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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 86
Edited by: B.H.V. Topping
Paper 128

Vibration Control using Smart Piezoelectric Materials and Response Surface Metamodels

C.P. Providakis1, D.-P.N. Kontoni2 and M.E. Voutetaki1

1Division of Mechanics, Department of Applied Sciences, Technical University of Crete, Chania, Greece
2Department of Civil Engineering, Technological Educational Institute of Patras, Greece

Full Bibliographic Reference for this paper
C.P. Providakis, D.-P.N. Kontoni, M.E. Voutetaki, "Vibration Control using Smart Piezoelectric Materials and Response Surface Metamodels", in B.H.V. Topping, (Editor), "Proceedings of the Eleventh International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 128, 2007. doi:10.4203/ccp.86.128
Keywords: vibration control, electromechanical admittance, PZT, response surface metamodeling, design of experiment, finite elements.

The present work is an extension of previous works of the present authors [1,2] and is devoted to the development of a finite-element based methodology, for the vibration control of a cantilever plate simulated model, based on the numerical evaluation of the 'secondary' forces at lead zirconate titanate (PZT) patches locations through a statistical metamodeling technique. In the present case, a response surface metamodel is a reduced order polynomial model constructed by fitting a model to a set of points in the design space. The design space is a set of all possible simulations or experiments that interest the analyst. With design of experiment (DOE) techniques [3] we may generate fewer data points, by intelligently determine which simulation or physical experiment should be run when resources are scarce [4]. By using fewer data points the analyst may be able to efficiently investigate the response space to more successively determined topics of interest for his design.

Thus, response surface design of simulations approaches are employed in the present paper to reduce the computational effort by efficiently controlling the size of the design space. A finite element model of a cantilevel plate is addressed to demonstrate the process of using simulations to produce ('train') a response surface metamodel. Response surface metamodels are constructed using as input parameters the voltages applied at the boundary surfaces of distributed PZT actuators and as output features the (E/M) admittance signatures generated at the boundary surfaces of PZT sensors. These metamodels are then used in inverse formulation to predict the required values of voltages to produce desired signatures of (E/M) admittance

In the results a numerical cantilever plate example is demonstrated to illustrate the efficiency of the proposed method. The design consists of integrated PZT actuators and PZT admittance sensor patches attached to the vibrating host structure. An active vibration reduction scheme for solving the nonlinear optimization problem is proposed to obtain a desired damping level of the discretized structure, through matching the numerically computed from the response surface model procedure to the desired E/M admittance on the PZT admittance sensors. The results obtained were satisfactorily representative.

C.P. Providakis, D.-P.N. Kontoni and M.E. Voutetaki, "Development of an electromechanical admittance approach for application in vibration control of intelligent structures", Smart Materials and Structures, 16, 2007 doi:10.1088/0964-1726/16/2/005
C.P. Providakis, D.-P.N. Kontoni and M.E. Voutetaki, "FEM Modeling of electromechanical impedance for the analysis of smart damping treatments", Proceeding of 1st CISSE 2005, November 2005, pp. 129-134, 2005 doi:10.1007/1-4020-5261-8_22
D.C. Montgomery, "Design and analysis of experiments", 3rd edition, John Wiley & Sons, Inc., New York, 1991.
R.H. Myers and D.C Montgomery, "Response surface methodology", John Wiley & Sons, Inc., New York, 1995.

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