Load Estimation from Natural input Modal Analysis

Stiffness matrix []k Mass matrix []m Damping matrix []c Force vector () {}tf FRF matrix () []ωH Spectral matrix () []ωS Natural frequency rω Scaled mode shape {}rφ Un-scaled mode shape {}rψ Scaling factor rα Damping factor rζ One application of Natural Input Modal Analysis consists in estimating the unknown load acting on structures such as wind loads, wave loads, traffic loads, etc. In this paper, a procedure to determine loading from a truncated modal model, as well as the results of an experimental testing programme, are presented. The method involves the inversion of the FRF matrix partly solving the numerical problems that appear because of the truncation of the modal space. However, the error in the load estimation depends on the degree of truncation of the modal space and on the accuracy of the modal parameter estimation. In the experimental program a small structure subjected to vibration was used to estimate the loading from the measurements and the experimental modal space. The modal parameters were estimated by Natural Input Modal Analysis and the scaling factors of the mode shapes obtained by the mass change method [ 2] [ 3] [ 4]. Finally, the calculated loading is compared with the actual loading in order to determine the magnitude of the errors