A procedure to restore measurement induced violations of reciprocity and passivity for FRF-based substructuring

Frequency-based substructuring is a very popular approach to predict the vibroacoustic behaviour of built-up mechanical systems. Even if extensively used since a long time for sundry purposes, yet this method may encounter difficulties when attempting to include test-based substructure models. The reason is that the characteristics of the experimentally obtained subsystems are corrupted by unavoidable measurement inaccuracies. Such inaccuracies often drastically affect the prediction of the combined system behaviour, especially when the problem is badly conditioned. Here we will focus on two types of measurement induced inaccuracies: reciprocity and passivity violations. A new approach that enforces these two physical properties upon a test-based frequency response function (FRF) model is proposed. A well-behaving system is created while affecting the original corrupted FRF matrix as little as possible. Besides guaranteeing a physically consistent behaviour, the approach considerably reduces the impact of noise for coupling applications and hence decreases the quality requirements for experimental data.

In this work the method is presented and applied to a poorly-conditioned hybrid substructuring approach: a test-based plate model coupled through its rotational degrees of freedom with an analytical model of a damping layer. This is a particularly critical test case as the noise and physical anomalies already present in the experimentally obtained plate data turn out to be further amplified by the finite difference procedure needed to estimate its rotational degrees of freedom. It is shown that the removal of the physical inconsistencies from the plate data using the novel procedure, indeed yields more stable and reliable results after coupling.