A contribution to the resolution of structural dynamics problems using frequency response function matrix

In structural dynamics, several problems are solved using formulations using frequency response function matrices. This work focuses on the exploitation and evaluation of these matrices. A technique of structural modifications, based on knowledge of the introduced modifications and the frequency response functions relating to the original structure, will first be described. Next, we will interest in the evaluation of the used flexibility matrices. These latter can be either calculated from a mathematical model or derived from experimental observations. In practice, only a limited number of columns of the dynamic flexibility matrix can be measured. A technique for completing this matrix is proposed after having described classical techniques. The idea is combined with a procedure which permits to choose, for numerical tests, an optimal placement of excitations. The proposed formulations are validated by a numerical example; and the effects of choice of number and positions of exciters, and the effect of damping on the results are discussed.