A novel smeared method for investigating the free vibrations of sandwich conical shells with lattice cores

In this study, an analytical model was presented for investigating the free vibrations of sandwich conical shells with lattice cores. A novel smeared method was employed to determine the stiffness contribution of the stiffeners. In this approach, the lattice core was approximated with an equivalent composite conical shell. The stiffeners were considered as a beam which support the shear loads and bending moments in addition to the axial loads. For this purpose, the stiffness contribution due to the stiffeners was firstly determined through the forces and moments analysis of a unit cell and then superimposed with those of the inner and outer skins in order to obtain the stiffness parameters of the whole structure. The governing equations were deduced using the classical shell theory of Donnell type and Galerkin method. In order to validate the analytical results, a 3-D finite element model was also created using ABAQUS software. Comparison of the results, revealed good agreements between the two approaches and demonstrated that the proposed analytical model is qualified enough to investigate the free vibrational behavior of sandwich conical shells with lattice cores. Results given are novel and can be used as a benchmark for future studies.