Experimental Determination of the Mass Matrix Using a Constrained Least Squares Solution

摘要

The method uses a sum of weighted acceleration signals to experimentally predict the external force which excites a mechanical system. The predicted force is compared with the measured force and a constrained least squares solution is found for the optimum set of weights for the acceleration measurements. The weights calculated are equivalent to the effective mass of the system at the measurement locations. The method is sensitive to the bandwidth of the excitation and the spatial distribution of the measurement locations. For this reason the weights are calculated as a function of bandwidth and an error measure is calculated at each bandwidth to help evaluate the optimum bandwidth for a particular set of measurements. The use of constraints is strongly recommended to achieve a set of physically realizable weights. Several examples are given to demonstrate the technique. The primary use of the technique to date has been to estimate the dynamic forces acting on non-rigid bodies. (ERA citation 12:020810)