Structure borne sources

Structure borne sources (for example, motors, pumps, compressors, engines, etc.) are very common in machinery and automobiles. Thus, a large part of the TPA work has been dedicated to the structure borne source characterisation and sound transmission

problem through paths. Some of the early work by Ten Wolde and Verheij referenced in Section 2.4 was based on diagnosing structure borne sound transmission through ships. In source characterisation, the source quantity should describe the action of the source on a passive receiver. The other criterion for a source characterisation is that it should be ideally a property of the source and independent of the receiver. This would mean the source characteristic quantity is transferable to different receiver for diagnosing the sound transmission. Two quantities satisfy this criterion, namely the free velocity of the source and the blocked force of the source. The source mobility is also an independent property of the receiver however used rarely to describe the source activity.

Free velocity –The free velocity of a source is the velocity of the source at the coupling points when the source is operational under free-free boundary conditions, i.e. when no receiver is coupled to the source.

Blocked force –The blocked force of the source on the other hand is the force that the source applies to a blocked receiver. A blocked receiver is a rigid receiver compared to the source and is not excited into vibrations when coupled with an operational source. Figure 2.5 illustrates the concept.

Thus, the free velocity or the blocked forces can be measured for an independent characterisation of the source. However, it turns out that these measurements are often not practical if one implements the scenarios illustrated in Figure 2.5.

Figure 2.5: Active source substructure with velocity v_si at interface ‘i’. Left –interface is free and interface velocity is the free velocity (v_sf) of the source, right –interface is blocked and forces

acting at the interface are blocked forces (f_bl) of the sources

The free velocity of a source can be measured if the source is operated under a free-free boundary condition uncoupled from any receivers. Usually this would require hanging the source from resilient ropes or cables and then operating the source. However, this method is not very suitable as one has to remove the physical source from an assembly which can be highly impractical especially for large sources. This increases the measurement time. The blocked force similarly could be measured if the source is coupled to a rigid receiver whose mechanical impedance is very high than the source impedance. Some scenarios have been investigated namely the ‘Reception plate’ method [95] where the source is coupled to a really massive reception plate and the forces then obtained are the blocked forces. However, some in-situ approaches to source characterisation were also developed which are discussed here.

In the characterisation of structure borne sources by force quantity, indirect force determination methods were developed in the late 20th _{century. Blau et al. [96] presented a}

review of the inverse method of force measurement. Linden et al. [97] presented an experimental case of the same method. In this method, the source is first disconnected from the receiver and the receiver mobility is measured. Then the source is connected to the receiver and the operational velocities at the source receiver interface are measured. The forces measured by this approach are the contact forces and they are not independent of the source structure [98] however they could be used to rank the different sound transmission paths. This approach formed the ‘Classical TPA’ technique.

Verheij et al. [99] outlined a pseudo force method based on inverse measurement where the source was characterised by a number of correlated point forces over the source. Unlike the contact forces, which are determined at the interface, the pseudo forces could be determined for any positions of choice on the source structure. In theory, an infinite set of pseudo forces could exist for the structure borne source and was also shown for the case study of a pump considered by the authors. Janssens et al. [100] presented multiple case studies on the pseudo forces methodology to characterise different structure borne sources but also highlighted the need for regularisation techniques such as ‘Singular Value Decomposition’ (SVD) [101] to obtain reasonable predictions of receiver response. In case of airborne excitation this methodology would not be feasible as it would be practically difficult to determine point forces on the source which is the air volume. This is because the measurement techniques involve structural FRF measurements (mobility) which is not feasible for fluids where acoustic or vibroacoustic FRF’s are specified. In other study, Janssens et al. [102] also outlined an equivalent forces methodology, which is rather used to characterise the transmission through a single path. The pseudo force and equivalent force characterisations are not independent. Additionally, as one can choose random locations on the source for characterisation, one cannot really assure that all Degree of Freedom (DoF) are accounted for. For the case of airborne excitations, the source is air, thereby making it more important to select the appropriate locations for characterisation and a force characterisation may not be feasible as the source essentially is a pressure field rather than a set of forces. However, if we consider the pressure acting on a surface, then using Classical TPA, the airborne excitation could be in principle characterised at the surface. However, one cannot remove source (air) from the structure for measurements as required by Classical TPA techniques.

Elliott et al. [103] first proposed an in-situ technique for measurement of blocked forces of a structure borne source. This made it possible to characterise the source independently of the receiver structure [104]. An advantage of such characterisation is that it can be done in- situ without removing the source physically from the source receiver assembly, unlike classical TPA techniques. This method came to be known as the Blocked force TPA or iTPA

(in-situ TPA). This would be especially useful for the case of airborne excitations where the source is air and cannot be removed from the receiver (partition) for measurements. Therefore, it is worthwhile to explore the application of iTPA for case of airborne sound transmission through building partitions. It may then be in principle possible to measure the contributions of sources through different paths (elements) in a multi-layered partition.