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

Numerical simulation of CLT floors and comparison with empiricalpredictive models and measurements
Marco Caniato1; Federica Bettarello2; Andrea Gasparella11Free University of Bozen, Italy
2

University of Trieste, Italy

ABSTRACT
Wooden constructions are becoming more and more present in the global building market. They are built
very quickly, combining structural and thermal performance in a single layering. They are industrially
produced and then assembled on site to minimize building yard problems and increase construction speed.
In this scenario, acoustics is often not addressed or is delegated to additional layers that are often inserted
without a studied ratio. Many studies have been carried out to predict the acoustic behavior of walls andfloors using numerical or empirical methods. Recently, by means of validation with in situ measurements,
the acoustic behavior of raw wooden partitions has been defined with empirical or semi-empirical laws. In
this work, a new method for the determination of the floor noise of raw CLT floors comes through the use ofnumerical simulation with transfer matrices. Then, the results are compared to the available empirical
forecasting models and real measurements.
Keywords: Cross Laminated Timber; Impact force; Impact noise; Transfer method matrix; numericalsimulation

1. INTRODUCTION
Over the years, timber buildings have become a reference point for new sustainable, lightweight,
prefabricated and energy-saving buildings. The growing environmental awareness of ordinary people,
as well as of designers and builders has enhanced the popularity of these buildings have in both theEuropean and Italian scenarios.
However, the increasing presence of wooden buildings has posed a series of questions about how
such buildings can and should be designed. In the field of acoustics, few innovations in design
methods have been introduced in recent years for this type of element. For example, in the revision of
the ISO 12354 series of standards [1,2] in 2017, little more information, based on laboratory
experience [3], was included as regard to timber elements for airborne and impact noise.
The classic numerical modelling approaches, often used for heavy constructions in the traditional
system, are advantageous for predicting the acoustic behavior of homogeneous walls or walls with anaddition of few layers. Moreover, the methods used today relate to well-defined products or layers
and are not extensible to different geometries, shapes or layers. The only versatile and generalizable
mathematical model is that of progressive impedances, which, as has already shown [4,5], is effective
until the succession of layers does not become too complex or does not include rigid connections
between different layers. However, this method only applies to airborne noise insulation and not to
impact noise forecasting. In the timber buildings research related to numerical simulation , many
attempts have been made, using Combined Finite Element FE and Statistical Energy Analysis SEA
dedicated exclusively to wood components [6], as well as mathematical models of both floors andceilings [7] and impact sources modelling [8]. Many simulations have been validated for specificcases both in the laboratory and in the field [9], but no general method has been applied so far for theprediction of the reduction of impact noise on timber floors made of Cross Laminated Timber (CLT).
1
2

marco.caniato@unibz.it; andrea.gasparella@unibz.it
fbettarello@units.it

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In fact, for the determination of impact noise reduction, the formula provided by the international
standard [2] is usually used, which provides for the knowledge of the bare floor noise the resonancefrequency of the floating floor according to eq. (1)‫ܮ‬௡ ൌ ‫ܮ‬௡ǡ଴ െ  ο‫ܮ‬௡
(1)where ‫ܮ‬௡ is overall impact noise (dB), ‫ܮ‬௡ǡ଴ is the noise produced by the bare floor (dB) and ο‫ܮ‬௡
is the impact noise reduction provided by a floating floor (dB).
The determination of such parameters is not always immediate. The standard provides a forecast
formulation for solid concrete slabs or beam and pot type slabs, but not a model for timber slabs. In
addition, it has been demonstrated that the reduction of theoretical impact noise cannot be applied tosuch lightweight structures, because the relationship between mass - spring - infinite mass is notrespected.
One possible method of investigation is the use of transfer matrices (TMM). Using this technique,in fact, the addition of layers, structural connections and impact sources of different nature is easy to
implement. Within this numerical simulation, it is also possible to make use of the equivalenthomogeneous medium technique. This method allows adding additional layers to the basic structure,modifying its mechanical properties in frequency and incorporating the properties of the second layer
within the first, which becomes an equivalent homogeneous medium that has acoustic characteristics
formed by the superposition of the two layers. With the addition of another layer, the procedure isrepeated until all layers are considered [10]. The use of the equivalent homogeneous medium provides
clear advantages as long as you know all the acoustic properties in frequency of the materials used.
However, if these characteristics are not known and if you want to proceed to an optimization of thegiven stratigraphy, the equivalent medium is not a good choice, because it will incorporate all thecharacteristics of the various layers into a single equivalent one, not allowing the study of single
influences.
For these reasons, the purpose of this work is to use the TMM method without the use of equivalent
media and to verify its possible application first to the impact noise generated by a bare CLT floor
and then to the complete structure with floating floor. The numerical simulations have been comparedwith previous experimental measurements by the authors, using a standard ISO tapping machine on 6
different bare floors and the equivalent complete structures.

