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Modeling And Parameter Estimation For An Imperfectly Clamped Plate
 Computation and Control IV
, 1995
"... In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment t ..."
Abstract

Cited by 9 (9 self)
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In this paper, the modeling of boundary conditions for an imperfectly clamped circular plate is discussed. This model is derived under the assumption that there is some variation in both the boundary displacement and slope when the plate oscillates. To account for this oscillation, boundary moment terms, involving parameters to be estimated through fittodata techniques, are included in the model. The wellposedness of the model is demonstrated and appropriate approximation techniques are outlined. Finally, under natural assumptions for this model and approximation scheme, results leading to parameter convergence are given. 1 Introduction An important consideration in the modeling of structural and structural acoustic systems involves the determination of appropriate boundary conditions for the vibrating structure. In many applications, the clamped nature of the structure leads to the use of clamped or fixed boundary conditions, in which case, it is assumed that zero displacements an...
Experimental Confirmation of a PDEBased Approach to Design of Feedback Controls
 SIAM Journal on Control and Optimization
, 1997
"... Issues regarding the experimental implementation of PDEbased controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surfacemounted piezoceramic patches, the general techniques described here wil ..."
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Cited by 7 (6 self)
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Issues regarding the experimental implementation of PDEbased controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surfacemounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vectorvalued initial value problem. Optimal control theory is used to determine continuoustime voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented. 1
A Galerkin Method for Linear PDE Systems in Circular Geometries with Structural Acoustic Applications
 SIAM Journal on Scienti c Computing
"... A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximati ..."
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Cited by 5 (5 self)
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A Galerkin method for systems of PDE's in circular geometries is presented with motivating problems being drawn from structural, acoustic and structural acoustic applications. Depending upon the application under consideration, piecewise splines or Legendre polynomials are used when approximating the system dynamics with modi cations included to incorporate the analytic solution decay near the coordinate singularity. This provides an e cient method which retains its accuracy throughout the circular domain without degradation at the singularity. Because the problems under consideration are linear or weakly nonlinear with constant or piecewise constant coe cients, transform methods for the problems are not investigated. While the speci c method is developed for the 2D wave equation on a circular domain and the equation of transverse motion for a thin circular plate, examples demonstrating the extension of the techniques to a fully coupled structural acoustic system are used to illustrate the exibility of the method when approximating the dynamics of more complex systems.
The Estimation of Material and Patch Parameters in a PDEBased Circular Plate Model
 JOURNAL OF SOUND AND VIBRATION
, 1997
"... The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches 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 ..."
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Cited by 4 (3 self)
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The estimation of material and patch parameters for a system involving a circular plate, to which piezoceramic patches 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, exural rigidity, Poisson ratio and KelvinVoigt 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 physicallyderived 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.
Utilization of Coupling Effects in Compensator Design for Structural Acoustic Systems
, 1996
"... The quantification and utilization of coupling effects in a prototypical structural acoustic system are examined in this paper. In typical systems, the coupling mechanisms are manifested in two ways. The first leads to the transfer of energy from an ambient field to an adjacent structure and is ofte ..."
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Cited by 2 (2 self)
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The quantification and utilization of coupling effects in a prototypical structural acoustic system are examined in this paper. In typical systems, the coupling mechanisms are manifested in two ways. The first leads to the transfer of energy from an ambient field to an adjacent structure and is often responsible for exogenous structural excitation. The second involves the transfer of energy from the vibrating structure to an adjacent field. This is the source of structureborne noise and is ultimately the mechanism through which structural actuators are utilized to attenuate noise. The examples presented here demonstrate that in fully coupled systems, both mechanisms should be incorporated to accurately model system dynamics. The examples also illustrate advantages and limitations of compensators which utilize the accurate modeling of the structural coupling.
EExperimental Confirmation of a PDEBased Approach to Design of Feedback Controls
 SIAM Journal on Control and Optimization
, 1995
"... Issues regarding the experimental implementation of PDEbased controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surfacemounted piezoceramic patches, the general techniques described here wil ..."
Abstract
 Add to MetaCart
Issues regarding the experimental implementation of PDEbased controllers are discussed in this work. While the motivating application involves the reduction of vibration levels for a circular plate through excitation of surfacemounted piezoceramic patches, the general techniques described here will extend to a variety of applications. The initial step is the development of a PDE model which accurately captures the physics of the underlying process. This model is then discretized to yield a vectorvalued initial value problem. Optimal control theory is used to determine continuoustime voltages to the patches, and the approximations needed to facilitate discrete time implementation are addressed. Finally, experimental results demonstrating the control of both transient and steady state vibrations through these techniques are presented.