Using near-field acoustic measurements to characterise mechanical andacoustic properties of lightweight building structures
Andrea SANTONI(1) , Patrizio FAUSTI(2) , Paolo BONFIGLIO(3)(1) Engineering Department - University of Ferrara, Italy, andrea.santoni@unife.it(2) Engineering Department - University of Ferrara, Italy, patrizio.fausti@unife.it(3) Materiacustica s.r.l., Italy, paolo.bonfiglio@materiacustica.it

Abstract
The evaluation of the vibrational field on a certain surface has a great importance in noise control engineering
applications. It can be helpful, both for noise reduction purposes, and diagnostic purposes, in product optimisation, or in order to characterise the mechanical properties of the vibrating structure. Accelerometers are still
the most used sensors to measure vibration. However, contactless transducers, such as scanning laser doppler
vibrometers (LDV), have been widely used recently, presenting several advantages. Near-field acoustic holography may represent a valid alternative to LDV, in order to reconstruct the vibrational field on a surface fromsound pressure measurements performed with an array of microphones. This paper presents the preliminary
results, of a ongoing project regarding the use of near-field acoustic holography to characterise the elastic andacoustic properties of a lightweight building structure. The used test rig allows to scan the sound pressure overthe vibrating surface on a grid of points, using an array of microphones. The panel’s dynamic response was used
to evaluate its elastic properties. The reliability of this experimental approach was assessed by comparing theresults with the ones obtained using miniature accelerometers. These elastic properties were finally used as input
data to model sound transmission through the plywood panel using the transfer matrix method, investigating theaccuracy by comparing the numerical results with the experimental sound insulation.
Keywords: near-field acoustic holography, building acoustics, mechanical characterisation, structural wavenumbers

1

INTRODUCTION

Nowadays, lightweight solutions are increasingly employed in building construction, as in many other fields
of engineering, since they present several advantages compared to traditional massive systems. However, sincethese systems cannot rely on their mass to provide a satisfying sound insulation, it is necessary to properly
design and optimise each building partition, in order to guarantee a comfortable indoor environment, providing
an adequate acoustic performance [1, 2, 3, 4]. Several models have been proposed by different authors in orderto accurately predict sound radiation from and sound transmission through building partitions [5, 6, 7, 8, 9, 10].
To this purpose, the elastic properties of the materials the considered partition is made of are required as input
data by all the different vibro-acoustic simulation models [11]. Several experimental methods can be used inorder to evaluate the mechanical characteristics of the different elastic or viscoelastic materials employed inbuilding construction [12, 13, 14, 15]. Lately, wave correlation approaches have been successfully adopted inorder to determine the experimental wavenumber dispersion relation, which can be used to evaluate the elastic
and the damping properties of the investigated structure [16]. In order to apply such methods, the dynamic
response of the investigated structure due to a broadband mechanical excitation needs to be measured along
a line of equally distributed points. Measurements of the vibrational filed are commonly performed by using
accelerometers attached to the surface of the vibrating structure. By using miniature transducers, it is possible
to investigate a wide range of materials, even though contactless transducers are sometime preferred, in order
to avoid any small influence of added masses on the dynamic response of very lightweight elements. Besides,
the measurement performed by using accelerometers requires a great time effort in order to have a good spatial1302

resolution. By using a scanning laser doppler vibrometer (LDV), having the possibility to automatically movethe laser beam over the different grid points, the time required to measure the dynamic response over theentire surface can be drastically reduced. Moreover, it also allows to overcome the issue of the influence ofadded masses on the dynamic behaviour of the investigated structure. By using near-field acoustic holography(NAH) [17, 18] or very-near-field acoustic holography [19], it is possible to reconstruct the structural dynamic
response from acoustic measurements, performed with an array of microphones. Such experimental approach
can be used in order to measure the dynamic response of a given structure by using contactless transducer, as avalid alternative to optical-based approaches. The good agreement of NAH measurements compared to standard
LDV was proven by Martarelli and Revel [20], also highlighting the advantages and disadvantage of these two
methods.
In this study, a plywood panel was experimentally investigated, by using a test rig specifically designed tocharacterise the dynamic behaviour of lightweight building partitions. The dynamic response of the structure
was determined by using an array of microphones as described in section 2. By using a wave correlation
approach, the wavenumber dispersion relation, associated to a given propagation direction was evaluated. Fromthe vibrational field measured over a line of points it was possible to evaluate the velocity of the structural
wave propagating in that direction, which in the case of a point-force mechanical excitation, is strictly related
to elastic properties of the investigated element. The reliability of the results has been determined by comparing
the wavenumber dispersion relations and the elastic properties derived from sound pressure measurement withthe results obtained form accelerometers, as discussed in section 3. The evaluated elastic properties were finallyused as input data to model sound transmission through the plywood panel by using the transfer matrix method.
The accuracy was investigated comparing numerical results with the experimental sound insulation. Finally, thepossible future developments of this approach are discussed, since it offers several possibilities for a complete
vibro-acoustic experimental characterisation of lightweight structures: for example the experimental evaluationof the damping properties, or the resonant radiation efficiency [21] of the investigated structure.

