Step-by-step decoupling method for inverse substructuring analysis of a three-component coupled packaging system

Based on a step-by-step decoupling method, an inverse substructuring method is developed for the analysis of the dynamic characteristics of a single-coordinate coupled three-substructure system. The closed-form analytical solution to inverse substructuring analysis of the system is derived. The proposed method is validated by a lumped mass-spring-damper model, the predicted frequency response functions (FRFs) of substructures and the coupling stiffness; in addition, the most relevant system-level FRFs are compared with the direct computations, showing exact agreement. Finally, the sensitivity of the proposed method to measurement error is studied. The method developed offers an approach to extract the unknown substructure-level FRFs and coupling stiffness from system-level FRFs purely for single-coordinate coupled substructures.