2. MATERIALS AND METHODSA TMM model was implemented to investigate the impact noise produced by (i) a bare CLT floorand (ii) a complete CLT with the addition of a floating floor.
CLT floors are composed by 5-ply panels of a total thickness of 18 cm, with area of 3 m x 4 m.
The acoustic and mechanical properties of the used materials are reported in Table 1.
Table 1 – Acoustical mechanical parameters
Young’s

Density

Poisson Ratio

Damping

Thickness

Modulus [GPa][kg/m3]

[-]

[-]

[cm]

CLT

11

450

0.01

0.02

18

Foamed screed

0.8

500

0.01

0.01

10

Resilient layereq. (2)

30

0.20

0.40

1

Heavy screed

25

1500

0.01

0.01

5

MediumFor the determination of the Young’s Modulus of the resilient layer, the equation (3) was used,
inverting the impact noise reduction model ('Ln):ଶ݂ήʹήߨ‫ ܧ‬ൌ  ൭ '௅ ൱ ή  ݉ᇱ ή ݀
೙
ͳͲ ଷ଴

(2)

where ݂ is the frequency of the excitation [Hz], ݉ᇱ is the mass per unit area of the heavy screed

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[kg/m2 ] and ݀ is the thickness of the resilient layer [m].
In a general TMM simulation, the materials within the various coupled layers are assumed in thefirst instance to be infinite in the lateral direction, possibly leading to a significant differences between
the measured values and the simulated ones, especially at low frequency. This has been avoided byusing the windowing with finite limitations [13].
In order to reproduce the measurement correctly, the right impact force by single hammers has tobe determined. In literature, for a perfect homogeneous rigid floor Cremer and Heckl [13] proposed amodel for this force using the hypothesis that a perfect rebound was verified. In the present research,
this cannot be assumed, because the interaction between the hammer and the timber floor will not
produce such rebound. In literature, it could be found that a hammer impacting timber structures
provides a bell-shaped frequency trend, so that such trend is more reliable for simulation purposes
than a linear one [15]. In a more recent view, Lietzén et al. [16] highlighted the difference between
the impact force imposed by a hammer of the tapping machine on a bare timber CLT floor from theone on a concrete floor. The first one is linear only at low frequencies and then it assumes a logarithmic
drop from the middle-high range. In the second case, the force shows a linear progression, but in avery reduced range, compared to the timber one.
For these reasons, a punctual stimulus was chosen as an acting force, modeling individually thehammers of the ISO tapping machine, using a variable imposed force in frequency (Figure 1).
Conversely, when applying the impact stimulus to a heavy screed, the perfect rebound hypothesis
is more appropriate and a linear trend is preferred (Figure 2). All the forces were derived from thecomparison of the measured trends with the simulated ones. The models where then adjusted to fit theagreement between measured and simulated trends, in order to verify the initial hypothesis related to
the force variation in frequency.

Force trend on timber
2.5

Force [N]

2.0
1.5

1.0
0.5

4000

3150

2500

2000

1600

1250

800

1000

630

500

400

315

250

200

160

125

100

0.0

frequency [Hz]Figure 1 – Frequency spectrum of the imposed punctual stimulus for bare timber floor

Force trend on heavy screed
2.5

F [N]

2
1.5

1
0.5

4000

3150

2500

2000

1600

1250

1000

800

630

500

400

315

250

200

160

125

100

0

frequency [Hz]Figure 2 – Frequency spectrum of the imposed punctual stimulus for bare timber floor

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3. RESULTS AND DISCUSSION
In this section, the reliability of the proposed TMM numerical simulation is compared withmeasured results.
The measured impact noise frequency trend is reported in Figure 3. In Figure 4 the averagemeasured trend with the corresponding uncertainty is compared to the literature one for a 25 cm barefloor [11]. As it is evident, at medium-high frequencies, the two trends are in good agreements, while
for lower ranges the influence of the thickness is highlighted. This result is in agreement with previous
studies [12].

