Coupling finite element and experimental modal analysis frequency response functions of jointed structures using the frequency-based substructuring method

Achieving accurate coupling remains a major challenge due to the complexities of boundary conditions and coupling interfaces, especially in bolted structures, where bolted joints are common in aerospace, automotive and civil engineering serve as coupling interfaces. The presence of bolted joints further complicates the coupling process, requiring in-depth and systematic experimental and analytical investigation. To address these challenges, this study proposes a methodology for coupling FE-FRFs with EMA-FRFs, improving the effectiveness of the Frequency-Based Substructuring (FBS) method. The proposed methodology is developed based on the integration of the Finite Element Method (FEM), Experimental Modal Analysis (EMA) and the FBS method for coupling FE and EMA FRFs for the investigation of the dynamic behaviour of a jointed structure. In this study, a Flanged Elbow Pipe (FEP) substructure and a Flanged Pipe (FP) substructure are assembled to form an assembled structure, namely a Bolted Flanged Pipe assembly (BFPA). They are used as a case study for the proposed methodology. The FE model of the FP substructure is carefully constructed to include the coupling interfaces and to calculate the FRFs under free-free boundary conditions. Special jigs are specifically designed and fabricated to measure the FRFs of the coupling interfaces of the FEP substructure using EMA under fixed-free boundary conditions, which are very difficult to represent analytically. The FRFs determined at the coupling interfaces of both substructures are coupled using the FBS method to form the coupled FRFs of BFPA. The accuracy and capability of the proposed coupling methodology is evaluated by comparing the coupled FRFs with the measured FRFs of the physical test BFPA. The comparison shows that the proposed methodology is highly capable of representing the EMA results, achieving 83 percent accuracy for seven modes and 95 percent accuracy in the low-frequency range, which is particularly important for analysing structural dynamics. Moreover, the proposed methodology is able to incorporate substructures such as FP and FEP with complex boundary conditions for which only coupling interfaces are available. The impressive performance of the proposed methodology shows that the proposed methodology has the potential to improve the accuracy and efficiency of predictions for complex structures consisting of a large number of substructures with complex boundary conditions. Furthermore, the proposed methodology can help speed up product manufacturing decisions or improve the performance and safety of products, which will have a positive impact on the industry concerned.