The free vibration behaviour of a GNP-reinforced conical shell with an adhesive lap joint

This paper studies the free vibration analysis of a nanocomposite conical shell with an adhesive lap joint. As the adherents, two polymer-based nanocomposite conical shells enriched with graphene nanoplatelets (GNPs) are considered, which are connected with an elastic adhesive. The distribution patterns and mass fractions of the GNPs in two adherents are not necessarily the same. The set of coupled partial differential equations is solved analytically by considering appropriate trigonometric functions in the circumferential direction, and approximately by applying the differential quadrature method (DQM) in the meridional direction. Numerical results demonstrate that the natural frequencies increase as the lap joint length increases. However, the variation of each natural frequency versus the variation in the thickness of the adhesive depends on the vibrational mode. It is demonstrated that the natural frequencies reach their maximum values when the GNPs are distributed as far away as possible from the middle surfaces of the outer and inner parts of the shell. The presented study is the first theoretical work regarding to the free vibrational analysis of a nanocomposite conical shell with an adhesive lap joint.