Finite differencing methods for the measurement of dynamic bending strain

Finite differencing formulations for dynamic bending strain are used to def ine measurement methods for autospectral, spatial and time history predicti ons of dynamic bending strain. These measurement methods provide prediction s of dynamic bending strain in both nearfield and farfield regions from dis crete measurements of displacement, velocity or acceleration. The differenc ing formulations considered use either three- or four-point finite differen cing requiring simultaneous measurements at three or four positions, respec tively. The number of simultaneous measurements required is reduced to two if the response is stationary and frequency response methods are used. The main limitation of these differencing methods is that the spatial extent of the measurement array precludes the prediction of dynamic bending strain a t locations such as a clamped boundary where dynamic strain is usually larg est. Experimental results are presented demonstrating autospectral, spatial and time history predictions of dynamic strain in both nearfield and farfi eld regions, and sources of errors in predictions are discussed. As structu ral intensity is given by the product of dynamic stress and velocity, the w ork presented here is also of interest for structural intensity measurement s, particularly in nearfield regions when evanescent waves cannot be neglec ted. (C) 1999 Academic Press.