2

EXPERIMENTAL MEASUREMENTS

2.1 Experimental Setup
The used test rig is constituted by a steel frame, in which a small rectangular sample, with a surface area ofapproximately 1 m2 (Lx = 0.98m, Ly = 1.18m), can be installed. Two moving parts allow the investigated plate
to be held in place by clamping all the four edges, as shown in Figure 1(a). The height of the frame can be adjusted in order to place a shaker, representing the exciting source, underneath the panel. A two-direction sliding
carriage, hosting 9 microphones, is mounted on the top of frame, as shown in Figure 1(a,b). The shaker needs
to be encapsulated within a wooden box, internally lined with porous material in order to reduce the sound field
generated by the shaker, which could influence the measurements. It was rigidly attached to the investigatedstructure, a 15 mm thick plywood board made of 5 thin plies with density ρ = 400Kg/m3 , and driven witha 10 seconds exponential sine sweep from 20 Hz up to 6000 Hz. In order to evaluate the dynamic responseof the investigated plate, the sound pressure was measured by using 9 PCB 1/200 microphones simultaneously,
placed at a stand-off distance r from the radiating surface, as shown in Figure 1(c). The microphones werepreviously calibrated in amplitude, by using a B&K type 4231 sound level meter calibrator. By installing animpedance head between the shaker stinger an the panel’s surface it was possible to obtained the input force
and acceleration of each single measurement. All the acquired signals - force, acceleration and sound pressure- were then convolved with the inverse filter of the sine sweep to obtain the impulse responses (IR) of thatparticultar suorce receiver configuration [22], a well established experimental technique widely used in room
acoustics [23]. In order to guarantee the same relative phase relationship between the signals acquired by nonsimultaneous measurements, the IR associated to each input channel was aligned in time with a reference IR,
represented by the force signal of the impedance head transducer, placed on the shaker’s stinger. The complex
spectra of the IRs were obtained by means of a fast Fourier transform algorithm.

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(a)

(b)

(c)

∆xarray∆xarray∆xexprRadiating Surface

Figure 1. Test rig for the mechanical characterisation of lightweight panels: (a) exploded diagram of the testing
frame and the scanning microphone carriage; (b) views of the the scanning microphone carriage; (c) digram ofthe sound pressure scanning system.
2.2 Material characterisation
The set of measured IRs can be used in order to evaluated several physical properties and acoustic descriptorsof the investigated structure, such as its elastic and damping properties, its resonant radiation efficiency andthe point mobility. The results presented in this paper are focused on the determination of the panel’s elastic
properties from sound pressure measurements. Many different techniques can be used to determine the elastic
properties of a structure, based either on resonant methods [13], or on wave propagation analysis, performed
both within the audible frequency range [24] and in the ultrasound domain [25]. However, the wave correlation
approches [16, 26] are particularly suitable to the experimental setup presented in the previous paragraph. The
wavenumber dispersion relation can be obtained by maximasing the correlation function between the structuraldynamic response, measured along a line of equally spaced positions with a propagating wave. One of the mostcommonly used approaches is known as inhomogeneous wave correlation method (IWC) [27]. This method
was applied in order to evaluate the elastic properties of the investigated plywood panel. The panel’s dynamic
response was evaluated from sound pressure IRs measured on a number of points in line with the excitation
position, equally spaced at ∆x = 2.5 cm apart, along the two principal directions. For each angular frequency
ω the complex spectra w̃ (ω, x) is correlated to an inhomogeneous propagating wave õ (x, kr , ki ) = −i (kr + iki ) x,
by the function:∑Ni=1 w̃ (ω, xi ) õ (xi , kr , ki )I (kr , ki ) = q(1)
22∑Ni=1 |w̃ (ω, xi )| ∑Ni=1 |õ (x, kr , ki )|The structural wavenumber is determined by maximising the function I (kr , ki ) given in Eq. 1. The real partkr of the complex wavenumber is strictly associated to the elastic properties of the panel, while its imaginary
part ki is proportional to the structural damping. Being interested in the panel elastic characteristics, rather thenin its damping, the imaginary part has been neglected: ki = 0.

