Author(s)

Muhammad Nawaz Naeem¹, Awais Gul Khan¹, Shahid Hussain Arshad^2*, Abdul Ghafar Shah³, Madiha Gamkhar⁴

¹Department of Mathematics, G. C. University Faisalabad, Faisalabad, Pakistan.
²Aerospace Research Institute and North-West Composites Centre, University of Manchester, Manchester, UK.
³Department of Mathematics, Government Post Graduate College Jhang, Jhang, Pakistan.
⁴Department of Statistics and Mathematics, Agricultural University Faisalabad, Faisalabad, Pakistan.

In the present study, vibration analysis of a three-layered cylindrical shell is performed whose inner and outer layers are composed of functionally graded materials whereas the middle one is assumed to be of isotropic material. This formation of a cylindrical shell influences stiffness modulii and the resultant material properties. The shell problem is formulated from the constitutive relations of stresses and strains with the displacement deformations and they are taken from Love’s thin shell theory. This problem is transformed into the integral form by evaluating the expressions for the strain and kinetic energies of the shell. Rayleigh-Ritz method is employed to solve the shell dynamic equations. Vibration characteristics of these cylindrical shells are investigated for a number of physical parameters and configurations of the fabrication of shells. The axial modal dependence is approximated by the characteristic beam functions that satisfy the boundary conditions. Results evaluated, show good agreement with the open literature.

Functionally Graded Material, Isotropic Material, Three-Layered Cylindrical Shell, Love’s Thin Shell Theory Rayleigh-Ritz Method, Natural Frequency

Naeem, M. , Khan, A. , Arshad, S. , Shah, A. and Gamkhar, M. (2014) Vibration of Three-Layered FGM Cylindrical Shells with Middle Layer of Isotropic Material for Various Boundary Conditions. World Journal of Mechanics, 4, 315-331. doi: 10.4236/wjm.2014.411032.