Suppression of nonlinear panel flutter at supersonic speeds and elevated temperatures

Abstract

Coupled structure-electrical nonlinear panel flutter equations of motion are derived using the finite element method for composite panels with embedded piezoelectric layers subjected to thermal loads. The von Karman large-deflection strain-displacement relations, quasisteady first-order piston theory aerodynamics, quasisteady thermal stress theory, and linear piezoelectricity theory are used. Following a modal transformation and reduction, a set of coupled nonlinear modal equations of motion is obtained. By using the linear optimal control design for the linearized modal equations, an optimal shape and location of piezoelectric actuators can be determined. Numerical simulations based on the nonlinear modal equations show that the maximum flutter-free dynamic pressure with the linear optimal control can be increased as high as six times of the critical dynamic pressure. The panel's large-amplitude limit-cycle motions, as well as periodic and chaotic motions at moderate temperatures, are shown to be completely suppressed within the maximum flutter-free dynamic pressure region. Flutter suppression on composite panels with different aspect ratios, boundary conditions, and thermal effects are also studied. The results reveal that piezoelectric actuators are effective in nonlinear panel flutter suppression.