Measurement of time-dependent external moments and forces by the sum of weighted accelerations technique

Force identification using a sum of weighted accelerations technique (SWAT) is developed for measurement of externally applied force and moment which dynamically excite a structural system. Mode shape coefficients, from a free-body modal characterization, are used to determine two sets of weighting factors which, when used in the SWAT, eliminate the free-body vibrational response. One set of weighting factors, having the units of mass, are used in the SWAT measurement of the resultant force vector. The second set of weighting factors, having the units of first-moment-of-mass, are calculated to measure the moment acting at the center of mass of the external force with a similar sum of weighted accelerations. The theory for determining the force and moment vectors is developed in this paper. We illustrate the technique through the analysis of a simple beam and a rectangular plate. We then demonstrate the analytical predictions with the laboratory testing of softly suspended structures.