A reduced eigenvalue method for broadband analysis of a structure with vibration absorbers possessing rotatory inertia

Multi-tuned vibration absorbers are attractive in reducing vibration and noise over a broadband. Here, an efficient and robust dynamic reanalysis algorithm is presented for predicting the dynamic response of a base structure to which are attached multiple absorbers. The ‘reduced eigenvalue method’ uses the modal analysis results of the base structure without absorbers, computed just once, to obtain the response of the modified structure. The method presented has two salient features. One is that the resonances of the modified structure are provided, and can be summed directly to estimate broadband measures of the dynamic response. The other is that rotatory inertia of the absorbers is properly captured, which has been found from experiment to be significant when an absorber is attached to a point on the base structure undergoing rotation. The method is contrasted with the impedance-based approaches. The method is used to model a three-dimensional absorber on a structure, which has been built, and is shown to correlate with experiment and full-scale finite element analysis.