Dynamic Instability of a Three-Layer Conical Shell with Honeycomb Structure Made by Additive Technologies

A mathematical model of the dynamic instability of a three-layer conical shells with honeycomb structure made using additive technologies has been obtained. Dynamic instability is recognized as the interaction of the shell with a supersonic gas flow. The middle layer of the structure is a honeycomb that is homogenized into an orthotropic homogeneous medium. The top and bottom layers of the shell are made of carbon fiber. The vibrations of the structure are described by fifteen unknowns. Each layer of the structure is described by five unknowns: three projections of displacements of the layer middle surface and two rotation angles of the normal of the layer middle surface. The high-order shear theory is used to describe the deformation state of the structure. The relation between stresses and strains is expressed by a power expansion in the transverse coordinate up to its cubic terms. To obtain a system of ordinary differential equations describing dynamic instability, the method of given forms is used. To assess the dynamic instability, characteristic indicators are calculated by solving the generalized problem of eigenvalues. The natural vibrations of the structure are studied by