Inverse approach for load identification in structural dynamics

Goal of this thesis is the identification of the external force field in the frequency domain at low and high frequency range. At low frequency the solution of the investigated problem is carried out by modal analysis. Input-Output relationship between force and velocity is defined by using the Frequency Response Function (FRF) calculated both by modal expansion and measurements. The identification procedure is performed for deterministic and random loads. By considering deterministic loads, the solution of this problem is obtained by the inversion of the FRF, that implies to deal with an ill-conditioning problem. Since it can be shown that the ill-conditioning of FRF matrix is strictly related to the selection of the DoF considered on the structure, a procedure to investigate the best experimental setup that allows to identify the deterministic load is proposed, by using classical regularization techniques based on the Singular Values Decomposition (SVD). Then, with the same purpose the relationship between the modes contribute and the ill-conditioning of the problem is investigated. Different input-output relationships from that used in the case of deterministic loads are adopted when random loads are considered. In fact, they are deduced by a probabilistic approach also for the solution of the direct problem. The results obtained by numerical simulation suggest that the identification of not deterministic loads requires a different methodology. So, a procedure based on the reduction of ill-conditioning it is not considered the conclusive approach; hence the issue has been tackled by a different modal formulation. In a first step the analysis of the coherence function allows to select the number of applied forces, once the position and the amplitude are identified. The validation of this proposed technique is tested in different experimental cases: Single Input Multi Output (SIMO) and Multi Input-Multi Output (MIMO). The numerical identification of deterministic and random loads is conducted also in the instance in which the measurement set of points do not overlap the excitation points. Whilst the first part of the thesis is focused on the identification of deterministic and random loads at low frequencies, the second part is focused on the identification of random loads at high frequencies. Let us remind that a high frequency problem is one in which the wavelength of the waves propagating in the studied media is shorter than the characteristic dimension of the media itself. Therefore the solution of a high frequency problem by a classical technique implies the study of a very large number of degrees of freedom of the model. The consequence is a high computational cost and large uncertainty on the simulation results. Therefore the problem is tackled by using the Statistical Energy Analysis (SEA). The identification is performed in two steps. The first step considers the identification of a "energy based" model of the structure by using the Power Injection Method (this technique allows to carry out the SEA parameters of the structure by experimental tests). The second step is the identification of the power injected by using the identified model and solving an "inverse problem" of SEA.