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

Determining the airborne sound insulation improvement of thermal
cladding systems in combination with heavyweight exterior walls
Claire CHURCHILL1; Maximillian NEUSSER2; Simon HINTERSEER3
1 TU Wien, Austria
2 ACOM Research, Austria
3 TU Wien, Austria

ABSTRACT
Prediction of the sound insulation (SI) of modern thermal insulation systems for exterior walls is
considered. These products all have in common a lightweight insulating layer of primarily thermalfunction (which may consist of a porous or non-porous material), and a weatherproof finish; thesystems measured in the laboratory included a grout and skim finish or a prefabricated cladding
system. In all cases, a typical heavyweight exterior wall was cladded. Modern examples of such
systems are ETICS (External thermal insulation composite systems) and curtain walls. In theirsimplest form, such cladding systems can be modelled as a spring-mounted mass. However,Austrian standards demand that the spring-mounted layer be combined with structural fixings. In
the examined cases sparse distributions (up to 12 connections/m2) of point connections were used.
The SI of simplified and typical thermal cladding systems (i.e. with and without structural fixings)
were measured in an accredited laboratory facility and these results were compared with acalculation method to determine SI. The possibility of using established methods to determine thecoupling loss factors in such combined systems was considered. The structural wall is ofheavyweight construction, and the SEA problem can be simplified to a primary path analysis.
Keywords: SRI, thermal cladding, insulation

1. INTRODUCTION
Current state of the art to determine accurate sound insulation data for heavyweight
thermally clad exterior wall systems in Austria is to methodically measure each system or todetermine an airborne sound insulation improvement (1) (Annex B) and sum it with a basewall construction. The potential exists to establish a model that can predict the soundinsulation (SI) of thermal insulation systems for exterior walls. Prerequisites of a prediction
model are flexibility and general applicability; providing a planning tool with current data
for modern systems. In the historical development of such systems, insulation thicknesses ofbetween 40mm and 80mm (typical in the 1980s) have risen to more frequently used 200mm
to 300mm thicknesses today, due to significantly higher thermal insulation requirements.
Refurbishment can also include the application of thermal insulation to an exterior wall ofan old building with the intention of improving building physics parameters and the added
benefit of an enhanced architectural appearance.
All such systems have in common a typical heavyweight exterior wall cladded with alightweight insulating layer (of primarily thermal function which may consist of a porous or
non-porous material), and a weatherproof finish; This finish can be a grout and skim or aprefabricated cladding system. Modern examples of such systems are ETICS (External
thermal insulation composite systems) and curtain walls. In their simplest form, suchcladding systems can be modelled as a spring-mounted mass. However, in the real world,
Austrian (2) (and European (3)) standards demand that the spring-mounted layer be
Claire.churchill@tuwien.ac.at
Maximilian.neusser@acom-research.eu
3 Simon.hinterseer@tuwien.ac.at
1
2

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combined with structural fixings.
The SI of simplified and typical thermal cladding systems (i.e. with and without structural
fixings) were measured in an accredited laboratory facility and these results are comparedwith calculation methods to determine SI. The project work is framed by an underlying desire
among participating manufacturers to augment a single-figure weighted sound-reduction
index (RW) with frequency-dependent data. The structural walls are all of heavyweight
construction. The systems were measured in an accredited Austrian laboratory and werecompared with simple modelling methods.

2. SAMPLE DESCRIPTIONS
A 320mm brickwork wall constructed from rockwool filled cellular brickwork was clad with
160mm expanded polystyrene (EPS) with varying detail. Two thickness of weatherproof layer
were used and sparse distributions (up to 12 connections/m2 ) of point connections wereconsidered. Five samples and the base wall were examined. The constructions are
summarized in table 1.
Table 1 – Wall samples (1for this construction a calculated result only is presented)
EPS thickness,

Render thickness,

Number of anchors,

mm

mm

/m2

320mm cellular brickwork

--

--

--

320mm cellular brickwork

160

10.2

--

320mm cellular brickwork

160

3.9

--

320mm cellular brickwork

160

10.2

6

320mm cellular brickwork1

160

10.2

10

320mm cellular brickwork

160

10.2

12

Base wall

To measure the acceleration level difference, small samples consisting of one EPS plate(dimensions 1000 mm x 500 mm) were attached to the brickwork wall and a thin layer ofrender <4.0mm was applied. Four small samples each with increasing percentage areas ofadhesive covering were compared to assess the effect of differences in the glue layer. The
coverings were 100%, 70%, 40% and 20% of the area of the EPS panel.

