Modal analysis of a thin coupled composite shell

The results of the study of natural vibrations of a coupled shell of revolution are presented. The shell is a spherically biconical structure that has sharp bends in the mid-surface at the junction of different shapes. The material is a unidirectional fibrous carbon/epoxy composite. The shell structure, by its geometric shape and material parameterss, is an approximate model of the fairing of the launch vehicle. The modal analysis of a thin elastic shell is based on the use of a finite element model of a inhomogeneous shell and the application of a universal 3D finite element. The governing finite-element equations are constructed using a moment scheme of finite elements. The universal finite element is based on a standard isoparametric 3D finite element with polylinear shape functions for coordinates and displacements. It is characterized by the presence of additional variable parameters. Two nonclassical hypotheses are used to describe the features of the stress-strain state of a thin inhomogeneous shell. The static hypothesis of the constant of compressive stresses throughout the thickness of the shell layer is used. The kinematic hypothesis of deformed straight line is used, which is not necessarily normal to the mid-surface of the shell. The hypothesis allows us to join three-dimensional finite elements, keeping compatibility of the coordinates and displacements, and naturally modeling sharp bends. This phenomenon is inherent, for example, to folded and coupled (combined) shells. The performed modal analysis of the spherical biconical structure demonstrates the effectiveness of the method. Based on the universality of the approach, the method can be applied in studying the behavior of structures whose shell elements are made of different materials.