Structure-borne Sound Source Characterization Research Articles

Interface mobilities for characterization of structure-borne sound sources resiliently mounted via multiple contact points

This paper introduces an expansion of the interface mobility method for structure-borne sound sources that are resiliently mounted to a receiving structure at multiple discrete contact points. Subsystems of source, receiver and isolators are represented by Fourier transforms of their mobility matrices. Along with the source activity, a formulation for the transmitted power fed into the receiver is obtained. Furthermore, the source descriptor and a coupling function for resiliently mounted multi-point sources are obtained which both form recognized concepts for structure-borne sound source characterization. The method is based on a neglection of cross-order terms which describe a coupling between Fourier coefficients of different order. With regard to a subsystem of discretely placed isolators, cross-order terms were found to account for variations of isolator parameters along the contact points. In a set of numerical studies it was shown that errors introduced by neglecting cross-order terms are most pronounced in the higher frequency region where isolators show resonant behavior due to internal wave effects. A subsystem of identical isolators is completely described by equal-order terms, therefore no error is introduced considering such cases. Moreover, errors inherent in the rigidly mounted case due to cross-order source or receiver mobilities are reduced significantly when isolator mobilities are large compared to those from source and receiver. Findings from theoretical studies were validated in practical settings considering structure-borne sound transmission from a ship diesel engine and a magnetic resonance imaging (MRI) device.

Intrinsic characterization of structure-borne sound sources and isolators from in-situ measurements

The paper addresses the problem of how to characterize vibration sources and isolators with measurements made in-situ, either on a working installation or on a test bench. For example, automotive components are often characterized by test bench measurements, but there is a need to know how they will behave when coupled to components with potentially different properties in a vehicle. Ideally all components should be characterized by intrinsic properties, which can then be transferred to other installations. In the paper, some novel in-situ measurement methods for obtaining these properties are presented. First, the active properties of a source are characterized by the blocked force measured in situ. Structural dynamic properties are represented by frequency response functions (mobilities) and it is shown how, if necessary, these may be obtained by indirect measurements, for example when access to measurement points is difficult. New results for dynamic stiffness of isolators are then presented obtained using a novel in-situ measurement approach. The method allows rotational (moment) as well as translational (force) dynamic stiffness to be obtained over a wider frequency range than many test rigs. Results are validated by measurement on an ideal laboratory structure.

Interface Mobilities for Characterization of Structure-Borne Sound Sources with Multi-Point Coupling

The concept of source descriptor and coupling function is commonly recognized to form a rigorous basis for structure-borne sound source characterization. While this concept initially is valid for the single-point case only, it can be extended to sources with multi-point coupling by including the interface mobility approach. By considering a continuous interface that passes all contact points, the velocities, forces and mobilities are series expanded into interface orders by means of a spatial Fourier decomposition. The use of a continuous formulation for the multi-point case, however, can be problematic from a practical point of view. This paper discusses a reformulation of the interface mobility approach for a simplified calculation and clarified interpretation of the interface orders. With a discrete Fourier series as a basis for the interface mobility approach, the interface is reduced to a set of points and the interface orders are shown to describe the interplay of the data at the contact points. A discrete formulation furthermore yields simplified equations and a strict upper bound for the number of orders that have to be included, thus enhancing the practicability of interface mobilities for source characterization.

The influence of cross-order terms in interface mobilities for structure-borne sound source characterization

For the characterization of structure-borne sound sources with multi-point or continuous interfaces, substantial simplifications and physical insight can be obtained by incorporating the concept of interface mobilities. The applicability of interface mobilities, however, relies upon the admissibility of neglecting the so-called cross-order terms. Hence, the objective of the present paper is to clarify the importance and significance of cross-order terms for the characterization of vibrational sources. From previous studies, four conditions have been identified for which the cross-order terms can become more influential. Such are non-circular interface geometries, structures with distinctively differing transfer paths as well as a suppression of the zero-order motion and cases where the contact forces are either in phase or out of phase. In a theoretical study, the former four conditions are investigated regarding the frequency range and magnitude of a possible strengthening of the cross-order terms. For an experimental analysis, two source–receiver installations are selected, suitably designed to obtain strong cross-order terms. The transmitted power and the source descriptors are predicted by the approximations of the interface mobility approach and compared with the complete calculations. Neglecting the cross-order terms can result in large misinterpretations at certain frequencies. On average, however, the cross-order terms are found to be insignificant and can be neglected with good approximation. The general applicability of interface mobilities for structure-borne sound source characterization and the description of the transmission process thereby is confirmed.

