A semi-analytical solution for dynamic stability analysis of nanocomposite/fibre-reinforced doubly-curved panels resting on the elastic foundation in thermal environment

Investigating the dynamic stability of doubly-curved shells resting on the elastic foundation and made of the laminated composites reinforced by carbon fibres, carbon nanotubes (CNTs), and graphene nanoplatelets (GPLs) is focused in this paper. In this type of composite, some layers are reinforced by CNTs and some others are reinforced by GPLs. In order to get this target, all of the governing equations corresponding to doubly-curved orthotropic shells subjected to the periodic in-plane loading in thermal environment are extended based on the first-order shear deformation theory. Then, the obtained system of equilibrium and compatibility differential equations are solved by a semi-analytical approach based on the Galerkin method which leads to a closed-form solution. In the mentioned closed-form solution, because of the complexity of integrations through the thickness of shells, the terms related to mechanical specifications are obtained by Gauss quadrature rule as a numerical method. Consequently, the proposed method is categorized in the group of the semi-analytical methods. Comparing the obtained results for some benchmark problems with those are existent in the present literature shows the good accuracy of the present solution. The evaluation of dynamic stability of shells has been done by performing a comprehensive parametric study which considers the effects of geometrical and mechanical specifications, and also the boundary conditions (BCs) on their dynamic unstable regions. The effects of mentioned factors have been investigated for four types of panels incorporating the flat panel (plate), cylindrical panel, doubly-curved panel with positive radii, and also doubly-curved panel with negative and positive radii.