3. CALCULATION METHODS
3.1

Non-resonant path

The non-resonant path through the heavyweight wall was defined using (4):𝜂 =𝑐 𝑆
2𝜌 𝑐 𝐾4𝜔𝑉 𝜔(𝜌 𝜌 𝜔 − 𝐾(𝜌 + 𝜌 ))(1)

Where c 0 is the speed of sound in air, S is the surface area of the wall, ω is the angularfrequency, Vi is the volume of the adjacent room, ρ 0 is the density of air, K is the dynamic
stiffness per unit area, ρ i and ρ j are the mass per unit area of the coupled plates. This formula
is typically used to define an air spring but is equally applicable to any spring attachedelement to the wall. In this case, the spring stiffness of the resilient material layer and thespring stiffness of point (or line) fixings can be summed in parallel (4).

3.2

Resonant path

The resonant path was defined using a point connection model described in Hopkins (5)and Craik et. al. (6):𝑟Re{𝑌 }𝜂 =(2)
𝜔𝜌 𝑌 + 𝑌 + 𝑌
Or an area spring defined by (7):

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𝜂 =

|𝑌 |
1
1
Re
𝜔𝜌
𝑌 |𝑌 + 𝑌 |(3)

Where in each case r s is the number of point connections per unit area Yi and Y j are thepoint mobilities of the plates and Y c is the connector stiffness defined by Hopkins (5):
𝑌 =

𝑖𝜔
𝐾

(4)

Where K is the dynamic stiffness in the case of eqn. (2) or the dynamic stiffness per unit
area in the case of eqn. (3). In the latter case, the spring stiffness of the resilient material
layer and the spring stiffness of point (or line) fixings could be considered to act in parallel
to sum the total stiffness. This allows for the wall covering to be attached by spring
connections. An alternative expression for the resonant path was proposed by Neusser et. al.
(8) from Vigran (9):𝛥𝑅 = −10 ∙ lg

𝜔
𝜔

+𝑟

𝑢 .
𝜎
〈𝑢 〉 ,(5)

Where ω 0 is the angular frequency of the mass-spring-mass resonance, r is the number ofpoint connections, ũ 22,B is the r.m.s velocity on the point connections, <ũ 2 1> is the mean r.m.s
velocity on the surface of the render and σ B,point is the radiation efficiency of the plate due tothe point connections given by Vigran (9):𝜎 ,=2𝑐 1 1𝜋 𝑆𝜔

(6)Where ω c is the critical angular frequency of the plate. The second term in eqn. (5) isequivalent to Craik´s coupling loss factor between the heavyweight wall and receiving room
(4):
𝜂 =

2𝜌 𝑐 𝑟𝜋 (𝜌 + 𝜌 ) 𝜔(7)

One underlying assumption of eqns. (5) and (7) is an infinitely stiff connection between
the heavyweight wall and the lining. It would therefore be conceptually incorrect to sum inparallel the spring stiffness of the point connectors in a calculation of non-resonanttransmission as described in section 3.1 when using these methods. However, this possibility
may not be completely excluded in the case of measured velocity level data (eqn. 5). A
comparison of the methods was made and the results are shown in section 0.

3.3

Path analysis

An analysis is made using a “path-by-path” analysis which defines the energy level
difference between two subsystems according to Craik (4):𝐸𝜂 𝜂 …𝜂
=𝐸𝜂 𝜂 ⋯ 𝜂()(8)

Where ηi are the total internal loss factors and η ij are the coupling loss factors. This isused to obtain the velocity level differences or sound reduction index respectively forcomparison with measured results.

4. MEASUREMENT METHODS
4.1

Acceleration level difference

The acceleration level difference between the brickwork wall and the render on several
small samples was measured using a shaker and pair of accelerometers. Three source
positions and eight accelerometer positions per source were used. (It was not possible to excite
one side of the wall with an airborne source because the measurements were not made in an
enclosed space.) The shaker was attached to the opposite side of the brickwork wall from thesamples using a screw thread and metal rawl plug. A MLS excitation signal was used. The
accelerometers on the brickwork wall were attached to the wall on the same side as the small

251samples. Only the acceleration level difference above 400Hz was of interest, therefore, theminimum distance between measurement positions, between the shaker source andmeasurement position, or between the measurement position and the edges of the sample was
100mm. A Norsonic 840 was used to acquire the level difference. The sample size was one
EPS plate (dimensions 1000 mm x 500 mm).

