Simplified calculation of structure-borne sound from an active machine component on a supporting substructure

The background to the work is the increasing interest in virtual acoustic prototypes, and the need to predict sound pressure radiated from machines without having to assemble them physically. The focus of the paper is on structure-borne sound, and the objective is to investigate ways of simplifying the calculation of contact forces between a vibro-acoustically active component and its passive supporting structure. An analysis shows the importance of the singular values of the mobility matrices in determining the error due to simplifications. Errors are also analysed using Monte Carlo simulations for the case of an electric motor installed on a machine frame. The results show that at frequencies above the first anti-resonance, the off-diagonal elements of the source mobility matrix can be neglected. However, at lower frequencies no such simplification is possible. A hybrid mobility matrix is therefore proposed: at high frequencies it is diagonal, consisting of measured point mobilities, and at low frequencies the entire matrix is calculated using a simple rigid mass-stiffness model. Only point mobilities need to be measured rather than a full set of point and transfer mobilities, giving a significant reduction in measurement and data handling. Validation measurements show that the contact forces calculated using the hybrid matrix are, if anything, more accurate than those based on a purely measured matrix. It is argued that this is because the mass model is more robust than measured mobilities for this type of behaviour, being based on radii of inertia and mass only. It is noted that the conclusions are likely to apply to other structure-borne sound sources because of general similarities in low-frequency behaviour.