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  4593      Downloads  91
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.
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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
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