With the continued introduction of stringent noise abatement polices [1922], along side the growing importance of product sound quality [23], the ability to accurately predict the acoustic behaviour of an assembly (be-it a vehicle, a washing machine or a
Chapter 2. Literature 14 desktop fan) is of interest. Key in the development of such prediction methodology is the successful characterisation of the contributing noise sources (for example; gearboxes, motors, compressors, etc.).
In the characterisation of an acoustic source (air-borne or structure-borne) the fun- damental aim may be stated as follows; to determine a physical set of quantities that describe both the active and passive behaviour of the source in such a way that they may later be used to predict an operational response in some other scenario. To aid the development of an appropriate method the International Organization for Standardization (ISO), Technical Committee on Acoustics TC43, Working Group outlined the following set of requirements that a suitable characterisation method should allow [24]:
1) Comparison of one source with another. 2) Comparison of sources with set limits. 3) Prediction of sound levels when installed.
4) Quantication of improvement in new low noise designs.
For many years the general consensus had been that the above were best achieved through a single valued frequency dependent quantity [25], for example sound power. However, as will be discussed shortly, such methods are generally unsuitable for the characterisation of structure-borne sources.
Depending upon the characterisation method employed, determined quantities may, or may not, be independent properties of the source. An independent quantity may be dened as one whose behaviour is an intrinsic property of the sub-structure under investigation, and therefore unaected by any modications made to its surround- ings. An independent characterisation is generally preferable in that it not only fulls above objectives, but satises the transferability requirements of dynamic sub-structuring (and therefore facilitates the construction of VAPs).
Broadly speaking, characterisation methods may be categorized as either direct, or indirect. Direct methods concern the direct measurement of desired quantities, whilst indirect methods infer the sought after quantities from others that are more easily, or accurately, measured (often using inverse methods).
Chapter 2. Literature 15 An acoustic source may be considered either air-borne (or more generally uid-borne) or structure-borne depending upon the nature of the noise generating mechanisms, or the level at which the practitioner considers the problem. The characterisation of an air-borne source is more than often a simple procedure, owed in part to the weak coupling between the source and receiver sub-structures (i.e. the surrounding environment).3 As such, a number of well established sound power based measure-
ment procedures have been developed, standardised and subsequently adopted with industry [2628]. Unfortunately, procedures for the characterisation of structural sources are less well developed, not because they are of less signicance, but due to their greater complexity. The strong mechanical coupling between source and re- ceiver sub-structures results in the contamination of any directly measurable source quantity by the coupled receiver sub-structure. As such, the adoption of standard air-borne measurement procedures for structural source characterisation is inappro- priate. Consequently, the characterisation of structural sources has been a topic of great interest for many decades and a number of alternative methods have been proposed, including; the free velocity [29], operational force [30], blocked force [13], the source descriptor [31], the characteristic power, mirror power and maximum available power [32] and pseudo forces [33], to name but a few.
Further clarifying its requirement, Mondot and Peterson [31] proposed a potential independent source characterisation, the source descriptor and coupling function. It was shown that an expression for complex power between source and receiver sub-structures could be manipulated in such a way that yields two coecients; a source descriptor and a coupling function. The source descriptor is an independent source property that is proportional to power and involves both its active and pas- sive properties. The source descriptor may be interpreted as the source's ability to deliver power, whilst its product with the coupling function, a term proportional to the ratio of the source and receiver mobilities, determines the active power transmit- ted from the source to receiver. The original single contact point formulation was extended to multiple-contacts through the application of both `eective mobilities' [3436] and `interface mobilities' [37]. In the former, the resulting multi-point source descriptor became a function of force distribution and therefore dependent upon the receiver and no longer an independent property of the source. An independence re- taining generalization of the source descriptor to multi-point connected systems was later presented by Moorhouse [32] and termed the `characteristic power'. Dened as the dot product of the blocked force and free velocity vectors, the characteristic
Chapter 2. Literature 16 power provides an equivalent single point model for multi-point connected struc- tures. Unlike its single case counterpart, the determination of characteristic power requires the inversion of a measured source mobility matrix and is therefore suscep- tible to inversion error and ill-conditioning. Also presented by Moorhouse [32] were the concepts of mirror power and maximum available power, describing the power delivered by a vibrating source into a passive receiver structure whose properties are the mirror and complex conjugate of the source, respectively. With both the source descriptor and its generalization, the characteristic power, being dened on a power basis, translational and rotational contributions are dimensionally compatible and can therefore be collapsed into a single value. The characteristic power has since been introduced as part of the European standard EN 12354-5 for the prediction of structure-borne sound levels from building equipment [38].
Alternative power based methods, where the source is coupled to a standardized receiver structure have also been investigated, most notably the reception plate method [25, 39, 40]. Analogous to the reverberation method for the measurement of air-borne sound power, the reception plate method determines the power transmitted into a plate from the plate's loss factor, averaged velocity, mass per unit area, and surface area. Idealizations such as velocity and force sources hold for light (source mobility much less than plate mobility) and heavy structures, respectively. However, the characterisation is not independent and does not usually allow for the transfer of data, other than for approximate predictions in specic environments. Regardless of its limitations, the reception plate has been introduced as part of the European standard EN 15657-1 for the characterisation of structure-borne sound sources under laboratory conditions [41].
