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Vibrometry Assessment of the External Thermal Composite Insulation Systems Influence on the Façade Airborne Sound Insulation^{ †}

^{1}

^{2}

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^{5}

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^{†}

## Abstract

**:**

## Featured Application

## Abstract

## 1. Introduction

_{W}[20], the effect of ETICS on the sound insulation is likely to be audible.

_{W}, the dip in the insulation curve, which occurs typically at rather low frequencies, can pose a considerable problem when insulation against traffic noise is concerned [28,29,30,31]. The sophisticated numerical prediction model to determine ETICS cladding system transmission loss was introduced based on transfer matrix method [32,33]. Discussions on harmonization and standardization of assessment procedures of the sound insulation in dwellings resulted in EU networking action [34]. The particular impact of noise from road, rail and air traffic is expressed in the spectrum adaptation terms C and C

_{tr}[20]. In some countries, spectrum adaptation terms are not considered, but the contribution of low frequencies is included by means of extended assessment range, i.e., from 50 to 5000 Hz [35,36,37,38,39]. In [13,40], the insulation of low frequency noise produced by traffic is considered by calculation of single number quantities R

_{W}+ C

_{tr}or R

_{W}+ C

_{tr,}

_{50–5000}. In the case of ETICS, the adapted single number quantities rate the insulation performance substantially lower than R

_{W}, due to the dip in low frequencies. In some cases, the adapted single number quantity is lower after applying ETICS walls than before. This motivates the research on how to affect the ETICS dip by tuning the resonance frequency of the system into less audible lower frequencies [41] or by reducing the depth of the dip.

_{W}(sound reduction index improvement) is often predicted by empirical relations. Based on extensive investigations by Weber et al. [13], a semi-empirical approach involving the spectrum adaptation terms C and C

_{tr}has been implemented in the recent draft of ISO 12354-1 [42]. This has led to sound insulation values that are more adequate in relation to subjective perception.

_{W}due to the ETICS is then added to the weighted sound reduction index value R

_{W}(or R

_{W}+ spectrum adaptation term) of the bare original wall to get the resulting sound reduction index of the entire assembly.

## 2. Experimental Approach

_{1}= 375 kg/m

^{2}. The ETICS addition in Wall 2 consisted of a layer of adhesive mortar (1.5 mm), a layer of (thermally insulating) dense mineral wool (35 mm; s’ = 15 × 10

^{6}N/m

^{3}; ρ = 112.7 kg/m

^{3}; r = 18.3 kNs/m

^{4}) and a layer of lime plaster (25 mm; m

_{2}= 28 kg/m

^{2}).

_{sending}= 50.2 m

^{3}and V

_{receiving}= 53 m

^{3}. The Schroeder frequency of the rooms was approximately f

_{Schroeder}≈ 330 Hz. The surface of the test wall element, which fully filled the test opening, was S = 10.7 m

^{2}. Pink noise of 97 dB in each 1/3rd octave band was used to acoustically excite the test walls. The sound transmission was determined by both microphone and vibrometry measurements.

#### 2.1. Determination of Airborne Sound Insulation Based on ISO 10140-2

_{p}

_{1}− L

_{p}

_{2}), corrected with a term to account for the amount of sound absorption in the receiving room:

^{−1}) is the speed of sound in air, and T (s) and V (m

^{3}) are the reverberation time and volume of the receiving room (RR), respectively. A (m

^{2}) and S (m

^{2}) are the receiving room absorption area and tested wall area, respectively.

#### 2.2. Determination of Airborne Sound Insulation Based on Vibrometry

_{n}(

**r**, ω) of the vibrating surface at positions

_{s}**r**on the wall, the acoustic pressure p(

_{s}**r**, ω) at position

**r**in the receiving room (denoted by distance R = |

**r**−

**r**) can be calculated by

_{s}|**r**, ω) and the measured normal velocity v

_{s}_{n}(

**r**, ω), the active acoustic intensity I along the surface and the total radiated active sound power P can be computed as:

