A LOW-COST PERTURBATION METHOD FOR THE ACCURATE ESTIMATION OF THE VIBRATION SPECTRUM FOR BEAM AND PLATE PROBLEMS

摘要

In the vibration control of flexible structures, boundary feedback schemes are employed in order to damp vibrations and achieve stabilization. A knowledge of the vibration spectrum is crucial to this process. We have developed a perturbation approach that, when combined with a standard asymptotic method, yields highly accurate spectral results for certain beam and plate problems. Here, we illustrate the method by applying it to the Kirchhoff thin plate problem, on rectangular domain. (Due to lack of space, we will present the simpler beam problems (see [1], [2]) at the conference, without including them here.).