Currently, the only internationally recognised standard measurement method for structural source characterisation is ISO 9611 [29], where a direct procedure for measuring the velocity of resiliently mounted machinery is described, from which a free velocity may be approximated. The free velocity describes the active component of a source in terms of the motion of its contact interface whilst uncoupled and freely suspend. The free velocity is therefore an independent property of the source. To provide a complete source characterisation the free velocity must be accompanied by some measure of the source's passive properties, i.e. its free mobility. Although the standard provides a simple measurement procedure it is seldom used in practise. Its lack of uptake may be put down to the practicality of achieving the 'freely suspended' mounting condition. Additionally, the potential variation in mounting conditions
Chapter 2. Literature 17 between characterisation and installation may well pose problems. Furthermore, unlike power based methods, the dimensions of translational and rotational compo- nents are not compatible and therefore the free velocity can not be collapsed to a single frequency dependent variable. A practical application of the free velocity in the prediction of structure-borne noise emission from resiliently mounted machinery was demonstrated by Moorhouse and Gibbs [42, 43]. Assumptions based on the coupling and phase between contact DoFs allowed for a multi-contact theory to be established. Unfortunately the simplifying assumptions led to a reduction in appli- cability to a narrow range of cases. Recent work by Moorhouse et al. [44] has shown that the free velocity may be determined from in-situ operational measurements via the application of the round trip [45] and in-situ blocked force [13] relations. In doing so the free velocity may be determined from measurements conducted under representative mounting conditions, partly avoiding the need to freely suspend the source. Through a similar application of the round trip and in-situ blocked force relations it was also shown that the aforementioned characteristic power [32] may also be determined partly through in-situ operational measurements.
Perhaps the most common approach to source characterisation, particularly within the automotive and aerospace sector [30, 46] is the operational force method, also referred to as indirect force determination [47]. The operational force method deter- mines the forces acting on a receiver structure through an inverse approach whereby a measured receiver mobility matrix is inverted and subsequently multiplied by an operational velocity vector. Unfortunately, this does require the source and receiver sub-structures to be decoupled for the FRF measurement. In contrast to the direct measurement of free velocity, the operation force method does allow for operational measurements to be made in-situ, and thus avoids discrepancies between mounting conditions. Sadly, as with the characteristic power, the inverse approach is suscep- tible to ill conditioning. Fortunately, however, with the operational force method forming the basis of the well established diagnostic method `transfer path analysis` (TPA) [12], much work has been focused on the minimization of this error, with par- ticular emphasis on regularisation techniques, see [48, 49].4 Although well adopted
within industry and having become more or less standard practice, the operational forces obtained are not independent properties of the source and can not transferred between assemblies.
4An overview of the general concept of regularisation with regards to force identication may
Chapter 2. Literature 18 Janssens and Verheij proposed an alternative in-situ approach, referred to as the pseudo-force method, whereby the internal excitation of a source is reproduced by a set of ctitious forces on its outer surface [33]. Unlike the operational force method, pseudo forces may be determined using entirely in-situ measurements, thus allowing for diagnostic methods (similar to TPA) to be carried out without having to disman- tle the assembly. The pseudo force method has since been used to compare source strengths of dierent machines [50], and conduct diagnostic tests on ships [51, 52]. A similar method was presented by Ohlrich, instead termed the equivalent force method [53, 54]. Unfortunately, the forces determined using these methods have little physical meaning, and their transferability is limited. Furthermore, although they may produce equivalent response elds, it is dicult to directly compare the pseudo-forces of two dierent sources due to their dependence upon measurement position.
In stark contrast to the free velocity, the blocked force oers an alternative inde- pendent source characterisation [55]. Dened as the force required to completely restrain a contact interface, the blocked force, like the free velocity, suers from practicality issues. Unlike the free velocity, where the source is required to be freely suspended, the blocked force requires the source to be coupled to an immovable object. This is clearly not achievable, however, an approximation may be obtained over a limited frequency range, at the cost of a large, impractical test rig. Ignoring the practical limitations, the blocked force does, in theory, like the free velocity, provide an independent measure of a sources activity. Recent work by Moorhouse et al. [13] has shown that blocked force may be determined in-situ using an inverse method similar to that the operational force method. A similar conclusion was ar- rived at independently by D'Klerk [56]. The blocked force approach of Moorhouse and De'Klerk [13, 56] allows for a structural source to be independently characterised whilst in-situ, and therefore under representative mounting conditions, thus com- bining the advantages of both the free velocity and operational force methodologies. Furthermore, unlike the pseudo-force approach of Janssens and Verheij [33], blocked forces have signicant physical meaning, and moreover, being dened at the source- receiver interface, they may be readily used in the comparison of dierent sources. Since its realisation, the in-situ blocked force approach has received much attention, leading to a number of publications [5759], particularly within the automotive [60], aerospace [61, 62] and domestic product [63] sectors. Its popularity has since led to the development of a blocked force based TPA procedure, referred to in the literature as `in-situ TPA' [12, 64, 65]. In-situ TPA allows for an entirely in-situ measurement
Chapter 2. Literature 19 based diagnostic procedure which, unlike the pseudo force methodology, pertains to quantities of physical meaning. It is perhaps of interest to note that pseudo forces, when determined at a source-receiver contact interface, are in fact identical to the blocked forces, unfortunately however, Jannsens and Verheij do not appear to have been aware of this at the time. The in-situ blocked force approach may additionally be considered a generalization of the single point synthesised force presented by Lai [66], and further realised as a consequence of an equivalent eld representation as shown by Bobrovnitskii [67].
As the eld currently stands, the in-situ blocked force method appears to oer the most suitable approach to independently characterising the activity of structural sources. To this end, the method is currently in the process of standardisation by the International Organisation for Standardisation, Technical Committee ISO TC43/ SC1/ WG57.