Nonlinear viscoelastic heated panel flutter with aerodynamic loading exerted on both surfaces

A nonlinear flutter analysis of viscoelastic heated panels with aerodynamic loading exerting on its both surfaces is presented. The aeroelastic motion equations of such panels can be formulated by using the von Karman large deflection plate theory and piston aerodynamics theory, while the thermal induced membrane force and the Kelvin type viscoelastic damping are taken into account. By using Galerkin method, the continuous partial differential motion equation can be transformed into a set of nonlinear ordinary differential equations with coupled aerodynamic stiffness and aerodynamic/viscoelastic damping terms. By applying Routh-Hurwits criterion, the static divergence stability (buckling) boundary and the elastic/viscoelastic flutter stability boundaries of the panel initial flat equilibrium can be obtained. The obtained linear stability results revealed that the system dynamic bifurcation boundary can be significantly affected by the additive structural viscoelastic damping, and such effect can be enhanced by increasing the dynamic pressure of the external flow exerting on either single panel surface. Additionally, the sum of dynamic pressures exerting on both panel surfaces functions as the dynamic pressure exerting on either single pane surface. The corresponding nonlinear viscoelastic response can be simulated by using the fourth order Runge-Kutta numerical integration method, thus the system bifurcation diagrams with varying dynamic pressures can be obtained. The results revealed that the additive viscoelastic damping may exhibit the paradoxical effect on the system dynamic stability with lower temperature elevation, while the post flutter chaotic motions can be regulated as periodic motions with reduced amplitudes. However, with a higher temperature elevation, the effect of the additive viscoelastic damping can be always stabilizing to both the aeroelastic system stability and the post flutter chaotic motions.