Abstract In this paper, frequency behavior of the joined conical-conical panels is investigated while the structures are reinforced with uniform or functionally graded (FG) embedment of carbon nanotubes (CNTs). To consider both rotary inertia and in-plane effects, the formulation is developed upon FSDT considerations. By means of Hamilton’s principle the dynamic equations for two cones are derived. To attach two individual panels accurately, continuity conditions is performed at the junctions to satisfy the compatibility of displacements and stress resultants. After imposing simply supported boundary conditions at the straight edges, the set of governing equations are discretized meridionally on the basis of generalized differential quadrature (GDQ) technique. The proposed discretization approach is applicable for arbitrary boundary types imposed on the two curved edges at the initiating and terminating points of the structure. The validation of results is primarily assessed via some comparisons between present data and those previous researches in the favor of individual conical panels and also finite element model for joined conical-conical type. Thereafter, the significant roles of semi-vertex angle, embrace angle, CNT parameters and boundary types on the vibrational features are discussed.