It is of high importance to be able to decouple a system to obtain the dynamic characteristics of its substructures; however, the necessary frequency response functions (FRFs) of the coupling interface are usually challenging to measure due to the limited accessible space and complex geometries. In this paper, a measurement technique in the decoupling process of a coupled system is proposed in order to obtain the FRFs at coupling interface. Specifically, a variable cross section rod is adopted to transmit the dynamic behavior of coupling interface. The proposed technique has three advantages: (a) the thick end with large cross section can provide enough area for applying excitation force like using impact hammer and/or setting up sensors; (b) the slender end with small cross section can break through the spatial limitation more easily; and (c) the convenience that no additional experimental setup is required but just using an available variable cross section rod. Vibrational equation of the variable cross section probe method is derived and then combined with the existing decoupling theories. Finally, the proposed probe method and the new decoupling theory combining probe theory are validated through numerical simulations (FEM) and laboratory experiments, respectively. The results show its great practicability in decoupling process especially in low frequency range.

The inverse sub-structuring method can predict the component-level frequency response functions (FRFs) of product (critical component) for product transport system from only measured system-level FRFs, facilitating the cushioning packaging design. However, the FRFs of the coupling interface between product and vehicle are usually of extreme difficulty to be measured due to the limited accessible space. To overcome this difficulty, the authors suggested a so-called FRF probe technique method in the previous study, which may be more suitable for the single-coordinate coupled system. In practice, most of the product transport systems should be treated as multi-coordinate coupled system. The aim of this paper is to derive a new FRF-based inverse sub-structuring method for multi-coordinate rigidly coupled product transport system and develop a new shearing probe technique to obtain the difficult-to-monitor FRFs at the coupling interface, which will be validated by a lumped mass model and finite element models, respectively, showing perfect agreement. Finally, the experiment on a physical prototype of multi-coordinate rigidly coupled product transport system is performed to further check the feasibility of the application prospect of the shearing probe technique for inverse analysis of product transport system. The method proposed in this study will provide the packaging designers an alternative method to monitor the integrity of product transport system.