Vibratory source identification by using the Finite Element Model of a subdomain of a flexural beam

This paper proposes the identification of vibration excitations by an inverse method. The use of the local operator of a structure, for which the vibration field is obtained by measurements, is investigated. This method has already been developed on analytically known structures, but there are as yet few applications. The goal of this paper is to adapt the same technique by using an operator obtained with the Finite Element Method rather than a discretised differential motion equation. The first difficulty is the measurement of rotational degrees of freedom. A concept analogous to an observation matrix enabling only the measurement of displacements is then proposed. The method of extracting the operator on a part of the structure is also discussed. Two variants are proposed: an operator with free boundary conditions and a truncated operator without boundary conditions. The first permits identifying internal forces at the boundaries of the subdomain, whereas the second ignores them. In order to regularise the inverse method, a Tikhonov approach is used. An important point of this paper is the discussion of the effect of this regularisation which implies ambiguities between reconstructed forces and moments in the results. The possibility of an a priori “force only” assumption is then demonstrated and recommended. After illustrations obtained from numerical simulations on beams, an experimental validation is provided for a beam excited by a shaker where several signals are used, giving several signal to noise ratios. The results are discussed and compared to the force measured directly by a piezoelectric sensor.