_{s}_{W}= 10 log

_{10}(P/P

_{ref}), with P

_{ref}= 10

^{12}W/m

^{2}, is independent of the acoustic response of the receiving room and, in contrast with microphone-based measurements, not affected by room acoustic aspects of the receiving room, such as reverberation and mode formation. In the microphone-based ISO 10140-2 approach, sound reflections and reverberation can be adequately considered using the reverberation time in the calculation of the sound reduction index Equation (1). In principle, the non-uniformity of the measured acoustic field in the receiving room is also considered by averaging receiving room sound pressure values over multiple positions, and by exploiting the fact that, in 1/3 octave band averaging, strongly frequency dependent spatial non-uniformities of room acoustic modes are cancelled out. However, the latter averaging effect is cumbersome at low frequencies, when the modal density becomes very low and the spatially slowly varying pressure field of modes is difficult to sample. This violation of the acoustic diffuseness assumption makes the measured sound power radiated into the room using microphones strongly dependent upon the room size and shape at low frequencies, and thus varying from laboratory to laboratory. The value of L

_{W}obtained by means of the Rayleigh integral approach does not suffer from this issue and, by means of the relation between the radiated sound power P

_{rad}(Watt), the intensity I (Watt/m

^{2}) and root mean square sound pressure p

_{rms}(Pa) of a plane source with surface S (m

^{2}), ${P}_{rad}=IS=\frac{{p}_{rms}^{2}}{Z}S$, with Z the specific acoustic impedance of air, so that ${p}_{rms}=\sqrt{{P}_{rad}Z/S}$, it can be used as follows to determine the sound reduction index:

_{1}and C

_{2}are meteorological correction factors [54]. K

_{a}involves high frequencies correction factors [53] and K

_{W}the Waterhouse correction for low frequencies, which includes effects of the boundaries of the receiving room [52]. K

_{d}is the random-incidence factor (directivity factor), which corrects for effects of the radiated acoustic near field.

_{0}= 1 m

^{2}is the reference area.

#### 2.3. Determination of ETICS Induced Weighted Sound Reduction Index Improvement

_{W}[12,13].

_{0}(Hz), the resonance frequency. For frequencies below f

_{0}, the model assumes no effect: ΔR

_{W}= 0 dB. Equation (8), which holds for frequencies below the coincidence frequency of the basic wall, f

_{c}, predicts an increase of ΔR

_{W}with 12 dB per octave.

## 3. Results

#### 3.1. Assessment in Accordance to ISO 10140

_{0}≈ 125 Hz in the ETICS treated wall, caused by the reduced acoustic impedance (mismatch with the air) of the multilayer at resonance, agrees with Equation (9), using the following known values for the involved material properties: m

_{1}= 375 kg/m

^{2}, m

_{2}= 28 kg/m

^{2}, and s’ = 15 MN/m

^{3}[13,42]. In addition, other features of the ETICS effect are as expected. On the one hand, below resonance, the added mass of the plaster and mineral wool layer is too small to significantly increase the sound insulation. On the other hand, above the dip, the addition of a (thin) mass layer and cavity leads to a dual mass law behavior of 12 dB/octave-behavior, in contrast with the single mass law behavior of 6 dB/octave-behavior of the bare Wall 1. Both spectra also show a dip at f

_{c}≈ 160 Hz due to the coincidence effect. However, in the case of ETICS Wall 2, the mass-spring-mass dip is clearly dominant. Figure 2 illustrates that, despite the drastic differences between the insulation curves of both walls, the effect on the respective shifted “matching” reference curves is pretty small.

_{1}is a total mass per unit area of Wall 1 (kg·m

^{−2}); m

_{2}is mass per unit area of the used plaster (kg·m

^{−2}); and the “spring” of the system, (i.e., mineral wool placed in the cavity between the two walls) is characterized by its dynamic stiffness s′ (N·m

^{−3}) measured in accordance with EN 29052-1 [55]. Typical values are given in the Section 2 of this article. In addition to the properties of materials used for ETICS, the sound insulation is also affected by aspects of workmanship, e.g., related to how the insulation slabs are mounted onto the supporting wall.

