A Comparison of Shaped Piezoelectric Actuators for Divergence Control

Abstract

The characteristics and effectiveness of shaped piezo-actuators for use in controlling the divergence of a simplified forward swept wing model are analytically investigated. The forward swept wing is modeled as a simplified cantilever beam with surface mounted piezo-actuators on the upper surface of the beam. A constant electric field is applied to the actuator inducing a constant external force on the wing, and the effects of actuator location, size, thickness, and shape are evaluated using the principle of virtual work by maximizing the modal amplitude of the first bending mode. For control purposes, strain at the wing root is used as an error signal to minimize the beam deflection. Results suggest that the optimum actuator size should span the entire wing. The required actuator thickness for divergence control decreases with increasing airspeed due to the effectiveness softening of the wing in the presence of air loads. A uniform rectangular actuator is more effective for controlling divergence; however, a linearly shaped actutor is more efficient from the standpoint of control effectiveness per actuator weight. Application is currently limited by the large thicknesses and applied voltages required by the actuators to achieve effective divergence control. However, this investigation suggests that, because of the softening of the wing near divergence, only a small control effort is required to deform the wing thus allowing the airstream to act as the power source for control actuation.

Get full access to this article

View all access options for this article.

References

Bailey, T.B. and J.E. Hubbard , 1985, "Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam", Journal of Guidance and Control , 8(5):605-611.

Burke, S.E. and J.E. Hubbard. 1987. "Active Vibration Control of a Simply Supported Beam Using a Spatially Distributed Actuator", IEEE Control Systems Magazine, pp. 25-30.

Kim, S.J. and J.D. Jones. 1990. "Optimal Design of Piezo-Actuators for Active Noise and Vibration Control", AIAA Paper 90-3925.

Kim, S.J. and J.D. Jones. 1991. "Optimization of Piezo-Actuator/ Substructure Coupling for Active Noise and Vibration Control", Proceedings of Recent Advances in Active Noise and Vibration Control, Blacksburg, VA, pp. 78-91.

Kim, S.J. and J.D. Jones. 1991. 'A Study of Actuators for Active Control of Distributed Elastic Systems", Proceedings of NOISE-CON 91

Kuethe, A.M. and C.Y. Chow. 1976. Foundations of Aerodynamics: Bases of Aerodynamic Design, 3rd ed., New York: John Wiley and Sons, Inc.

Meirovitch, L. 1986. Elements of Vibration Analysis, 2nd ed., New York: McGraw-Hill, Inc.

Noll, T.E. , F.E. Eastep and R.A. Calico. 1984. 'Active Suppression of Aeroelastic Instabilities on a Forward Swept Wing", Journal of Aircraf t, 21(3):202-208.

Weisshaar, T.A. 1983. "Fundamentals of Static and Dynamic Aeroelasticity", Course Text, Purdue University.

10.

Weisshaar, T.A. and S.M. Ehlers. 1991. "Adaptive Static and Dynamic Aeroelastic Design", Presented at the 1991 International Forum on Aeroelasticity and Structural Dynamics, Aachen, Germany, June 6.