Towards dynamic substructuring using measured impulse response functions

The Impulse Based Substructuring (IBS) method has been proposed lately as an alternative approach to evaluate the dynamic response of a system, using the experimentally determined Impulse Response Functions (IRFs) of its components. In previous research a first experimental IBS analysis was performed using measurements on two interface points of a POM bar. It was observed that the IRFs obtained from the imperfect impulses (by means of impact hammer testing) result in stability issues in the substructuring analysis. To obtain IRFs associated with a “true” Dirac impulse, several approaches are discussed. It is known that frequency domain averaging leads to small phase errors and thereby non-causality in the IRF obtained through inverse Fourier transformation. Alternatively a time-domain approach is presented which allows for averaging of multiple impacts while avoiding Fourier transformations. By writing the convolution product of the dynamic system using a Toeplitz matrix, the IRF can be found from solving a least-square linear system. To improve efficiency, the system can be formulated as an inverse filter operation. The time-domain procedure is illustrated by application to the one-dimensional POM bar.