The estimation of material and patch parameters in a PDE-based circular plate model

Abstract The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic are bonded, is considered. A partial differential equation (PDE) model for the thin circular plate is used with the passive and active contributions from the patches included in the internal and external bending moments. This model contains piecewise constant parameters describing the density, flexural rigidity, Poisson ratio and Kelvin-Voigt damping for the system, as well as patch constants and a coefficient for viscous air damping. Examples demonstrating the estimation of these parameters with experimental acceleration data and a variety of inputs to the experimental plate are presented. By using a physically derived PDE model to describe the system, parameter sets consistent across experiments are obtained, even when phenomena such as damping due to electric circuits affect the system dynamics.

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