Linear Vibrations Analysis of a Composite Sandwich Conical Shell Manufactured by Additive Technologies

Abstract

The sandwich conical shell with elastic honeycomb structure, which is studied in this paper, is manufactured by additive technologies and has three layers. The honeycomb structure is made of ULTEM material, and the upper and lower face layers of the structures are made of carbon fiber. Each layer of the structures is an orthotropic material and satisfies Hooke's law. Thanks to the homogenization procedure using the finite element method, we will obtain an equivalent orthotropic medium instead of the honeycomb structure. The elastic properties of this medium satisfy Hooke's law. The modified high-order shear theory is used to model the deformation of the structures. The deformations of each layer of the structures are described by five variables, which include three projections of the displacements of the median surface and two angles of rotation of the normal to the median surface. To calculate the displacements of the layers, boundary conditions for stresses and boundary conditions that describe the continuity of displacements at the layers’ boundaries are used. The vibrations of a three-layer sandwich shell are expanded into basis functions that satisfy the kinematic boundary conditions. The Rayleigh-Ritz method is used to study the vibrations. The vibration parameters of structures are calculated from the eigenvalue problem. To verify the obtained results, the natural frequencies are compared with the data of finite element modeling. As follows from the calculations, the natural frequencies obtained by the Rayleigh-Ritz method and the finite element method are close. The spectrum of natural frequencies is very dense. The minimum natural frequency of vibrations is observed when the number of waves in the circular direction is equal to one.