6 - Active Control of Vibration in Structures

Abstract

This chapter reviews a number of different approaches to the active control of mechanical vibration in structures. The structure is governed by a partial differential equation rather than an ordinary differential equation. In other words, the structure is to be distributed rather than having “lumped” springs, masses and dampers. There are a number of ways of describing the motion of such a structure, each of which is consistent with the governing partial differential equation. One way of expressing the velocity distribution over an entire structure, for example, is in terms of the sum of the contributions from a number of structural modes. Another approach is to describe the motion in terms of the amplitudes of a number of different types of mechanical waves in the structure. Both of these representations and their relation to each other are discussed. The parameters to describe the motion of the structure depend very much on the geometry of the structure, its boundary conditions and the frequency of excitation. These two descriptions of the motion of a distributed structure lead to two rather different approaches to active control.