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18 April 2007 Tracking of transient displacements of plates with support excitations
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Abstract
The present paper is concerned with dynamic shape control of linear elastic plates under the action of transient forces, with prescribed time-dependent boundary conditions, and with given initial conditions. We consider anisotropic linear elastic plates. The following displacement tracking problem is treated: We ask for an additional distribution of actuation stresses such that the resulting displacements of the plates under consideration follow exactly some desired trajectories in every point and at every time instant. We present relations that must be satisfied for the actuation stresses in order that this goal of transient displacement tracking is reached. The actuation stresses we have in mind for enforcing tracking of transient displacements are induced by eigenstrains, such as thermal expansion strains or, more technologically important, piezoelectric parts of strain. Transient vibrations of circular plates in axi-symmetric bending are studied as an exemplary case. The vibrations are excited by support excitations. Actuation stresses are superimposed, which enforce the plate to track prescribed transient deflections. We present analytical solutions for the tracking of prescribed plate deflections with time-dependent support excitation. Coupling between electric and mechanical field is taken into account already at the level of plate theory. The analytical plate solutions are validated by Finite Element computations. Electromechanically coupled three-dimensional piezoelectric elements are used in these numerical calculations. Excellent coincidence between the analytical and the Finite Element computations is observed.
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Michael Krommer, Manfred Nader, and Hans Irschik "Tracking of transient displacements of plates with support excitations", Proc. SPIE 6523, Modeling, Signal Processing, and Control for Smart Structures 2007, 65230T (18 April 2007); https://doi.org/10.1117/12.715631
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