Vorticity characteristics of the vibrational intensity field in an actively controlled thin plate

Abstract

<jats:p>It is the purpose of this paper to elucidate quantitatively the generation mechanism of structural intensity patterns induced in an actively controlled thin plate vibrating harmonically in a steady state. Particular emphasis is placed upon the vortex-type intensity response pattern, which has a potential for confining the vibration power into a specific area of the plate. First, a formulation is developed for minimizing structural kinetic energy with active vibration control on a planar structure. The results are used to develop expressions for vibration intensity in the controlled structure, which are then used as the basis for investigating intensity distributions in an actively controlled rectangular panel excited harmonically. It is shown that when a vortex pattern exists, the plate response is dominated by two vibration modes. The vibration intensity field associated with these two vibration modes is defined, and both an approximate energy stream function and a vortex function are derived. It is shown that the vibration intensity vector is tangential to the contour of the approximate energy stream function, and that fundamental characteristics such as the number and direction of the vortices can be determined from the approximate energy stream function. Finally, it is found that the major vortex with multiple subvortices inside appearing in the structural intensity field is a derivative or an image of subvortices, and does not carry the characteristics of the vortex from the viewpoint of fluid dynamics.</jats:p>