Vibrations of graphene platelet reinforced composite doubly curved shells subjected to thermal shock

An investigation is performed in this research to study the response of doubly curved shells subjected to rapid surface heating. Doubly curved shell is made from a composite laminated media where each layer is reinforced with graphene platelets (GPLs). Also each layer may have different amount of GPLs which results in a piecewise functionally graded graphene platelet reinforced composite (FG-GPLRC) shell. The elasticity modulus of the shell is estimated by means of the Halpin-Tsai rule where the size of the reinforcements is also included. It should be noted that mass density, thermal expansion coefficient, Poisson's ratio and specific heat are evaluated using the simple rule of mixture approach. The one-dimension transient heat conduction equation is established and solved for each layer of the composite media. The continuity of the temperature change and heat flux are also considered between the layers. After that, time dependent thermal moment and thermal force are evaluated and inserted into the equations of motion of the structure. First order shear deformation theory of shells and Donnell kinematics are applied to establish the basic equations of the shell. With the aid of the Ritz method and Chebyshev polynomials as the basic functions, the matrix representation of the motion equations of the doubly curved shallow shells subjected to rapid surface heating are established. These equations are traced in time using the Newmark time marching scheme. Results of this study are compared with the available data in the open literature. After that novel results are provided for vibrations induced by rapid surface heating in FG-GPLRC doubly curved shells.