PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Single rig two-stage method for characterizing structure-borne
sound sources in buildings
Barry Marshall GIBBSAcoustics Research Unit, University of Liverpool School of Architecture, U.K.

ABSTRACTTwo source quantities are required to predict the structure-borne power into lightweight buildings andother structures: source mobility and free velocity or blocked force. The average source quantities canbe measured using the reception plate method (RPM). A thin reception plate gives an estimate of thesum-square free velocity. A thick reception plate gives an estimate of the sum-square blocked force.
The ratio of these quantities approximates the square of the average source point mobilit ies. In thisproposal, only one reception plate is required. The transfer mobilities from several remote points to asingle measurement centre are recorded. The source is attached about the measurement centre and thetransfer mobilities re-recorded. The ratio of the transfer mobilities gives an estimate of the source
mobility. The source then is operated and the velocities at the remote points recorded. For each remote
point, the recorded velocity and previously estimated source mobility give an estimate of the source
free velocity. In this method the installation conditions are unchanged; knowledge of source-receiver
mobility ratio is not required; the reception plate can be relatively thin/light; the method automaticallycollapses the source quantities to single equivalent values.
Keywords: Building noise control; structure-borne sound sources: 51; 43

1. INTRODUCTION
Structure-borne sound in buildings is generated by vibrating or impacting sources, which injectvibrations into supporting and connecting building elements. To predict the structure-borne soundpower into the supporting structure(s), two source quantities (vibration activity and structuraldynamics at the contacts) are required for all likely installation conditions, including in lightweightbuildings (1,2). For activity, the source quantity is either free velocity or blocked force; for structuraldynamics, the source quantity is the mobility, or its inverse impedance, at the contacts. The source
quantities are obtained by laboratory measurement to provide input data for building propagation
models (3,4).
The source quantities can be measured directly or indirectly using reception plate methods (5).
Direct measurements can be time-consuming and costly. Reception plate methods are generally
simpler but less accurate. To obtain the two source quantities, a two-stage measurement method isrequired. One method is by measuring the source free velocity directly and then attaching theoperating source to a low-mobility reception plate to obtain the blocked force as a sum-square value(6). Alternatively, the free velocity is obtained as a sum-square value by attaching the operating source
to a thin high-mobility plate (1,2). There are practical problems in such two -stage methods, which
require the source to be set up on two test rigs. It is not always possible to ensure repeatable operating
conditions.
In this proposal, only one reception plate is required. The transfer mobilities from several
remote points on the plate to a single ‘measurement centre’ are recorded. The source then is attachedabout the measurement centre and the transfer mobilities re-recorded. The ratio of the transfer
mobilities corresponds to the ratio of the velocities at the centre, which gives an estimate of the source
mobility. The source then is switched on and the velocities at the same remote points recorded. For
each remote point, the recorded velocity and previously estimated source mobility gives an estimateof the source free velocity. Repeating the process for several remote points allows averaging andestimates of standard deviation. This method offers the following advantages: the installation andoperating conditions are unchanged; knowledge of source-receiver mobility ratio is not required; thereception plate can be relatively thin/light and easily installed in laboratories; the method
automatically collapses the source quantities to single equivalent values.

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2. THEORY OF METHOD
2.1

Set-upThe source mobility is measured indirectly by recording the transfer mobility of a single
reception plate before and after attaching the source under test. Figure 1 is of a rectangular reception
plate of arbitrary dimensions and thickness, with a designated measurement centre c.

FiFi
Vc*

Figure 1 - Transfer mobility from a remote point on reception plate to measurement centre without(left) and with (right) the source attached.
௖The transfer mobilities to the measurement centre ܻ௜௩ൌ ೎, without the source attached, are recordedி೔from several (ten in this study) remote points i. The measurement centre is not at the plate centre but
located such that the remote locations surround it.
2.2 First Stage
The source under test is placed at the measurement centre and attached at contact points j and the௖‫כ‬transfer mobility from the remote points to the measurement centre ܻ௜
new velocity at the centre is due to the forces Fj at the contacts‫כ‬‫ݒ‬௖௜ൌ ‫ܨ‬௜ ܻ௜௖ െ ‫ܨ‬௝ ܻ௝௖௩‫כ‬ൌ ೎ are re-recorded. Theி೔(1)The forces Fj result from the plate velocities at the contact points and the. source and plate mobilities
combined at the same pointsೕ‫ܨ‬௝ ൌி೔ ௒೔ೕ(2)ೕቀ௒ೄ ା௒ೕ ቁ

Y sj is the source mobility at contact j and Y j j is the plate mobility at contact j. For multiple contacts,
these are matrices. From equations (1) and (2) the coupled transfer mobility isೕܻ௜௖‫ כ‬ൌ ܻ௜௖ െ௒ೕ೎ ௒ೕೕ(3)ೕቀ௒ೄ ା௒ೕ ቁ

