Free vibrational characteristics of GNP-reinforced joined conical–conical​ shells with different boundary conditions

Abstract

The current study is devoted to analyzing the free vibration characteristics of joined conical–conical shells made of epoxy enriched with graphene nanoplatelets (GNPs). The mathematical modeling of the shell is performed utilizing the first-order shear deformation theory (FSDT) to incorporate the effects of shear deformations and rotational inertia. The effective modulus of elasticity is estimated using the Halpin–Tsai model and other effective mechanical properties are evaluated utilizing the rule of mixture. The set of the governing equations, associated compatibility conditions at the intersection of two shell segments, and boundary conditions are obtained using Hamilton’s principle. These equations are solved in the circumferential direction using trigonometric functions and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). Through this semi-analytical solution, the natural frequencies of the shell and corresponding mode shapes are determined and the validity of the presented solution is confirmed via the benchmark results reported by the other authors. The effects of various parameters on the natural frequencies of the GNP-reinforced joined conical–conical​ shells are examined including the circumferential wave number, the boundary conditions, the length-to-small radius ratio and semi-vertex angle in two shell segments, thickness-to-small radius ratio of the shell, and also mass fraction, aspect ratio, and dispersion pattern of the GNPs.