24 R. Fagiani et al. 0 500 1000 1500 2000 2500 3000 10-3 10-2 10-1 100 101 102 Frequency (Hz) |a1/F1|(m/s 2/N) Gn Gn RS (only x,y,z) Fig. 2.6 Numerical case study. Comparison between numerical FRF for the coupled structure Gn and those obtained coupling the FRF matrices of the source and the receiver GnRS using Eq. (2.12) when rotational responses were neglected freedom were considered. This implies that the matrices used in Eq. (2.7) GnR and GnS are now6 6 matrices, as measured in the experimental case, instead of 12 12. As expected the curves are now different showing that neglecting moments and rotational degrees of freedom lead to inaccurate results. 2.5 Conclusions In this paper a frequency response coupling technique (or impedance coupling technique) was revised for the prediction of the overall impedance matrix of a coupled structure. The data required are the frequency response functions (FRFs) of the source and the receiver and the velocity/accelerations at the connecting points under operating conditions. These can be either experimental data, or numerical data obtained from finite element analysis or modal analysis, or both experimental and numerical results for different substructures. A simplified model was considered for investigating the validity of the procedure numerically and experimentally. Numerical results showed very good agreement between the FRF functions of the coupled structure and those obtained coupling the impedance matrices of the source and the receiver, while experimental results showed significant differences between at higher frequencies. These were investigated using the numerical model. Although some experimental errors were introduced due to lack in modelling the connections between the source and the receiver and uncertainties in measuring (e.g. force applied in z direction is not perfectly aligned along the z axis and so on) it was found that the main errors is introduced in neglecting moments and rotational responses. References 1. Di Sante, R., Revel, G.M., Rossi, G.L.: Measurement techniques for the acoustic analysis of synchronous belts. Meas. Sci. Technol. 11, 1463–1472 (2000) 2. Di Sante, R., Rossi, G.L.: A new approach to the measurement of transverse vibration and acoustic radiation of automotive belts using laser Doppler vibrometry and acoustic intensity techniques. Meas. Sci. Technol. 12, 525–533 (2001) 3. Petersson, B.A.T., Plunt, J.: On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure, part I: theoretical background and basic experimental studies. J. Sound Vib. 82, 517–529 (1982) 4. De Klerk, D., Rixen, D.J., Voormeeren, S.N.: General framework for dynamic substructuring: history, review, and classification of techniques. AIAAJ. 46, 1169–1181 (2008)
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