The ratio R of the coupled and uncoupled transfer mobilities corresponds to the ratio of coupled anduncoupled velocities at the centre, which is the measured quantity of interestܴൌ௩೎‫כ‬௩೎ೕൌͳെ ೎௒ೕ೎ ௒ೕೕೕ௒ೕ ቀ௒ೄ ା௒ೕ ቁ(4)1233

If it is assumed that the velocity at the measurement centre is due to a single equivalent sourcewith mobility Y seq at the centre, the ratio now isܴ‫ כ‬ൌ ͳ െ

௒೎೎

(5)

൫௒ೄ೐೜ ା௒೎೎ ൯

Assuming R * = R, then the equivalent single source mobility isோܻௌ௘௤ ൌ ܻ௖௖ ሺଵିோሻ
2.3

(6)

Second Stage
The source under test is switched on and the velocities at the remote points i are recorded௝‫ݒ‬௜ ൌ ‫ܨ‬௝ ܻ௜‫ܨ‬௝ are the forces at the contact positions j where௩೑೔‫ܨ‬௝ ൌ ೕ ೕvfj is the source free velocity at contact j.

(7)ቀ௒ೄ ା௒ೕ ቁ

Assume that the remote velocity is due to a single equivalent source with single equivalent freevelocity v feq , again at the measurement centre. The remote velocity at the ith point‫ݒ‬௜‫ כ‬ൌ
From (8)௩೑೐೜ ௒೔೎(8)൫௒ೄ೐೜ ା௒೎೎ ൯௩೔‫ כ‬൫௒ೄ೐೜ ା௒೎೎ ൯‫ݒ‬௙௘௤ ൌ(9)௒೔೎The process is repeated for each remote point and average values calculated from all points.

3. NUMERICAL MODEL
3.1

Plate ModelPrior to the experimental investigation, the transfer mobilities were modelled by modalsummation of a free (FFFF) plate, which corresponds to a resiliently supported reception plate in alaboratory. The plate eigenmodes are expressed as products of orthogonal beam eigenmodes (7). Theplates modelled were of aluminium and the thicknesses were varied between 5-20mm. Dimensions
were varied between 2.8m x 2.0 m and 4m x 3m. The total plate loss factor was assigned a frequency
independent value 0.03. The process, represented by equations (1) to (9), was completed for to givean estimate of source mobility and free velocity squared for each remote point. Figures 2-4 show someof the calculated plate point and transfer mobilities.

FiFigure 2 - Point mobility at measurement centre (red) and transfer mobility from a remotelocation to centre (black).

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Fi

vj

Figure 3 -Transfer mobility from remote location to a contact point.

Fj

Figure 4 - Transfer mobility from a contact point to measurement centre.
3.2

Tested sources
The average point mobility and sum square free velocity were measured for a compact air pump(Figure 5) and for a small fan unit (Figure 6). Also shown are the transfer mobilities between mountpoints, which are lower than the point mobilities. The average point mobilities were taken as the target
quantities to be evaluated by the proposed method.
The free velocities of both sources were tonal with significant low-frequency components, andthe frequency range of interest was 20-2000 Hz.

Figure 5 – Left, pump point and transfer mobilities and average point mobility over four mounts(black line); right, free velocities squared over four mount points and sum-square (black line).
The pump measured source data was for four mount points. The point mobility varies little withmount location and displays a mass-law behaviour below 400 Hz and a stiffness-controlled behaviour
above 400 Hz. The free velocity spectrum is tonal with a fundamental frequency of 25 Hz and firstharmonic at 50 Hz.
The fan measured source data was for four mount points. Figure 6, left, shows the point andtransfer mobilities between mount points. Figure 6, right, shows the free velocity squared at each1235

contact and the sum-square value. The fan point mobility varies significantly with mount location anddisplays resonance behaviour. The free velocity spectrum also is tonal with a fundamental frequencyof 50 Hz and first harmonic at 100 Hz.

Figure 6 - Point and transfer mobilities of fan and average point mobility over four mounts (bla ckline, left) and free velocities squared over four mount points with sum-square (black line, right).
3.3

Results
Figure 7 shows estimates of pump mobility and sum square free velocity from a simulation of
the steps described by equation (1) to equation (6), as modelled for a 10mm aluminium plate. The
average estimates and standard deviations are in one-third octaves and assume a log-normaldistribution. The estimate of mobility tracks the measured value within 5 dB, but with greater
discrepancies above 1600 Hz. The estimate of free velocity squared, from equation (9), is within 10
dB of the measured value at the peaks at 25 Hz and 50 Hz, and at 125 Hz and above. The estimate at
the 100 Hz peak is 15 dB less than the measured value.

Figure 7 - Pump mobility (left) and free velocity squared (right) from modelled 10mm plate:
average from ten remote points (red); standard deviation (dashed); measured (black).
In Figure 8, the estimate of fan mobility is within 5 dB of the measured value, irrespective of thethickness of reception plate. In Figure 9, the estimate of free velocity squared is within 10 dB of thetrue value for the 5mm reception plate, with greater discrepancies for the 20mm reception plate.