#### 3.2. Assessment by Vibrometry Approach

_{v}(dB re ms

^{−1}; v

_{0}= 5 × 10

^{−8}m/s). The peaks in the spectrum of the velocity level L

_{v}indicates resonances occurrence. By evaluating the response for each point of the wall surface, the ODS was plotted. The lowest natural frequency f

_{(1;1)}is about 67 Hz. Although the phenomenon of coincidence is not related to a structural resonance, the velocity spectrum shows a peak at f

_{c}≈ 160 Hz, as a result of the increased coupling with the vibration exciting airborne waves at and above that frequency. The ETICS resonance appears as a peak in the L

_{v}spectrum at about f

_{0}≈ 119 Hz. At f ≈ 230 Hz, the L

_{v}spectra of Wall 1 and Wall 2 are equal, which is consistent with the equality at that frequency of the sound insulation spectra.

_{x}, k

_{y}):

_{x}

^{2}+ k

_{y}

^{2}) are shown versus frequency in Figure 4a. Next, the velocity c

_{B}of the bending waves along the supporting wall was obtained via ${c}_{B}=2\pi f/k$. Figure 4b. shows that the bending wave velocity exceeds the speed of sound in air for frequencies starting from and above 160 Hz, which is consistent with the coincidence induced dip in the in the insulation curve in Figure 2.

^{2}the total mass. Assuming ad hoc a typical value for Poisson’s ratio, ν = 0.3, the effective Young’s modulus E was found to be 4.88 GPa. For higher frequencies, the assumption of a thin shell is no longer valid. However, for frequencies near the coincidence frequency (approximately 160 Hz), the structural wavelength of flexural waves in the structure of interest (@160 Hz: k ≅ 3 rad/m, thus λ ≅ 2π/3 ≅ 2 m) was still large as compared to the thickness of the wall (0.26 m). This justifies the use of Kirchhoff’s thin shell theory in the lower frequency range, and thus the estimate of Young’s modulus in this frequency range.

_{n}is the component of the vibrational velocity normal to the surface. Vibrational patterns of layered structures are not spatially uniform, and the polarization of the motion is not fully perpendicular to the surface of the layers. Moreover, the match between the wavelength of bending waves and the one of acoustic waves in the air is frequency dependent. The radiation efficiency reflects to what extent these aspects are lowering or raising the coupling of the structural vibration energy into airborne radiated acoustic energy in the sending room and vice versa in the receiving room.

_{n}

^{2}> as extracted from the accelerometer signals, and the sound power P(ω) as calculated from those via Equation (5). The results are shown in Figure 5 for both walls. The local maximum at ca. 67 Hz for both walls can be associated with the first natural mode of the structural vibration spectrum of the supporting wall. The values of the frequency f

_{1,1}are consistent with expectations based on the bending velocity dispersion curve as determined in Figure 4 and Equation (10): setting the bending wavelength components λ

_{x}/2 = L

_{x}= 3.49 m, λ

_{y}/2 = L

_{y}= 3.09 m, using k = (k

_{x}

^{2}+ k

_{y}

^{2})

^{1/2}, with k

_{x}= 2ππ/λ

_{x}and k

_{y}= 2π/λ

_{y}, and inserting the best fitting dispersion curve c

_{B}(f) = a√f, with a = 38 m/s

^{3/2}in k = 2πf/c

_{B}(f), the expected structural mode frequency is f

_{1,1}= (a k/(2π))

^{2}= (a/2)

^{2}(L

_{x}

^{−}

^{2}+ L

_{y}

^{−2}) = 67 Hz. Below this frequency, the radiation efficiency increases 12 dB/octave, which is in accordance with theoretical behavior of a wall vibrating in its fundamental 1-1 mode (Fahy [50]). The width of the structural vibration induced maximum in the radiation efficiency is determined by the structural damping. The behavior below f

_{1,1}and above f

_{c}are known to be independent of the loss factor [45,58]. Apart from this feature, the radiation efficiency rises to the coincidence (critical) frequency region, which, consistent with the previous analysis, sets in around 160 Hz.

#### 3.3. Sound Reduction Improvement

_{p,RR(Mic)}) and calculated from ODSs (denoted in the legend as L

_{p,RR(Rayl)}).

