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Abstract:In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love's rst approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for di erent types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

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In the present manuscript, we developed a systematic formulation for some type graphene sheets having annular sector, sector shaped or curvilinear side graphene located on a silicone matrix via nonlocal elasticity theory for numerical solution. An eight-node curvilinear element is used for transformation of the governing equation of motion of annular sector graphene from physical region to computational region in conjunctions with the thin plate theory. Silicone matrix is modeled by using the Winkler-Pasternak elastic foundations. The formulation is usefully for different shaped graphene sheets.