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Figure 8 - Fan mobility from modelled 20mm plate (left) and from 5mm plate (right): average often remote points (red); standard deviation (dashed); measured average point mob ility (black).

Figure 9 - Fan free velocity squared from modelled 20mm plate, left, and 5mm plate, right:
average (red); standard deviation (dashed); from measured at four mounts (black).

4. EXPERIMENT
4.1

Set-upFigure 10, left, is a photo of the 5mm aluminium plate (1.96m x 1.22m) supported on resilientpads, with the pump attached. Ten accelerometers are distributed around the measurement centre. An
instrumented impact hammer registered the applied forces for mobility measurements. Figure 10, right,
shows typical ratios of transfer mobilities, for the fan in place and without the fan.

Figure 10 - Left: test arrangement with pump attached; right: ratio of transfer mobilities between
plate with source and plate without source.

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4.2

Results
Figures 11 and 12 show mobility and free velocity squared for the pump and fan, respectively.

Figure 11 - Pump mobility (left) and sum square free velocity (right) from measured 5mm plate:
average (red), standard deviation (dashed), measured (black).

Figure 12 – Fan mobility (left) and sum square free velocity (right) from measured 5 mm plate:
average (red), standard deviation (dashed), measured (black).
The estimated pump mobility is within one standard deviation (approximately 5dB) of themeasured value at frequencies above 63 Hz. The estimated sum square free velocity is within onestandard deviation (10 dB) of the measured value except at frequencies above 1000 Hz.
The estimated fan mobility is within one standard deviation (5 dB) of the measured value atfrequencies between 50 Hz and 630 Hz. The estimated sum square free velocity is within one standard
deviation (10 dB) of the measured value except at frequencies below 50 Hz.

5. CONCLUDING REMARKSThe numerical models and the experimental measurements ‘capture’ the frequency trends ofsource mobility and free velocity squared of both sources.
The numerical model results show that the estimates of source mobility and sum square freevelocity are not dependent on the reception plate dimensions and thickness, i.e. between that of a 5mm
free plate and a 20mm free plate. This has practical implications since it gives the designers oflaboratory test rigs a certain freedom of choice in the selection of plate dimensions and material.
The modelled and measured estimates of pump mobility are more promising than that of thefan. This is because the variation between mount points is smaller for the former than the latter.

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For both the fan and pump, the target measured mobility generally lies within one standard
deviation of the average estimate.
Likewise, the target measured sum-squared free velocity of the fan is within one standard
deviation, but with greater discrepancies away from tonal maxima.
Since the free velocity squared estimates depend on previous estimates of source mobility, thenthe standard deviations of the former are greater than those of the latter.
It is interesting to note that although the estimates are magnitudes, the source quantities initiallywere obtained as complex quantities. The corresponding measurement of transfer mobility to, orvelocity ratio at, the centre location is complex, and it remains to explore what happens if real -value
measurements only are performed.
The experimental investigation did not encounter signal-noise problems, either for the mobility
measurements in stage 1 or for the remote velocity measurements in stage 2.

6. AKNOWLEDGEMENTS
The author is grateful to Carl Hopkins, Head of the Acoustics Unit, for allowing laboratory
space and time for the experimental work, and Gary Seiffert for providing advice and help with themeasurements. Thanks also to Michel Villot, Convenor, and to the members of Working Group CEN
TC 126 WG7 for shared data and experiences on the practical implementation of the reception plate
method.

REFERENCES
1. Gibbs BM., Qi N., Moorhouse AT. A practical characterization for vibro-acoustic sources inbuildings. Acta Acustica united with Acustica, 93, 84-93 (2007).
2. Gibbs BM., Cookson R., Qi N. Vibration activity and mobility of structure-borne sound sources bya reception plate method. J. Acoustical Soc. Am. 123 (6), 4199-4209 (2008).
3. Building acoustics-Estimation of acoustic performance of buildings from the performance ofelements, Part 5: Sound levels due to the service equipment. European Standard BS EN 12354 -5,
European Committee for Standardization, Brussels, Belgium (2009).
4. Acoustic properties of building elements and of buildings – Laboratory measurement of structureborne sound from building services equipment for all installation conditions. European Standard
EN 15657, European Committee for Standardization, Brussels, Belgium (2017).
5. Späh MM., Gibbs BM. Reception plate method for characterization of structure-borne soundsources in buildings: Assumptions and application”, Applied Acoustics 70, 361-368 (2009).
6. Mayr AR., Gibbs BM. Approximate method for obtaining source quantities for calculation ofstructure-borne sound transmission into lightweight buildings. Applied Acoustics 110, 81-90,(2016).
7. Gardonio P., Brennan MM. Mobility and impedance methods in structural dynamics, Chapter 9 inAdvanced Applications in Acoustics, Noise and Vibration, ed. Fahy FF., Walker J., Spon Press,London (2009).

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