Hydrothermoelastic Stability of Functionally Graded Circular Cylindrical Shells Containing a Fluid

Abstract

The thermoelastic and hydroelastic stability of heated circular cylindrical shells made of functionally graded materials and interacting with an internal flow of an ideal compressible fluid was investigated. The effective properties of the material vary across the shell thickness according to a power law and depend on temperature. By way of a mathematical formulation the problem on dynamics the elastic structure, the classical theory of shells and the principle of virtual displacements are used. The radial temperature distribution is determined by solving the one-dimensional heat conduction equation. Behavior of the fluid is described using the potential theory. The corresponding wave equation, together with impermeability and boundary conditions, are transformed to a system of equations with the use of the Bubnov–Galerkin method. The solution of the problem, found by employing a semianalytical version of the finite-element method, is reduced to computing the complex eigenvalues of a coupled system of equations. A comparative analysis of the circular cylindrical shells is carried out at different boundary conditions and for different values of the consistency index of the functionally graded material. The effect of a thermal load on the critical speed of the loss of stability and of flow speed on the thermoelastic stability is estimated. It is shown that a flowing fluid has the greatest effect on the stability boundaries of heated cantilevered shells.