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Placement of Multiple Piezo Patch Sensors and Actuators for a Cantilever Beam to Maximize Frequencies and Frequency Gaps

Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA

J.C. Bruch, JR

Department of Mechanical Engineering and Department of Mathematics, University of California, Santa Barbara, CA 93106, USA, jcb{at}engineering.ucsb.edu

J.M. Sloss

Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

S. Adali

School of Mechanical Engineering, University of KwaZulu-Natal, Durban, South Africa

I.S. Sadek

Department of Mathematics and Statistics, American University of Sharjah, United Arab Emirates

Active vibration control is implemented using multiple piezoelectric actuators and sensors bonded to the top and bottom surfaces of a cantilever beam. The control is exercised using closed-loop displacement feedback. The objective of the study is to determine the optimal locations of patch actuators and sensors such that the fundamental frequency or the frequency gap between higher frequencies of the beam is maximized. Maximizing the fundamental frequency is useful to avoid resonance when the excitation frequency is less than the fundamental frequency. Alternatively, the excitation frequency can also be placed in between two higher order frequencies and the difference between the two higher order frequencies can be maximized. In the present study the fundamental frequency and the frequency gaps between the higher order frequencies are investigated with respect to actuator and sensor locations with a view towards determining their optimal locations for largest frequency gaps. The locations of the piezo patches to maximize first, second and third frequencies are also given. The differential equation governing the vibrations of a feedback controlled beam/piezo patch system is solved using an integral equation approach. The numerical results are given for various patch combinations and the optimal locations of the actuators and the sensors are determined. It is observed that the optimal locations of the piezo patches depend on the specific frequency gap as well as the patch configurations.

Key Words: Piezoelectric actuators and sensors • displacement feedback control • smart structures • maximum frequency gaps • optimal piezo patch locations

This version was published on May 1, 2009

Journal of Vibration and Control, Vol. 15, No. 5, 643-670 (2009)
DOI: 10.1177/1077546308094247


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