Frequency trend - measured
100
90

Ln (dB)

80
70
60
50
40

5000

4000

3150

2500

2000

1600

1250

1000

800

630

500

400

315

250

200

160

125

100

30

frequency [Hz]
1

2

3

4

5

6

Figure 3 – Impact noise frequency trend of the measured bare CLT floors

5000

4000

3150

2500

2000

1600

1250

1000

800

630

500

400

315

250

200

160

125

100
90
80
70
60
50
40
30
100

Ln (dB)

Frequency trend - average 18 cm vs.
literature 25 cm

frequency [Hz]average 18 cm

literature model 25 cm

Figure 4 – Average impact noise frequency trend compared to literature one
In Figure 5, the impact noise frequency trend of the complete structure with floating floor isreported.
In Figure 6 the comparison between the ο‫ܮ‬௡ measured and calculated values is reported,
highlighting how the traditional and most used formulation for the sound reduction of impact noise
could not be applied to timber floors. It is worthy to note that the ο‫ܮ‬௡ values obtained by themeasurements really differs from the one forecastable by the Cremer equation [17]. This result5032

strengthens the thesis that a variable force in frequency has to be used , coupled with a punctual noise
source.

complete measured structure
100.0090.00

Ln (dB)

80.00
70.00
60.00
50.00

40.00
5000

4000

3150

2500

2000

1600

1250

800

1000

630

500

400

315

250

200

160

125

100

30.00

frequency [Hz]Figure 5 – measured impact noise on complete floor

comparison of different 'Ln
60.0

50.0
40.0

30.0
20.0
10.0
4000

3150

2500

2000

1600

1250

1000

800

630

500

400

315

250

200

160

100

125

0.0

frequency [Hz]Cremer model

measured

Figure 6 – comparison between measured and calculated ο‫ܮ‬௡ values for complete floor
In Figure 7, the comparison between bare floor numerical simulated values and measured ones isreported, while in Figure 8 the same procedure was applied to complete structure. Even though several
approximations are made, especially regarding the determination of the exciting force, a satisfying
agreement is found.

Comparison between simulated and measured
values - bare floor
100.0
90.0

Ln (dB)

80.0
70.0
60.0

simulation

50.0

measure

40.0
100
125
160
200
250
315
400
500
630
800
1000
1250
1600
2000
2500
3150
4000

30.0

frequency [Hz]Figure 7 – comparison between measured and calculated values for the bare floor

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Comparison between simulated and measured
values - complete floor
7060

Ln (dB)50
40
30

simulated20

measured

10

4000

3150

2500

2000

1250

1600

800

1000

630

500

400

315

250

200

160

125

100

0

frequency [Hz]Figure 8 – Comparison between measured and calculated values for the complete floor

4. CONCLUSIONSIn this work, a TMM approach is applied to CLT floors, for the determination of impact noise.
Measurements and numerical simulations are performed both on a bare structure and on a complete
one, adding a floating floor.
A study on the force of tapping machine hammers is performed, because the impact impinged on
the CLT bare floors (non-perfect rebound) is not equal to the one on the heavy screed (perfect rebound).
For his reason, a punctual and frequency depending excitation is used in TMM simulation, in order toemulate the real behavior of the noise source.
Furthermore, a frequency dependent Young’s modulus is associated to the resilient layer, basing
on the inverse formula of the noise reduction.
The vibroacoustic response of the bare CLT panel is computed by means of a TMM numericalsimulation, in order to evaluate the impact noise level generated by a standard tapping machine, using
a bell-shaped frequency dependent punctual force excitation. Even though an approximate approachis used to determine the force spectrum, good agreement was found between numerical andexperimental data. The same procedure, but with a linear frequency trend punctual force , is applied
to complete structure, achieving again a good agreement between the two procedures.
Thus, the validation of the simulations demonstrates how TMM could be used to determine theimpact noise of CLT bare and complete floors, using a frequency depending punctual excitation anda frequency dependent Young’s modulus related to the resilient layer.

ACKNOWLEDGEMENTS
This work was funded by the Project “Klimahouse and energy production”, in the framework of
the programmatic-financial agreement with the Autonomous Province of Bozen-Bolzano of Research
Capacity Building. Special thanks to Dr. Paolo Bonfiglio from Materiacustica srl, Ferrara, Italy.

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