Abstract:

This paper studies the optimization of mass and frequency for a polymeric conical shell reinforced with graphene nanoplatelets (GNPs). The volume fraction of the GNPs and the thickness of the shell change along the meridional direction. The modeling of the conical shell is conducted by the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived by Hamilton’s principle. A semi-analytical solution is presented, including an analytical solution carried out in the circumferential direction and a numerical solution conducted in the meridional direction utilizing the differential quadrature method (DQM). To maximize the fundamental frequency and minimize the mass, the particle swarm optimization (PSO) is utilized, taking into account some constraints on the minimum thickness of the shell and the maximum volume fraction of the GNPs. The optimization process involves finding the optimal profiles of thickness and volume fraction of the GNPs.

Key words: optimization, free vibration, conical shell, graphene nanoplatelet (GNP), variable thickness