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Vibration control using smart materials and response surface metamodels

Providakis Konstantinos, Voutetaki Maria-Styliani, P.N. Kontoni

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Summary

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) admittanceIn 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.

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