Controls Based Hybrid Sub-Structuring Approach to Transfer Path Analysis

In the design of mechanical systems, there are constraints imposed on the vibration of mechanical equipment to limit the vibration transmission into its support structure. To accurately predict the coupled system response, it is important to capture the coupled interaction of the two portions, i.e., the mechanical equipment and the support structure, of the mechanical system. Typically during a design, the analysis of the full mechanical system is not possible because a large part of the system may be non-existent. Existing methods known as Transfer Path Analysis and Frequency Based Substructuring are techniques for predicting the coupled response of vibrating mechanical systems. In this paper, a control based hybrid substructuring approach to Transfer Path Analysis is proposed. By recognizing the similarities between feedback control and dynamic substructuring, this paper demonstrates that this approach can accurately predict the coupled dynamic system response of multiple substructured systems including operating mechanical equipment with a complex vibration source. The main advantage of this method is that it uses blocked force measurements in the form of a power spectral density matrix measured uncoupled from the rest of the system. This substructuring method is demonstrated using a simplified case study comprised of a two-stage vibration isolation system and excited by operating mechanical equipment.