Nanocomposite and sandwich plates with a honeycomb core are characterized by a high strength-to-mass ratio. Thus, such a solution is very promising for the aerospace and aircraft industry. This paper represents a mathematical model for a nanocomposite functionally gradient cylindrical shell interacting with a supersonic gas flow. To obtain such a model, the predetermined form method is used. An ordinary nonlinear differential equations system is obtained to describe the self-sustained vibrations of the shell. The structure model is developed using nonlinear strain-displacement relationships to analyze self-sustained vibrations. A model describing self-sustained vibrations of a sandwich conical shell interacting with a supersonic gas flow is obtained. The core layer of the shell is an FDM-manufactured honeycomb. The stress state of the structure is analyzed using the highorder shear deformations theory. Each layer’s stress state is described by five coordinates which are the three displacements of the midsurface and two angles of rotation of the normal to the midsurface. At the layers’ junctions, the border conditions of displacements’ continuity are used. To analyze self-sustained vibrations, the nonlinear strain-displacement relationships are utilized. Using the normal modes technique allows us to obtain a nonlinear autonomous dynamic system. Results of numerical simulations of self-sustained vibrations are provided. They are obtained by solving a nonlinear boundary value problem for the ordinary differential equations system using shooting and continuation techniques. Experimental investigation of sandwich plates’ fatigue with honeycomb core is considered. A method of fatigue testing of sandwich plates is described. The testing results are presented using S-N diagrams.
