Free Vibration Behavior of Three-skin Conical Shells with Composite Lattice Core Based on Semi-analytical and Finite Element Methods

In this paper, free vibration behavior of three-skin conical shells with arbitrary boundary conditions is studied based on semi-analytical and numerical methods. The three-layer shell consists of identical outer-inner composite face sheets and a lattice core with regular hexagonal cells made of composite helical and circumferential ribs. For this purpose, t, the dynamic equations along with the boundary conditions of such sandwich shells are derived using the equivalent stiffness method, Donnell’s classic shell theory, and Hamilton’s principle. The frequency equation is presented by solving the integral form of these governing equations based on the Galerkin method. The vibration mode shapes in the form of forward or backward waves in the circumferential direction and standing waves in the direction of the cone length (Euler-Bernoulli beam modal functions) are used in order to obtain natural frequencies. Also, ABAQUS FE simulations are carried out to verify the vibration behavior predicted by the Galerkin solution method. Finally, parametric studies are performed to investigate the effects of geometric dimensions and boundary conditions on the response quantities. Numerical results show that there is a very good agreement between the natural frequencies obtained by Galerkin and ABAQUS FE methods (i.e., the maximum difference in the results is less than 10%). Also, the effects of face sheet thickness and the rib width on the natural frequencies of three-layer composite lattice conical shell with different supports are significant.