Including directly measured rotations in the virtual point transformation

Dynamic substructuring methods serve as a powerful tool in the analysis of modern complex systems. The coupling of substructures has been successful with analytically obtained results. However, substructuring with experimentally obtained data remains challenging. One of the main problems associated with experimental substructuring is the coupling of the rotational degrees of freedom (RDoFs). A promising method where RDoFs are included implicitly is the virtual point transformation. Even though the transformation has been successfully used in the substructuring process, it is still highly susceptible to inaccuracies in the sensor sensitivity and positioning. In this paper an expansion to the virtual point transformation is proposed, which enables the projection of a directly measured rotation response on the interface deformation modes. A novel formulation of the weighting matrix is introduced to consistently include the measured rotations in the transformation. The proposed expansion is demonstrated on a numerical model of a simple beam-like structure and compared with the standard transformation. The effects of inaccuracies in the sensor sensitivity and placement on the overall quality of both transformation are analysed with a global sensitivity analysis. Finally, an experimental validation of the proposed expansion is carried out on a steel beam.