_{10}(A) in Equation (1). Nevertheless, due to the non-diffusiveness of the room below the Shroeder frequency of the receiving room (330 Hz), differences in the 1/3th octave R-spectrum with the ODS based spectrum, amount up to 8 dB (at 80 Hz). For higher frequencies, microphone measurements are not affected by room acoustics, by virtue of the high density per frequency band of room acoustic modes, which allows cancelling out their effect by spatial and frequency averaging. The accuracy of deflection shapes interpolation is related to the number of the samples per specific wave length. Vibrometry measurements however become less reliable, as they are based on a spatial scan along the wall with a finite grid spacing g = 15 cm. According to the Nyquist–Shannon sampling theorem, this only allows accurately sampling structural waves with wavelengths up to 4 g = 60 cm, which, based on the velocity dispersion curves in Figure 4, corresponds with a frequency of 1250 Hz (bending wave velocity 955 m/s).

_{W}value of Wall 1 is 1 dB lower than based on the microphone-based data alone (Table 2). The spectrum adaptation terms C and C

_{tr}are both 1–2 dB lower. The complementarity between the microphone and accelerometer-based results allows assessing the effect of ETICS on the sound insulation spectrum in an extended frequency range, as shown by ΔR = R

_{wall 2}− R

_{wall 1}in Figure 8. The most prominent ETICS induced effect on the sound insulation curve occurs below 250 Hz, where the ETICS resonance causes a large dip in the frequency spectrum. In this range, the microphone results are affected by the spatial non-uniformity of the pressure level pattern of room acoustic modes [44], so that the ΔR values extracted from vibrometry measurements can be considered as the more reliable.

_{W}value overestimates the measured value by about 7–9 dB (Table 2), due to the ΔR

_{W}spectrum overestimating the experimental data, especially above the coincidence frequency. The values in parentheses denote the average standard deviation (2 dB) of results presented by ISO standard [42].

_{c}= 1080 Hz):

_{0}the density of air.

## 4. Conclusions

_{W}using a model by Weber et al. [12,13]. For the single number quantity prediction, the difference was 7(9) dB (with the prediction model uncertainty (2 dB) considered).

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**(

**a**) Composition of the measured walls. Wall 1, without (left) and Wall 2, with ETICS (right). (

**b**) Schematic representation of accelerometer locations used for vibrometry: (1) lime plaster (15 mm); (2) hollow brick (220 mm); (3) concrete (200 mm); (4) adhesive mortar (1.5 mm); (5) mineral wool (35 mm); (6) lime plaster (25 mm); (7) B&K acceleration receivers 6×; (8) the measurement grid of 22 × 18 points with spacing of 150 mm; (9) the cross-section of the test wall; and (10) acoustic excitation.

**Figure 2.**Airborne sound insulation curves of Walls 1 and 2 obtained by ISO 10140-2, together with the respective shifted reference curves [26].

**Figure 3.**(

**a**) Mean value of velocity response (in dB) on the surface in narrow band spectrum; and (

**b**) operational deflection shapes (ODSs) visualization and mean value of measured velocity on the wall surface in the RR.

**Figure 4.**Dispersion data obtained by ODS and 2D dispersion data fitting approaches: mean of the wave number (

**a**); and wave propagation velocity (

**b**) dispersion curve data and best fit for Wall 1 and Wall 2. The symbols were obtained by estimating the wavelength of the modes from the ODS. The dotted line in (

**b**) depicts the speed of sound in air. The crossing point between the dispersion curve and the dotted line indicates where coincidence occurs.

**Figure 5.**Spectrum of the radiation efficiency, extracted from the pattern of the measured normal velocity component and the calculated sound power.

**Figure 6.**Sound pressure level (L

_{p}) spectrum in the receiving room during measurements: Wall 1 (

**a**); and Wall 2 (

**b**). The area highlighted in purple indicates the spectrum below the Schroeder frequency. Blue and red curves express the L

_{p}measured by standardized microphone approach in 1/3rd octave spectrum. Green and black curves are the results of L

_{p}achieved by vibrometry data processing in 1/3rd and 1/48th octave bands. f

_{c}is the coincidence frequency of the wall; f

_{0}is the ETICS resonance frequency; and f

_{i,I}is the wall structural modes (i.e., f

_{1,1}is the first wall natural mode frequency).

