Load Identification Through Structural Modification

Abstract

A load identification problem in structural dynamics has in general multiple solutions. Therefore, additional information, such as the locations of the unknown forces, has to be supplied a priori in order to make a unique solution possible. The present study focuses on cases where such information is not readily available. First, it is shown that, given (tentatively) the spatial shape and position of the load, the Betti reciprocal theorem together with a reference load case may be used to calculate the required magnitude of the unknown load so that the response fits the measurement data as well as possible in a defined sense. In this manner a large number of trial loads may be evaluated with only little computational effort, since no equation system needs to be solved. Second, the situation where several loads, each reproducing the same measurement data, have been identified is investigated. An optimization problem with added discrete masses as design variables is suggested. The solution of this problem yields a structure such that each set of responses generated by each one of the previously identified loads is clearly distinguishable at the transducer positions. The proposed method is a novel approach and should be useful in the load identification problem for an existing structure. A numerical example illustrates the application of the method.