Inverse dynamic problem: estimating system inputs from acceleration output records

This work starts from the acceleration response measured at several points of the structure and performs an analysis in the frequency domain. The modal parameters are estimated: first, frequencies and damping factors by means of the Least-Squares Rational Function (LSRF) estimation method and then, the residues measured by least squares of the Frequency Response Functions (FRFs). Non-proportional or general type damping is considered. The dynamic system is identified through the direct relationship of residues of the frequency response function matrix (complex analytical functions), with the residues measured from the system outputs excited by impulse type forces/inputs. Once identified the system, it allows the estimation of the physical properties: mass, stiffness and damping matrices and also the dynamic matrix of the system, which defines the inverse dynamic problem, it allows the estimation of the inputs from the system outputs, that is, estimate the forces from the recorded accelerations.