Nonlinear Response of Functionally Graded Panels with stiffeners in Supersonic Flow

This paper aims to study the nonlinear response of a stiffened functionally graded plate in supersonic flow. To model the geometrically nonlinear behavior of the stiffened panel, the von Karman large deflection plate theory is employed and the stiffener which is placed on the plate in different positions is modeled by using the Euler-Bernoulli beam theory. These two structural models are coupled to each other via a pair of action reaction forces. The plate is in the supersonic regime and the quasi-steady first order piston theory is utilized to estimate the aerodynamic pressure induced by the supersonic flow. By using the Hamilton’s principle the nonlinear partial differential equations of the stiffened panel are obtained. These partial differential equations are converted to ordinary differential equations by using the Galerkin’s method which then solved by numerical integration. It is found that by using the stiffeners, the onset of flutter and also the limit cycle oscillation amplitude of the system changes dramatically and the rate of this change extremely depends on the volume fraction index of the plate made of functionally graded materials and the plate aspect ratio. Moreover, the effect of number of stiffeners on the aeroelastic behavior of FG panel is studied and it is clarified that by increasing the number of stiffeners, the flutter boundary increases.