Force identification using the concept of displacement transmissibility

This paper presents a method for the identification of loads applied to a structure, using the concept of response transmissibility. The authors propose to perform the identification of the loads in two steps: the first identifies the number of forces and their location using an algorithm of “search for number and position”, based on the response transmissibility concept; the second step consists of the reconstruction of the load vector. To carry out the first step, a complete description of the structure in terms of degrees-of-freedom will be assumed and a numerical model (usually a finite element one) is built. In order to perform the identification of the number of forces and their location, the proposed algorithm combines both the dynamic responses experimentally measured and the transmissibility matrices obtained from the numerical model. The regeneration of the load vector is achieved during the second step, once the number of loads and their location are known, combining the dynamic responses obtained experimentally with the transmissibility matrix from the numerical model. A series of simulated and experimental results on a free–free beam are presented to illustrate the procedure.