A closed-loop model for single/multi-shaker modal testing

The traditional form of a frequency response function (FRF) measurement for a single-shaker modal testing (also for multi-shaker modal testing) using random excitation is an open-loop system. However, inevitable physical constraints cause such FRF measurements to be inherently of a closed-loop form. This paper presents the effect of hidden feedback paths on some current FRF estimators. Attention has been drawn to the effects of noise and leakage on these estimators. The closed-loop model is generalised to explore the effect of shaker-structure interaction in two-shaker modal testing. The complexity of multi-shaker modal testing is illustrated by using a multi-input multi-output model from which a frequency domain technique is developed to give noise-free estimates of the FRFs. The applicability of the closed-loop model in a two-shaker sine dwell test is validated using results from experiments carried out on a circular disk.