Characterization and reduction of dynamic models of vibrating systems with high modal density

The aim of this paper is to demonstrate that the vibration response of systems with high modal density excited by broadband forces can be obtained by decomposing the response on a small number of effective shapes instead of a large number of mode shapes. An approach for building effective shapes on the basis of a measured mobility matrix is presented. More precisely, effective shapes can be built from eigenvectors of the space-frequency mobility matrix and a reduced model can be obtained by using only a small number of dominant eigenvectors of the SFM matrix. Systems with high modal density are characteristic of mid and high frequency problems where, for the sake of robustness, energy is often preferred to local response in order to describe the behavior of vibrating systems. The models built from the eigenvectors of the SFM matrix can be used for energy prediction and we observe that very small models are sufficient for prediction to within 3 dB. Two applications of the method are presented: the first uses numerical results in the case of longitudinal beam vibrations while the second uses experimental results obtained from plate vibrations. The method is in fact an extension of experimental modal analysis to the vibration problems of systems with high modal density.