Supersonic flutter prediction of functionally graded conical shells

Aero-thermoelastic analysis of a simply supported functionally graded truncated conical shell subjected to supersonic air flow is performed to predict the flutter boundaries. The temperature-dependent properties of the FG shell are assumed to be graded through the thickness according to a simple rule of mixture and power-law function of volume fractions of material constituents. Through the thickness steady-state heat conduction is considered for thermal analysis. To perform the stability analysis, the general nonlinear equations of motion are first derived using the classical Love’s shell theory and the von Karman–Donnell-type of kinematic nonlinearity together with the linearized first-order piston theory for aerodynamic loading. Then the nonlinear equations of motion are linearized to obtain the linear equilibrium and aeroelastic equations. The equilibrium equations are solved using power series method to obtain the initial stresses induced by aerodynamic and thermal loadings. The results are then used as an input to the aeroelastic stability equations which are finally solved with the generalized Galerkin method. The flutter boundaries are obtained for the FG conical shells with different semi-vertex cone angles, different temperature distributions, and different volume fraction indices.