Date of Award
Doctor of Philosophy (PhD)
Mechanical & Aerospace Engineering
Carl E. Gray, Jr.
John E. Kroll
Nonlinear coupled finite element equations of motion are derived for composite panels with embedded piezoelectric layers subjected to aerodynamic, thermal loads and applied electric fields. The nonlinear equations of motion describe the coupling between a structure and an electrical network through the piezoelectric effect. The von Karman large-deflection strain-displacement relations, quasi-steady first-order piston theory aerodynamics, quasi-steady thermal stress theory and linear piezoelectricity theory are used to formulate the nonlinear coupled panel flutter finite element equations of motion in nodal displacements. The governing equations, which are referred to actuator and sensor equations, form a basis for piezoelectric actuation and sensing. Following a modal transformation and reduction in structural degrees-of-freedom, a set of nonlinear coupled modal equations of motion with much smaller degrees-of-freedom is derived. The modal equations are then employed for time domain simulation and controller design.
A self-sensing piezoelectric actuator is used as a sensor and actuator simultaneously. An optimal control design is developed based on the linearized modal equations while the numerical simulations are obtained based upon the nonlinear modal equations. An optimal shape and location of small-size or patched piezoelectric actuators are determined by using the norms of the optimal feedback control gains (NFCG). The strain rate feedback control design is also investigated due to its more practical usage. The strain rate signal is detected from piezoelectric sensor, and then amplified and fed back to the same piece of element to actively suppress the panel limit-cycle oscillations. The shape and location of the self-sensing actuator are still obtained based on the NFCG.
The nonlinear flutter characteristics of composite panels with embedded piezoelectric elements at elevated temperatures are first determined from the actuator equation without activating the piezoelectric material. The performance of panel flutter controller design can be evaluated by the value of maximum flutter-free dynamic pressures which is defined that a flight vehicle can fly without experiencing flutter with piezoelectric actuation. Numerical simulations show that the maximum flutter-free 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 to be completely suppressed within the maximum flutter-free dynamic pressure. Panels with different aspect ratios, boundary conditions, and thermal effects on flutter suppression are also investigated. The results reveal that the piezoelectric actuators are effective in nonlinear panel flutter suppression.
Zhou, Run C..
"Finite Element Analysis for Nonlinear Flutter Suppression of Composite Panels at Elevated Temperatures Using Piezoelectric Materials"
(1994). Doctor of Philosophy (PhD), Dissertation, Mechanical & Aerospace Engineering, Old Dominion University, DOI: 10.25777/9kak-pp41