Boundary Control of Beams
Distributed control of a PVDF laminated cantilever beam was studied in this chapter. The laminated cantilever beam had a distributed piezoelectric sensor and a distributed actuator; both were surface bonded. Closed-loop feedback controls of the beam using the displacement and velocity signals were respectively evaluated and results compared. The results showed that the displacement feedback controls were insignificant and the velocity feedback controls were much more effective. In the velocity feedback control, the system damping increased to an ultimate value and then gradually dropped down as the feedback gain continuously increased. This was caused by the additional constraint imposed by the boundary control moment at the free-end. The free-end boundary condition was gradually changing to a sliding-roller boundary condition as proved by finite element analyses and laboratory experiments.
- Harris, C.M. and Crede, C.E., 1976, Shock and Vibration Handbook, 2nd Ed., McGraw-Hill, 1976.Google Scholar
- Johnson, D., 1990, An Experimental Study on Feedback Control of a Piezoelectric Laminated Cantilever Beam, NSF–REU Report, Department of Mechanical Engr., University of Kentucky, August 1990.Google Scholar
- Liu, K.J, 1989, A Theoretical Study on Distributed Active Vibration Suppression of Mechanical Systems with Integrated distributed Piezoelectric Sensor and Actuator, MSME Thesis, Dept. of Mech. Engr., Univ. of Kentucky, 08/1989.Google Scholar
- Tzou, H.S., Johnson, D. and Liu, K.J., “Boundary Transition and Nonlinear Control of Distributed Systems,” Stability, Vibration, and Control of Structures, Vol.1: Wave Motion, Intelligent Structures, and Nonlinear Mechanics, A. Guran and D.J Inman, (Editors), pp. 163-193, World Scientific Publisher, 1994.Google Scholar
- Tzou, H.S., Johnson, D. and Liu, K.J., “Damping Behavior of Cantilever Structronic Systems with Boundary Control,” ASME Transactions, Journal of Vibration & Acoustics, Vol.121, pp. 402–407, July 1999.Google Scholar
- Zaveri, K., Modal Analysis of Large Structures – Multi–Exciter Systems, Bruel & Kjaer Technical Review, 1985.Google Scholar