**Figure 7.**Spectra of the sound reduction index of Walls 1 and 2. (

**a**) Comparison between the two measurement approaches in 1/3rd octave bands. Green and black lines: sound insulation curves obtained by vibrometry; blue and red lines: sound insulation curves obtained by means of ISO 10140-2. (

**b**) Spectrum in 1/48th octave bands of the sound reduction index determined by applying a Rayleigh calculation on vibrometry data (green: Wall 1; black: Wall 2); combined spectrum (combi) of the two walls in 1/3rd octave band (blue dashed: Wall 1; red dashed: Wall 2).

**Figure 8.**The sound reduction improvement index ΔR = R

_{wall 2}− R

_{wall 1}based on microphone measurement results and vibrometry technique.

Symbol | Wall 1 _{ISO} | Wall 2 _{ISO} | ΔR_{w}_{, ISO} |
---|---|---|---|

R_{w} (dB) | 59 | 58 | −1 |

C (dB) | −2 | −3 | −1 |

C_{tr} (dB) | −6 | −9 | −3 |

C_{50–3150} (dB) | −3 | −4 | −1 |

C_{50–5000} (dB) | −2 | −3 | −1 |

C_{100–5000} (dB) | −1 | −3 | −2 |

C_{tr,}_{50–3150} (dB) | −10 | −12 | −2 |

C_{tr,}_{50–5000} (dB) | −10 | −12 | −2 |

C_{tr,}_{100–5000} (dB) | −6 | −9 | −3 |

**Table 2.**Airborne sound insulation values of Wall 1 and Wall 2 and their differences, expressed in terms of single number ratings extracted from microphone-based data and from combined microphone-vibrometry data. Values in brackets give results with taking to account the recommended standard deviation 2dB of method.

Symbol | Wall 1 _{combi} | Wall 2 _{combi} | Wall 1 _{ISO} | Wall 2 _{ISO} | ΔR_{w}_{, combi} | ΔR_{w}_{, ISO} | ΔR_{w}_{, Weber} [13] |
---|---|---|---|---|---|---|---|

R_{w} (dB) | 58 | 58 | 59 | 58 | 0 | −1 | 8 (6) |

C (dB) | −2 | −5 | −2 | −3 | −3 | −1 | 5 (3) |

C_{tr} (dB) | −7 | −10 | −6 | −9 | −3 | −3 | 2 (0) |

C_{50–3150} (dB) | −3 | −6 | −3 | −4 | −3 | −1 | - |

C_{50–5000} (dB) | −2 | −5 | −2 | −3 | −3 | −1 | - |

C_{100–5000} (dB) | −2 | −4 | −1 | −3 | −2 | −2 | - |

C_{tr,}_{50–3150} (dB) | −11 | −14 | −10 | −12 | −3 | −2 | - |

C_{tr,}_{50–5000} (dB) | −11 | −14 | −10 | −12 | −3 | −2 | - |

C_{tr,}_{100–5000} (dB) | −7 | −10 | −6 | −9 | −3 | −3 | - |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Urbán, D.; Roozen, N.B.; Muellner, H.; Zaťko, P.; Niemczanowski, A.; Rychtáriková, M.; Glorieux, C.
Vibrometry Assessment of the External Thermal Composite Insulation Systems Influence on the Façade Airborne Sound Insulation. *Appl. Sci.* **2018**, *8*, 703.
https://doi.org/10.3390/app8050703

**AMA Style**

Urbán D, Roozen NB, Muellner H, Zaťko P, Niemczanowski A, Rychtáriková M, Glorieux C.
Vibrometry Assessment of the External Thermal Composite Insulation Systems Influence on the Façade Airborne Sound Insulation. *Applied Sciences*. 2018; 8(5):703.
https://doi.org/10.3390/app8050703

**Chicago/Turabian Style**

Urbán, Daniel, N.B. Roozen, Herbert Muellner, Peter Zaťko, Alexander Niemczanowski, Monika Rychtáriková, and Christ Glorieux.
2018. "Vibrometry Assessment of the External Thermal Composite Insulation Systems Influence on the Façade Airborne Sound Insulation" *Applied Sciences* 8, no. 5: 703.
https://doi.org/10.3390/app8050703