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Abstract
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In this thesis, we investigated the free vibration of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) toroidal panels in a thermal environment under the influence of internal pressure. The governing equations are obtained by first-order shear deformation (FSDT) theory using the Hamiltonian principle. In order to solve the equations, the quadrature differential numerical method (DQM) is used. The shell is composed of layers and each layer consists of a polymer material reinforced with graphene platelets and it is assumed that the graphene platelets are uniform and with random orientations are distributed in the polymer. In order to gradually change the material properties of the shell, the volume fraction of the graphene platelets in the adjacent layers will change slightly. The effective elastic properties of graphene platelets reinforced composites have been obtained using the improved Halpin-Tsai method and other properties have been calculated using the rule of mixtures. Initial stresses due to thermal environment and internal pressure are estimated by solving thermoelastic equations. Convergence analysis was used to validate the obtained results and compare the results with those of other researchers. Finally, are investigated the effects of temperature rise, shell geometry parameters, internal pressure and boundary conditions on the vibrations of the panel with graphene platelets.
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