Suppression of nonlinear flutter of composite panels at supersonic speeds and elevated temperatures

Abstract

Coupled structure-electrical nonlinear finite element actuator and sensor equations of motion for flutter control are derived for composite panels with embedded piezoelectric layers subjected to aerodynamic, thermal loads and applied electric fields. The von Karman largedeflection strain-displacement relations, quasi-steady first-order piston theory aerodynamics, quasi-steady thermal stress theory and linear piezoelectricity theory are used. Following a modal transformation and reduction, a set of coupled nonlinear modal equations of motion with much smaller degrees-of-freedom is obtained for time domain simulation and controller design. Two controller designs, linear optimal and strain rate feedback, are presented. The controller design is based on the linearized modal equations while the numerical simulations are based upon the nonlinear modal equations. An optimal shape and location of piezoelectric actuator can be determined by using the norms of the optimal feedback control gains (NFCG). A self-sensing actuator is used in the strain rate feedback control design. The performance of panel flutter controller design can be evaluated by the maximum flutter-free dynamic pressures which is defined that the dynamic pressure a vehicle can fly without experiencing flutter with piezoelectric actuation. Numerical simulations show that the maximum flutterfree dynamic pressure can be increased as high as six times of the critical dynamic pressure by using the linear optimal control design. The panel flutter large amplitude limit-cycle motions as well as periodic and chaotic motions at moderate temperatures are shown to be able completely suppressed within the maximum flutter-free dynamic pressure. Flutter suppression on panels with different aspect ratios, boundary conditions, and thermal effects are also investigated. The results reveal that the piezoelectric actuators are effective in nonlinear panel flutter suppression.