Ralph C. Smith

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Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system under consideration is a thin cylindrical shell with surface-mounted piezoceramic actua-tors. Donnell-Mushtari equations, modiied to include Kelvin-Voigt damping, are used to(More)
A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Fl ugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include(More)
This paper addresses the development of distributed models for the piezoceramic positioning mechanisms employed in current atomic force microscope designs. Two common con gurations for positioning mechanisms employ stacked actuators utilizing d33 motion and piezoceramic shells utilizing a d31 motion. In both cases, the relation between input voltages and(More)
A spline-based method for approximating thin shell dynamics is presented here. While the method is developed in the context of the Donnell-Mushtari thin shell equations, it can be easily extended to the Byrne-Fl ugge-Lur'ye equations or other models for shells of revolution as warranted by applications. The primary requirements for the method include(More)
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(More)
This paper addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed(More)
This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or(More)