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Proceedings Paper

New constitutive model for vibrations of a beam with a piezoceramic patch actuator
Author(s): Ziya Koray Kusculuoglu; Behrooz Fallahi; Thomas J. Royston
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Paper Abstract

Piezoceramic wafer (patch) actuators have been used for the excitation and control of vibrations of beam and plate-like structures. Accurate constitutive modeling of the beam or plate with a piezo-patch actuator adhered to it is an important aspect to understanding this problem. In this paper, a multi-layered beam model is presented that predicts natural frequencies of the open-circuited beam-patch system. Both the beam and the patch actuator are modeled as Timoshenko beams. Constraints are introduced to ensure continuity of the axial and transverse displacements at the interface of the two Timoshenko beams. The cross section of each layer is allowed to take different values, which adds an additional degree of freedom to the system. The displacement equation of each Timoshenko beam is represented in a factored matrix form. This factored matrix form is utilized to develop a procedure for derivation of element mass and stiffness matrices using a symbolic manipulation program (MAPLE). MAPLE is used to form the global mass and stiffness matrices. An eigenvalue analysis is conducted and natural frequencies of the layered beam are calculated. To verify the model, experimental studies are performed to determine cantilevered beam-patch system natural frequencies. Better agreement between the theoretical and experimental results is observed than could be obtained using Euler's (thin) beam theory.

Paper Details

Date Published: 10 July 2002
PDF: 12 pages
Proc. SPIE 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, (10 July 2002); doi: 10.1117/12.475206
Show Author Affiliations
Ziya Koray Kusculuoglu, Univ. of Illinois/Chicago (United States)
Behrooz Fallahi, Northern Illinois Univ. (United States)
Thomas J. Royston, Univ. of Illinois/Chicago (United States)

Published in SPIE Proceedings Vol. 4693:
Smart Structures and Materials 2002: Modeling, Signal Processing, and Control
Vittal S. Rao, Editor(s)

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