The influence of cross-order terms in interface mobilities for structure-borne sound source characterization: Force-order distribution

For the characterization of structure-borne sound sources with multi-point or continuous interfaces, the concept of source descriptor and coupling function can be reformulated by incorporating the interface mobilities. The applicability of this approach, however, depends on the admissibility of neglecting the so-called cross-order terms. Hence, the objective of the present work is to investigate the importance and significance of cross-order terms for the characterization of vibrational sources. Such cross-order terms consist of the previously studied cross-order interface mobilities and the force orders which are addressed herein. The distribution of force orders depends on both the complex data of the contact forces and their location along the interface. From measurements and numerical simulations it is found that the relative magnitudes of the force orders vary up to a factor 10. Only at low frequencies a larger range in magnitude can be observed. Combined with the knowledge of the cross-order interface mobilities, henceforth, a complete assessment of the influence of cross-order terms is possible.

The influence of cross-order terms in interface mobilities for structure-borne sound source characterization: Frame-like structures

The applicability of interface mobilities for structure-borne sound source characterization critically depends on the admissibility of neglecting the cross-order terms. Following on from a previous study [H.A. Bonhoff, B.A.T. Petersson, Journal of Sound and Vibration 311 (2008) 473–484], the influence of the cross-order terms is investigated for frame-like structures under the assumption of a uniform force-order distribution. Considering the complex power, the cross-order terms are significant from intermediate frequencies on upwards. At lower frequencies, the cross-order terms can come into play for cases where the in-phase motion of the structure along the interface is constrained. The frequency characteristics of the influence of cross-order terms for the zero-order source descriptor and coupling function are similar to those of the complex power. For non-zero source descriptor and coupling function orders, the quality of the equal-order approximation mainly depends on the presence of low-order cross-order interface mobilities. By analyzing the symmetry of an interface system, it is possible to predict which cross-order terms are equal to zero. The equal-order approximation manages to capture the main trends and overall characteristics and offers an acceptable estimate for engineering practice.

Vibration activity and mobility of structure-borne sound sources by a reception plate method

This paper considers a practical structure-borne sound source characterization for mechanical installations, which are connected to plate-like structures. It describes a laboratory-based measurement procedure, which will yield single values of source strength in a form transferable to a prediction of the structure-borne sound power generated in the installed condition. It is confirmed that two source quantities are required, corresponding to the source activity and mobility. For the source activity, a high-mobility reception plate method is proposed which yields a single value in the form of the sum of the squared free velocities, over the contact points. A low-mobility reception plate method also is proposed which, in conjunction with the above, yields the source mobility in the form of the average magnitude of the effective mobility, again over the contact points. Experimental case studies are described and the applicability of the laboratory data for prediction and limitations of the approach are discussed.

The influence of cross-order terms in interface mobilities for structure-borne sound source characterization: Plate-like structures

With the introduction of the concept of interface mobilities, substantial simplifications can be obtained for vibrational source characterization and the description of the associated transmission process involving multi-point or continuous interfaces. The applicability of interface mobilities, however, depends on the admissibility of neglecting the so-called cross-order terms. Under the assumption of a uniform force-order distribution, the cross-order terms reduce to the cross-order interface mobilities. It is demonstrated that the cross-order interface mobilities represent the dependence of point and transfer mobilities on the location relative to boundaries and discontinuities. From theoretical and experimental analyses of circular interfaces located on plate-like structures, it is found that the influence of the cross-order terms features three distinct frequency regions. Provided that the structure can vibrate freely along the interface, the cross-order terms are significant only at intermediate Helmholtz numbers. For engineering practice, however, the omission of the cross-order interface mobilities appears to result in an acceptable estimate throughout the entire frequency range.

