Investigation of panel flutter of functionally graded circular cylindrical shells

The paper is devoted to the analysis of panel flutter of functionally graded cylindrical shells in a supersonic gas flow. The aerodynamic pressure is calculated based on the quasi-static aerodynamic theory. The inner surface of the structure is made of aluminum and the outer surface is made of zirconium dioxide. The effective properties of the material continuously changes through the shell thickness with radial coordinate according to the power law. The geometric and physical relations and the equations of motion written in the framework of the classical shell theory are reduced to the system of eight ordinary differential equations for new unknown quantities. A solution of the problem is found by integrating the obtained system of equations by the Godunov’s orthogonal marching method at each step of the iterative procedure generally used in Muller’s method to evaluate complex eigenvalues. The reliability of the method was assessed by comparing the obtained results with the available experimental and theoretical data. The paper presents the results of numerical experiments carried out to estimate the effect of the properties of functionally graded materials on the stability boundary of circular cylindrical shells for different combinations of boundary conditions and linear dimensions. It has been found that the type of loss of stability is defined not only by geometrical characteristics of the structure and boundary conditions but also by given composition of the functionally graded material. It has been shown that an effective control of critical aerodynamic loading can be executed only for shells with certain geometrical dimensions.