Wave propagation sensors for structural control

This research develops novel methods for sensing actual disturbance information which can propagate along one-dimensional structural waveguides. The motivation for this work arises from the inability to realize most active wave control designs using output information from physical measurements such as deflection, slope, curvature and internal shear force. Often the use of actual physical measurements leads to instability and sub-optimal performance of certain active wave control loops. Thus, there is a desire to develop wave-component filters which can extract magnitude and direction of structural disturbances along dispersive and non-dispersive members. In this work two sensing schemes are reported. In each case, the solution of the partial differential equation which characterizes the dynamics of a one-dimensional structural members is written in terms of travelling waves. This form of the solution is then exploited in the first method to combine a sequence of spatially discrete measurements through a frequency dependent decoupling matrix to yield magnitude and direction of travelling wave components. This approach works well for non-dispersive members, however, for dispersive members a low order approximation to the frequency dependent decoupling matrix is not guaranteed to be causal. A further limitation is the introduction of spatial aliasing. In the second approach, a spatially distributed sensor which convolves past and future measurements along a member into a single temporal signal overcomes these problems of causality and aliasing for a dispersive member. Here mapping between the temporal and spatial domains permits acausal temporal filters to be realized by spatial filters. Thus, by imposing specific shapes to spatially distributed sensors, it is possible to combine the output of these sensors with point measurements to observe various propagating wave components. Because both methods require some approximation of the spatial domain, there will be errors due to spatial discretization and truncation. This work addresses these issues and presents some preliminary experimental results to confirm analytical examples. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)