4.2

Sound insulation measurement

The sound insulation was measured according to ISO 10140-2 (10) in an accredited test
laboratory at TGM faculty of acoustics and building physics.

5. RESULTS
5.1

Velocity level difference

Acceleration/velocity level difference (dB)

A comparison of measured and calculated velocity level difference is shown in Figure 1.
(Note that the measured acceleration level difference is a ratio, and in this case may be usedinterchangeably with the velocity level difference (5).) Equations (3) and (5) are used to
calculate velocity level difference across the whole frequency range. The amount of adhesive
used to attach the EPS insulation affects the spread of the measured acceleration level
difference especially in the vicinity of the mass-spring-mass resonance frequency, f 0 . The
collective standard deviations of the measured results are shown in Table 2.

Figure 1 – Velocity level difference. The solid line ‘–‘ corresponds to the results obtained using
eqn. (3) and the dashed line ‘--‘ to eqn. (5)Table 2 – Combined standard deviations with 100%, 70%, 40% and 20% glue surface
Freq. (Hz)

315

400

500

630

800

1k

1.25k

1.6k

2k

2.5k

3.15k

4k

5k

s.d. (dB)

4.6

4.9

5.1

6.1

5.2

5.2

5.0

4.7

3.9

4.6

4.3

3.7

3.7

Agreement between measured and calculated results is poor at high frequencies (>630Hz)
for a thin render (3.9 mm). This corresponds with poor agreement with SI in the model (seeFigure 3). (Note that the dynamic stiffness of the EPS in the small samples is not yet verified.)

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5.2

Sound insulation measurement (SI) and improvement (ΔR)

5.2.1 320 mm brick wallSound reduction index (dB)

The first step was to make a calculation for the base wall (320 mm brickwork). In themodel the longitudinal wavespeed ( c L,p) of the brickwork was estimated to be 2300ms -1 (5)and the surface density of the brickwork ( ρ) was calculated to be 231 kgm-2 from the mass of
one block. The results from measurement and calculation are shown in Figure 2.

Figure 2 – 320 mm brick wall (cL,p=2300ms-1, ρ=231 kgm-2)
Agreement, within 6dB, is obtained between the calculation and measurement in the data
ranges 50Hz-80Hz, 160Hz-1000Hz and 3150Hz-5000Hz. Poor agreement at high frequencies(>1000Hz) is likely due to thickness resonances of the wall. The calculated first and second
thickness resonances, ( f1,solid and f2,solid) assuming solid brickwork are also shown in Figure 2.
These do not correspond with the observed dip (f1 ) and consequent supposed second thickness
resonance ( f 2). This could be because the blocks are not solid but are cellular and filled withrockwool. It could also be due to an incorrect estimate of Young´s modulus when making the
calculation (which was determined using the estimated longitudinal wavespeed). The plateau
for thick plates (calculated assuming solid brickwork) is also shown in Figure 2. However, acorresponding plateau in the measured data is not observed. The reason for poor agreement
at 63Hz and 80Hz was not determined.

5.2.2 320 mm brick wall with 160mm EPS without point connections
The brick wall was cladded in 160mm EPS and a comparison between the results obtainedwith a thick (10.8 mm) and thin (3.9 mm) render was made. Measured and calculated results
for a thick render are shown in Figure 3, and for a thin render in Figure 4. A sound insulation
calculated using ΔR (eqn. (5)) is also shown in both figures by summing with the measured
results for the 320mm brick wall. The value of the spring stiffness (K ) of the EPS wasmodelled as 3.83x10 7 Nm -3 (the lower end of the measured values), the surface density (ρ) of
the thick and thin render was measured to be 14.2kgm -2 and 5.4kgm -2 respectively and thelongitudinal wavespeed ( cL,p ) of the render was estimated to be 1610ms -1 (5). (Value for
gypsum plasterboard used, although this may not reflect the actual material).

