New constitutive model for vibrations of a beam with a piezoceramic patch actuator

Ziya Koray Kusculuoglu; Behrooz Fallahi; Thomas J. Royston

doi:10.1117/12.475206

10 July 2002 New constitutive model for vibrations of a beam with a piezoceramic patch actuator

Ziya Koray Kusculuoglu, Behrooz Fallahi, Thomas J. Royston

Proceedings Volume 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control; (2002) https://doi.org/10.1117/12.475206
Event: SPIE's 9th Annual International Symposium on Smart Structures and Materials, 2002, San Diego, California, United States

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.

Citation Download Citation

Ziya Koray Kusculuoglu, Behrooz Fallahi, and Thomas J. Royston "New constitutive model for vibrations of a beam with a piezoceramic patch actuator", Proc. SPIE 4693, Smart Structures and Materials 2002: Modeling, Signal Processing, and Control, (10 July 2002); https://doi.org/10.1117/12.475206

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