SPATIALLY CONVOLVING WAVE-PROPAGATION SENSORS FOR STRUCTURAL CONTROL - PART I - ANALYTICAL DEVELOPMENT FOR ONE-DIMENSIONAL STRUCTURES

A novel method for sensing actual disturbance information which can pr opagate along one-dimensional structural waveguides is developed. The motivation for this work arises from the inability to realize most act ive wave control designs using output information from physical measur ements such as deflection, slope, curvature and internal shear force. Often the use of actual physical measurements leads to instability and suboptimal performance of certain active wave control loops. Thus, th ere is a desire to develop wave-propagation filters which can extract magnitude and direction of structural disturbances along dispersive an d non-dispersive members. In this work a distributed wave sensing sche me is reported which exploits the characterization of 1-dimensional st ructural motion in terms of traveling waves. This form of the solution is then combined with distributed sensors to convolve future and past measurements into a single temporal signal to overcome the problem of causality and spatial aliasing inherent in discrete sensor approaches . Thus, by imposing specific shapes to spatially convolving sensors, i t is possible to combine the output of these sensors with point measur ements to observe directional propagating wave components. Because thi s method requires some approximation of the spatial domain, there will be errors due to spatial discretization and truncation. This work add resses these issues and presents analytical results for one-dimensiona l structural elements.