Prediction of modal deflections and frequency response functions from experimental data: The longest vector approach

Abstract

Modern modal parameter estimation (MPE) algorithms are highly optimised for fast computations and limited memory footprint. However, a large redundancy exists in the data-sets that are fed to these algorithms. Considering that modal parameters are global properties of a structure, and for a linear time-invariant system (due to reciprocity) there exist multiple measurements for the same frequency response function (FRF), a novel utilisation of the structure of the modal residue is proposed. The modal and participation vectors that constitute the unity rank modal residue for a system pole, are scaled versions of each other. As such, given minimal information about driving points, not only can one be reconstructed from the other but missing components may also be predicted. To this effect, the construction and use of a “longest vector” is discussed, which includes information from both the input and output spaces by combining all measured degrees-of-freedom in a single vector. Its applications to the MPE process at various stages like data input, stabilisation diagrams, pole cluster charts and mode shape animations is discussed and supported by experimental verification. Additionally, the longest vector is used to predict a driving point FRF for the experimental case, where the force input was originally not measured.