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Sound reduction index (dB)Figure 3 – 320 mm brick wall with 160mm EPS (K=3.83107 Nm-3) and thick renderSound reduction index (dB)(cL,p=1610ms-1, ρ=14.2 kgm-2)

Figure 4 – 320 mm brick wall with 160mm EPS (K=3.83107 Nm-3) and thin render (cL,p=1610ms-1,

ρ=5.4 kgm-2)
Figures (3) and (4) show that sound insulation is divided into three frequency regions. A
low frequency region, below the mass-spring-mass resonance, f0 , where the panel and lining
is modelled as a single plate, a mid frequency region where Eqn. (1) is used to model nonresonant transmission and a high frequency region where Eqn. (3) is used to model theresonant transmission.
The model follows the general trend of the measured results for the thick render (Figure3); although the values are not within 6dB at 63Hz, 100Hz, 125Hz, 315 Hz or 4000Hz. Poor
agreement between the model and measurement for the thin render (Figure 4) at manyfrequencies is likely because the thin layer is no longer acting independently of the EPS anda combined material constant or some other model may be required. Therefore is a limiting
render thickness (within the range 3.9 mm to 10.2 mm) can be assumed below which good
agreement between measurement and calculation is not achieved. Sound insulation
calculated using ΔR diverges significantly from the measured data at high frequencies(>1250Hz).

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Sound reduction index (dB)

5.2.3 320 mm brick wall with 160mm EPS with point connections

Figure 5 – 320 mm brick wall with 160mm EPS, thick render and 6 point connections. The solidline ‘–‘ corresponds to the results obtained using eqn. (2), the dashed line ‘--‘ to eqn. (3) and theSound reduction index (dB)dotted line ’…’ to eqn. (7)Figure 6 – 320 mm brick wall with 160mm EPS, thick render and 6, 10 or 12 point connections/m2
Comparison of three models (eqns. (2), (3) and (7)) and measured data are shown in Figure
5. The area spring given by eqn. (3) agrees slightly better with measured data than point
springs only (eqn. (2)). The rigid point connection model (eqn. (7)) gives significantly poorer
agreement and the high frequencies therefore cannot be modelled by rigid point connections.
Where required the spring stiffness of the point connections was estimated to be 4.0x10 6Nm -1 .
The effect of increasing the number of point connections for the point spring model isshown in Figure 6. The effect of a shifting upwards mass-spring-mass resonance can also be
incorporated by summing the spring stiffness of the number of connectors per unit area inparallel together with the dynamic stiffness per unit area as described in Craik (4).

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6. CONCLUSIONS AND FURTHER WORKWhen modelling EPS cladding on brickwork exterior walls three distinct modelling regions
can be identified: The low frequency region; where the cladding and wall can be modelled asa single system. The mid frequency region; where non-resonant transmission due to a massspring mass resonance is observed. The high frequency region; where resonant transmission
through the area and point springs from plate to plate is observed. The limit to which eqn.
(3) can be applied to determine the resonant transmission is given by the render thickness
and lies within the range 3.9 mm to 10.2 mm. Energy transfer via non-resonant and resonant
paths through the system are governed by both the dynamic stiffness of the thermal
insulation layer and the spring stiffness of the point connections.
A simultaneous measurement of velocity level on the heavyweight wall, the individual
point connections and on the surface of the render could help to confirm the most appropriate
way to model resonant transmission at high frequencies. These measurements could also be
used to test whether eqn. (5), which makes use of a velocity level difference, can also be usedin the case of spring connections. Measurements with a laser vibrometer could be used todetermine the velocity ratio 𝑢 . ⁄〈𝑢 〉 which would allow different numbers of pointconnectors, r , to be added. Velocity level difference measurements could be repeated on alarge sample in an enclosed space. Thus allowing a comparison between the level difference
obtained with airborne and structural excitation. If the total loss factor of the render ismeasured a coupling loss factor between the brick wall and the render could also be calculatedusing the measured velocity level difference. The dynamic stiffness of the EPS in the small
samples should also be verified. Finally it would be interesting examine a curtain wallingsystem to determine if the same resonant and non-resonant loss factors can be used.

ACKNOWLEDGEMENTS
The work carried out this project, completed within an Austrian Collective Research Funding project titled “Schall.Hoch.Bau”, was financed 40% by the commercial project
partners and 60% by the FFG (Österreichische Forschungsförderungsgesellschaft).

REFERENCES
1. ISO10140-5. Acoustics -- Laboratory measurement of sound insulation of building elements. Part
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3. EN13499. Thermal insulation products for buildings - External thermal insulation composite
systems (ETICS) based on expanded polystyrene - Specification. 2003.
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