Protection of Continuous Structures Against Vibrations by Active Damping

Abstract

In this paper, we deal with the problem of active damping of vibrations of a continuous viscoelastic structure, and a general method of computation of the control system is developed. We define a mechanical model for this structure, the sources of perturbing vibrations, the control system, and different absorption criteria. The problem is set in an infinite dimension space, and an approximation problem is derived in n dimension spaces. Two methods of resolution are proposed for this approximation problem, and the solutions are compared. An example is given for the case of flexural vibrations in beams. Numerical results simulating the behavior of flexural vibrations in a rectangular plate, which is simply supported along the whole boundary, are presented for three different absorption criteria, thus permitting a quick evaluation of the comparative effectiveness of the chosen criteria.