Distributed vibration control and identification of coupled elastic/piezoelectric shells: Theory and experiment

doi:10.1016/0888-3270(91)90043-5

Mechanical Systems and Signal Processing

Volume 5, Issue 3, May 1991, Pages 199-214

https://doi.org/10.1016/0888-3270(91)90043-5 Get rights and content

Abstract

In the recent development toward building large and flexible aerospace structural systems, active distributed vibration control and structural identification are of importance to their high-demanding performance. In this paper, a generic distributed parameter systems—a generic layered shell made of a passive elastic material sandwiched between two piezoelectric layers—is proposed and analysed. One of the coupled piezoelectric layers monitors the structural oscillation via the direct piezoelectric effect and the other controls the oscillation via the converse effect. Theories on distributed structural identification and control are derived. System dynamic equations and state equations of the coupled shell are formulated using Hamilton's principle and Kirchhoff-Love theory. Distributed structural identification and control of elastic structures are demonstrated by laboratory experiments.

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Citation Excerpt :
Concerning the effect of the piezoelectric patch there are many parameters to be considered. For a thorough review of those issues the reader is referred to the works by Saravanos [45] and Tzou [46,47]. The elements of above matrices are derived in the Appendix.
This paper presents an analytical method for the application of piezoelectric patches for the repair of cracked beams subjected to a moving mass. The beam equations of motion are obtained based on the Timoshenko beam theory by including the dynamic effect of a moving mass traveling along a vibrating path. The criterion used for the repair is altering the first natural frequency of the cracked beam towards that of the healthy beam using a piezoelectric patch. Conceptually, an external voltage is applied to actuate a piezoelectric patch bonded on the beam. This affects the closure of the crack so that the singularity induced by the crack tip will be decreased. The equations of motion are discretized by using the assumed modes method. The cracked beam is modeled as number of segments connected by two massless springs at the crack locations (one, extensional and the other, rotational). The relationships between any two spans can be obtained by considering the compatibility requirements on the crack section and on the ends of the piezoelectric patch. Using the analytical transfer matrix method, eigensolutions of the system can be calculated explicitly. Finally, numerical simulations are performed with respect to different conditions such as the moving load velocity. It is seen that when the piezoelectric patch is used, the maximum deflection of the cracked beam approaches maximum deflection of the healthy beam.
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Distributed vibration control and identification of coupled elastic/piezoelectric shells: Theory and experiment

Abstract

ASME Journal of Engineering for Gas Turbines and Power

AIAA Paper No. 88-2418

Journal of Sound and Vibration

Theoretical development of a layered thin shell with integrated internal distributed controllers

Vibrations of Shells and Plates

Integrated sensing and adaptive vibration suppression of distributed systems

Recent Development in Control of Nonlinear and Distributed Parameter Systems, ASME DSC