3

RESULTSThe elastic properties of the investigated panel were determined by fitting the experimental wavenumbers, obtained from the wave correlation approach described in the previous section, with the analytical dispersion curve

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100
k sound pressure
90

k acceleration
k p,fit,M80

k a,fit,Mwavenumbers [rad/m]

70

k p,fit,K

60
50
40
30
20
10
0
0

500

1000

1500

2000
2500
3000
frequency [Hz]

3500

4000

4500

5000

Figure 2. Comparison between the experimental wavenumber dispersion relation determined by using the wave
correlation approach from sound pressure measurement k p and acceleration measurements ka , and between the
curves obtained by analytical fitting ki, f it, j .
derived from Mindlin’s theory for thick plates.
" 2 #kS(kL kS )24
2
2
kM − kL +kM− kK4 +
=0
T
T2

(2)

where kL and kS represents respectively the longitudinal and shear wavenumber propagating in the plate, T is acoefficient to take into account that the shear stress is not constant over the panel cross-section and kK is givenby the Kirchhoff’s dispersion relation for thin plates:r√ 4 12ρh (1 − ν 2 )kK = ω
(3)
Eh3
Moreover, in order to evaluate whether the thin plate assumptions are verified for the investigated structure
within the entire frequency range, the experimental wavenumeber were also fitted with Kirchhoff’s dispersion
relation, given in Eq. (3): were ρ is the panel density, h its thickness, ν its Poisson ratio and E the elastic
modulus, which represents the fitting parameters.
In order to reconstruct the vibration velocity field from the sound pressure measured in the vicinity of the panel
surface an adequate transfer function should be applied. However, as first approximation the wave correlation as
been applied directly on the sound pressure IRs measured along a line of points. A first validation of the method
is performed by comparing both the experimental and the fitted wavenumber dispersion relation obtained fromsound pressure measurements, with the results obtained from acceleration measurements. As show in Figure 2,
a good agreement is found between the two experimental data set. In both cases are evident some fluctuations,even though it is possible to accurately fit the experimental wavenumbers with the analytical dispersion relation,
obtaining consistent curves. Moreover, a good agreement is also found between the dispersion relations obtainedby the fitting procedure of the experimental data by using Eq. (2), k p, f it,M , and Eq. (3), k p, f it,K ; proving thatthe thin plate theory is suitable to describe the plate motion within the investigated frequency range.
In order to asses the influence of the stand-off distance, the sound pressure IRs were measured both at 5 mm
and at 20 from the panel’s surface. As shown in Figure 3, no significant difference were found by comparing

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100
k stand-off = 5mm
90

k stand-off = 20mm
k 5mm,fit

80

k 5mm,fit
wavenumbers [rad/m]

70
60
50
40
30
20
10
0
0

500

1000

1500

2000
2500
3000
frequency [Hz]

3500

4000

4500

5000

Figure 3. Comparison between the wavenumber dispersion relations determined by using the wave correlation
approach from sound pressure measurements performed at 20 mm and at 5 mm from the panel surface.
the experimental and the fitted dispersion relation obtained from this two sets of measurements. However, inorder to further investigate the influence of the stand-off distance it is necessary to analysis the reconstructedvelocity field over the panel surface.
At this stage of the study, the main goal was to characterise the structure’s elastic properties in order to determine the input data required for vibro-acoustic simulations. The structural wavenumbers were investigatedalong both the plate’s principal directions, in order to take into account a possible orthotropic behaviour. The
elastic moduli obtained from the three different set of measurements are reported in Table 1. A good trend wasTable 1. Elastic modulus of the plywood plate obtained from wavenumber fitting.
Ex,p,20mm [Pa]2.29E+09

