: Proceedings of the 1st UMT National Conference on Pure and Applied Mathematics (1st UNCPAM 2015). Vol. 3, No. 3-1, 2015, pp. 32-40. doi: 10.11648/j.ajam.s.2015030301.16
D. M. Egle, J. L. Sewall, An analysis of free vibration of orthogonal Stiffened cylindrical shells with stiffeners as discrete elements. AIAA Journal, 6(3), pp. 518-526, 1968.
C. B. Sharma, D. J. Johns, Vibrations characteristics of clamped- free and clamped- ring stiffened circular cylindrical shells. Journal of Sound and Vibration, 14, pp. 459-474, 1971.
S., Swaddiwudhipong, J. Tian, C. M. Wang, Vibrations of cylindrical shells with intermediate supports. Journal of Sound and Vibration, 187(1) , pp. 69-93, 1995.
C. T. Loy, K. Y. Lam, J. N. Reddy, Vibration of functionally graded cylindrical shells. International Journal of Mechanical Sciences, 1, pp. 309-324, 1999.
S. C. Pardhan, K. Y. Lam, J. N. Reddy, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions. Applied Acoustics, 61, pp. 111-129, 2000.
S. Li, X Fu, R. C. Batra, Free vibration of three-layer circular cylindrical shells with functionally graded middle layer. Mechanics Research Communication, 37, pp. 577-580, 2010.
S. Li, R. C. Batra, Buckling of axially compressed thin cylindrical shells with functionally graded middle layer. Thin-Walled Structures, 44, pp. 1039-1047, 2006.
R. D. Blevins, Formulae for natural frequency mode shapes. Van Nostrand Reinhold, New York, 1979.
Z. S Shao, G. W. Ma, “Free vibration analysis of laminated cylindrical shells by using Fourier series expansion method”. J Themoplast Compos Mater, 20, pp. 551-573, 2007.
M. Ahmad, M. N. Naeem, Vibration characteristics of rotating FGM circular cylindrical shell using wave propagation method. European Journal of Scientific Research, 36(2), pp. 184-235, 2009.
S. H. Arshad, M. N.Naeem, N. Sultana, Z. Iqbal, A. G. Shah, Effects of exponential volume fraction law on the natural frequencies of FGM cylindrical shells under various boundary conditions. Arch Appl Mach, 81, pp. 999-1016, 2011.
S. H. Arshad, M. N.Naeem, N. Sultan, Z . Iqbal, A. G. Shah, Vibration of bi-layered cylindrical shells with layers of different materials. Journal of Mechanical Science and Technology, 24(3), pp. 805-810, 2010.
Z. Iqbal, M. N Naeem, N. Sultana, Vibration characteristics of FGM circular cylindrical shells using wave propagation approach. Acta Mechanica, 208, pp. 237-248, 2009.
M. N. Naeem, C. B. Sharma, Prediction of natural frequencies for thin circular cylindrical shells. Proceeding of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214(10), pp. 1313-1328, 2000.
A.H. Sofiyev, O. Aksogan, Non-linear free vibration analyses of laminated non-homogeneous orthotropic cylindrical shells” Proc IME part K: J Multi-body Dyn, Vol 217, pp.293-300, 2003.
S. S. Vel, Exact elasticity solution for the vibration of functionally graded isotropic cylindrical shells. Composite Structures, 92,pp. 2712-2727, 2010.
A. G. Shah, T. Mehmood, M. N. Naeem, Vibration of FGM thin cylindrical shells with exponential volume fraction law. Appl. Math. Mech. –Engl. Ed. 30(5), pp. 607-615, 2009.
G. B. Warburton, Vibration of thin cylindrical shells, Journal of Mechanical Engineering Science, 7, pp. 399-407, 1965.
M. Mehparver, Vibration analysis of functionally greded spinning cylindrical shells using higher order shear deformation theory. Journal of Solid Mechanics, 1(3), pp. 159-170, 2009.
K.Y. Lam, C.T. Loy, Effects of boundary conditions on frequencies of a multilayered cylindrical shell. J.Shock Vibre 4(3), pp. 193-198, 1996.
M. Yamanouchi, M . Koizumi, T. Hirai & I. Shiota, In: Proceedings of the First International Symposium of Functionally Gradient Materials, Sendai, Japan, (1990).
Koizumi, M., The concept of FGM. Ceramic Transactions, Functionally Gradient Materials, 34, pp. 3-10, 1993.
Browse journals by subject