Active Control of Periodic Structures

Abstract

Conventional passive periodic structures exhibit unique dynamic characteristics that make them act as mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called the “Pass Bands” and wave propagation is completely blocked within other frequency bands called the “Stop Bands.” In this paper, the emphasis is placed on providing the passive structures with active control capabilities in order to tune the spectral width and location of the pass and stop bands in response to the structural vibration. Apart from their unique filtering characteristics, the ability of periodic structures to transmit waves, from one location to another, within the pass bands can be greatly reduced when the ideal periodicity is disrupted resulting in the well-known phenomenon of “Localization.” In the case of passive structures, the aperiodicity (or the disorder) can result from unintentional material, geometric and manufacturing variability. However, in the case of active periodic structures the aperiodicity is intentionally introduced by proper tuning of the controllers of the individual substructure or cell. The theory governing the operation of this class of Active Periodic structures is introduced and numerical examples are presented to illustrate their tunable filtering and localization characteristics. The examples considered include periodic/aperiodic spring-mass systems controlled by piezoelectric actuators. The presented results emphasize the unique potential of the active periodic structures in controlling the wave propagation both in the spectral and spatial domains in an attempt to stop/confine the propagation of undesirable disturbances.