Ex,p,5mm [Pa]2.21E+09

Ex,acc [Pa]1.96E+09

Ey,p,20mm [Pa]2.01E+09

Ey,p,5mm [Pa]2.06E+09

Ey,acc [Pa]1.65E+09

found between the elastic moduli obtained from sound pressure and acceleration measurements, highlighting asoft orthotropy, with the elastic modulus along the x−direction slightly higher than the value determined along
the y−direction. Even though the wave correlation performed on sound pressure IRs slightly overestimate theresults compared to the data obtained from acceleration measurements. In order to evaluate the influence ofsuch this deviation on the transmission loss (TL), these values were used as input data in a sound transmission
simulation based on the transfer matrix method (FTMM) [28, 29]. In order to validate the numerical results, thesound insulation provided by the investigated panel was experimentally measured into the sound transmission
test facility for small elements of Adler Evo acoustic laboratories, in Turin, Italy. Two sources were used togenerate the incident sound field within the reverberant emission room, driven with a white noise signal. The
sound pressure exciting the plate was measured by means of two rotating microphones, while, on the semianechoic receiving side, the radiated sound intensity was measured by scanning the panel’s surface with a p-p
probe. The plate TL was determined as:
T L = L p,1 − Li − 6(4)where L p,1 = 20 log (p1 /p0 ) is the sound pressure measured in the emitting room (dB re 20µPa) and Li is

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40
TL exp35

TL exp,1/3cotave band
TL FTMM,20mm

30TL FTMM,5mm[dB]
L = 10log

TL FTMM,acc
25
20
15
10
5
0
300
frequency [Hz]3000

Figure 4. Comparison between the experimental transmission loss of the plywood panel and the numericalresults calculated using as input data the elastic properties presented in Table 1
the sound intensity level measured on the receiving side (dB re 10−12 W). As shown in Figure 4 the FTMM
results well approximate the experimental TL over the entire investigated frequency range, except in the very
low frequencies where the structural resonances, which are not considered by this prediction method, governsound transmission, and the critical frequency region when a greater contribution of the damping is shown by
the experimental results. Comparing the three numerical curves, only small discrepancies are highlighted, witha maximum deviation lower than 3 dB in the 1600 Hz third-octave band.

4

CONCLUSIONSIn this paper, the early-stage results of a broader study, regarding the use of the near-field acoustic holography
for the mechanical and acoustic characterisation of lightweight building structure, are presented. The reliabilityof this approach is investigated in order to provide a valid contactless alternative to vibration measurements
performed by using a laser doppler vibrometer. The elastic properties of a plywood panel were evaluated fromthe structural wavenumbers propagating along a certain direction, determined by means of wave correlation
approach, from the sound pressure IRs measured in the vicinity of the vibrating surface. The accuracy ofthis experimental technique was evaluated by comparing the results with the elastic properties obtained fromacceleration measurements. The comparison showed a good agreement, with small discrepancies. In fact, theelastic modulus determined from sound pressure measurements only slightly overestimates the value obtained
from acceleration measurements. However, when the elastic constants are used as input data to calculate thepanel transmission loss, these deviations did not affect significantly the computed results. This was verified bycomparing the panel TL compute using a model implemented within the transfer matrix method framework withthe experimental sound insulation of the plywood plate.
Even tough the first stage of this study showed promising preliminary results, further investigations are requiredin order to assess the reliability of the presented methodology. The wave correlation approach should be applied
to the velocity field reconstructed from the measured sound pressure, also considering the imaginary part of thestructural wavenumber, other than the real one, in order to obtain information regarding the structural damping.
Moreover, other quantities can be computed from the velocity field over the vibrating surface, such as the1307

radiated sound power.

ACKNOWLEDGEMENTS
Some of the data presented in this paper were measured in the acoustic laboratory of Adler Evo in Villastellone,
Turin, Italy. We would like to acknowledge Maurizio Tarello and Massimiliano Tiengo for their availability andthe support they gave us.

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