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In this paper the meshless local Petrov-Galerkin (MLPG) method is implemented to study the vibration of a Functionally Graded Material (FGM) cylindrical shell. Displacement field equations, based on Donnell and first order shear deformation theory, are taken into consideration. Material properties are assumed to be temperature-dependent and graded in the thickness direction according to different volume fraction functions. A FGM cylindrical shell made up of a mixture of ceramic and metal is considered herein. The set of governing equations of motion are numerically solved by the Meshless method in which a new variational trial-functional is constructed to derive the stiffness and mass matrices so the natural frequencies are obtained in various boundary conditions by using discretization procedure and solving the general eigenvalue problem. The influences of some commonly used boundary conditions, variations of volume fractions and effects of shell geometrical parameters are studied. The results show the convergence characteristics and accuracy of the mentioned method.

Keywords: FGM, Free vibration, MLPG method, Cylindrical shells, Donnell theory

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