Stabilization of Aeroelastic Instabilities of Panels Using Bifurcation Control With Piezoelectric Actuation

Aeroelastic instabilities of a panel may result in buckling (divergence) or flutter (Hopf bifurcation), when it is acted upon by induced aerodynamic and externally applied loads under supersonic/hypersonic environment in this paper. These instabilities are stabilized using nonlinear bifurcation control with piezoelectric actuation. The center manifold theory is used to extract subsystems which completely capture the bifurcation behavior of the original system near critical parameter values represented by sets of parametrised first-order differential equations with feedback control. The principle of normal form is used to simplify the nonlinear terms of the lower dimensional systems. The proposed controllers, which employ purely nonlinear state feedback, are used to modify the nonlinear characteristics of the post bifurcation limit sets by setting the amplitudes and rates of growth to the desired values. Numerical results show that the resulting closed-loop systems are effectively stabilized at the neighborhood of critical values.