A pseudo-forces methodology to be used in characterization of structure-borne sound sources

In the analysis of machinery noise generation and transmission the aspect of sound source characterization is of importance. Unlike for airborne sources, no widely applicable and practical methods are available yet for structure-borne sound sources. This paper presents the ‘pseudo-forces’ methodology. In this approach the internal excitation in a source component is reproduced by fictitious forces on the outer surface. This method is intended to be applied for ‘compact’ sources and in situations where (prototype) machinery is available for measurements. On the one hand this method respects the complex coupling of source component and mounting structure and on the other hand aims at reducing measurement effort. Experiments have shown the practicability of the approach.

Towards a structure-borne sound source characterization

Characterization of mechanical sources is complicated since up to six forces and moments contribute at a contact and the response at one contact is the result of forces and moments at all contacts. For the transmission process, the quantity of prime interest is the complex power, and, therefore, a proper source characterization should relate to it. The source descriptor does so and offers a consistent base for studies of source characterization. Theoretical and experimental progress on the source descriptor is reviewed. From inspection of the source descriptors and the mobilities from which they are composed, it is observed that the uncoupled component source descriptors can establish the bandwidth and dominant components of excitation. The ‘signatures’ of the point mobilities required allows contacts to be classified as mass-, stiffness- or resonance-controlled component, establishing simplifications with respect to source characterization.

Structure-borne sound power through multiple contact points between machines and supporting structures

The structure-borne sound emission from machines through multiple contact points is highly influenced by the extent of coupling between these points. When the machine is unconstrained (i.e., disconnected from the supporting structure) the coupling can be assessed by comparing the point and transfer mobilities of the machine. Once connected however, account must be made too of the force distribution amongst the contact points. While the forces themselves at the points are sensitive to the structural characteristics of the particular installation, their distribution, which is most readily described by the ratios of the contact point forces, may be less sensitive. Using combinations of real and theoretical installations, force distributions have been investigated. Studies have also been undertaken on the estimation and approximation of the force ratios and their effect on the estimate of the total active power from the machine to the supporting structure. It will be shown that this has application to the characterization of structure-borne sound sources.

Use Of The Source Descriptor Concept In Studies Of Multi-Point And Multi-Directional Vibrational Sources

A study of the influence of multi-point and multi-component coupling on structure-borne sound source characterization has been carried out. In particular, the effects of cross-coupling between different components of excitation and motion at a contact point have been examined. Theoretical results are supported by results of experiments on real machines, a family of fan units. The significance of the various components of excitation and motion is interpreted in terms of the source descriptor, a quantity defined on a power basis. It is shown that measured source descriptors associated with force and moment can be equally important and, accordingly, none can be excluded a priori. It is also shown that multi-point and multi-component coupling can have a profound influence. The ability of the source to impart vibrational power at global anti-resonances of the source structure is demonstrated. In addition, this ability is spectrally transposed to a higher frequency range than that predicted from a single point, single component analysis.

Characterization of structure-borne sound sources: The source descriptor and the coupling function

An introductory, theoretical study for characterization of structural acoustic sources has been carried out. The concept source denotes any active structure with unknown internal elementary source mechanisms and unknown internal transmission paths from generation to the contact points with the receiving structure. An alternative description of the power transmission from the source to the receiver is presented in the case of one component of motion and one contact point. A general source parameter called the source descriptor is introduced. This parameter is a function of source data only. It is proportional to power and involves both the internal vibration of the source and its mobility at the contact point. From experimental measurement series, it can be emphasized that the velocity of the free source is a suitable and manageable quantity for describing the internal vibration of many structure-borne sound sources. The active power transmitted from the source structure to the receiving one is found to be the product of the source descriptor and a dimensionless function called the coupling function. This function illustrates the dynamic properties of the source-receiver interface.