Oracle separation of complexity classes and lower bounds for perceptrons solving separation problems

Abstract

Active periodic structures exhibit unique dynamic characteristics that make them act as tunable 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'. The spectral width of these bands can be tuned according to the nature of the external excitation.In this paper, the emphasis is placed on developing a new class of these periodic structures called active periodic struts (APS) which can be used to support gearbox systems on the airframes of helicopters. When designed properly the APS can stop the propagation of vibration from the gearbox to the airframe within critical frequency bands and consequently minimize the effects of transmission of undesirable vibration and sound radiation to the helicopter cabin. The theory governing the operation of this class of APS is presented and their tunable filtering characteristics are demonstrated experimentally as a function of their design parameters.The presented concept of the APS can be easily employed in many applications to control the wave propagation and the force transmission in an attempt to stop/confine the propagation of undesirable disturbances.