Finite Element Modelling of a Tim-
ber Volume Element Based
Buil-ding with Elastic Layer Isolators
Juan Negreira, Delphine Bard
AkuLite Report 11
SP Report 2013: 27
Förslag 1
Finite element modelling of a Timber
Volume Element based building with
elastic layer insolators
Juan Negreira
1, Delphine Bard
1Department of Construction Sciences
1Division of Engineering Acoustics
Lund University (Sweden) April 2013
SP Technical Research Institute of Sweden SP Rapport 2013:27
ISBN 978-91-87461-12-5 ISSN 0284-5172
Contents
1 Introduction 5
2 Project description 5
2.1 Timber Volume Elements (TVE) . . . 5
2.2 Method . . . 7
2.3 Literature review . . . 7
3 “First steps” 9 3.1 Finite element model . . . 9
3.2 Results . . . 11
3.3 Conclusions . . . 12
4 Improvements / Try-outs based on findings of [10] 13 4.1 Modelling of the whole TVE . . . 13
4.2 Damping . . . 15
4.3 Sylodyn linear viscoelastic model . . . 17
4.3.1 Static parameters . . . 17
4.3.2 Dynamic parameters . . . 19
4.4 New comparison Sylodyn / No Sylodyn . . . 21
4.5 Influence of evaluation points . . . 23
4.6 Connections . . . 25
4.7 Tie plates . . . 26
4.8 Metal studs . . . 27
4.9 Modelling of various TVEs . . . 28
4.10 Air influence . . . 30
5 Discussion and conclusions 31 6 Future work 31 6.1 Assembly of more TVEs . . . 31
6.1.1 Simplification of the elastomer blocks . . . 31
6.2 Scaling input force with source spectra . . . 32
6.3 Insulation . . . 32
6.3.1 Local and global influence . . . 32
6.4 Boundary conditions . . . 33
6.5 TVE configurations . . . 33
Abstract
Lightweight timber constructions have gained popularity in Sweden since 1994, when the national building regulations revoked a banning of constructing wooden multi-storey buildings. Ever since, regulations regarding impact and airborne sound insulation became more stringent due to complaints arised from the inhabitants and thus new building techniques were developed. Along those lines, the use of elastomers in the junctions, i.e. between walls, floors and ceilings, has been a frequent solution in order to reduce low frequency noise travelling throughout the structure. Their performance has been checked via measurements. However, development of prediction tools, e.g. using numerical methods such as the finite element method (FEM), are of need in order to tackle the flanking transmission issues during the design phase and thus saving time and cost to the builders. Along those lines, an ongoing investigation at Lund University aims at accurately predict and improve the flanking transmission performance of a lightweight timber building. In a more general way, it can be said that a reliable method to set-up FE prediction tools, in order to predict the acoustic and vibratory performance of lightweight timber buildings during the design phase is sought. Specifically for this investigation, a Timber Volume Based building using elastic layers in the junctions –Sylodyn R was
used in this case– was analyzed by means of the finite element method utilizing the commercial software Abaqus.
Sammanfattning
Sedan Boverket lättade på regelverket för flerbostadshus i trä 1994 har lättvikts-konstruktioner i trä ökat i popularitet i Sverige. Samtidigt har regelverket för stegljudsisolering och isolering mot luftburet ljud skärpts. Som en konsekvens av detta har nya byggtekniker utvecklats. En ofta använd lösning på problemet med ljudisolering är att använda elastomerer i kopplingspunkter mellan väggar, golv och tak. Tanken är att dessa elastomerer hindrar utbredningen av stomljud i konstruk-tionen. Mätningar har visat att elastomerer fungerar väl i detta avseende. Om konstruktören av en given byggnad har tillgång till verktyg vilka genom numeriska metoder kan förutsäga flanktransmissionen i en byggnad redan under designfasen skulle stora besparingar i tid och pengar kunna göras. I ett projekt vid Lunds Universitet undersöks möjligheten att med god precision förutsäga och förbättra flanktransmissionen i en lättviktsbyggnad i trä. Målet med projektet är att utveckla en tillförlitlig metod att förutsäga vibrationer och ljudtransmission i en lättvikts-byggnad i trä. I undersökningen har en konstruktion under uppförande undersökts. Konstruktionen utgörs av volymselement i trä med elastomerer Sylodyn R i
kop-plingarna mellan elementen. Konstruktionen har modellerats med finita element metoden i programmet Abaqus.
1
Introduction
When the Swedish construction code in 1994 allowed wooden multi-storey buildings, this type of lightweight structures became popular due to low cost and ease of construction [1]. The differences in weight, stiffness, density and repartition compared to traditional materials have repercussions on how the sound propagates throughout the structures. These types of structures should not just meet the demands of structural integrity but also the dynamic requirements. In fact, the main drawback in those buildings is disturbing vibrations and noise propagating in the construction, especially through the junctions within the low frequency range, i.e. up to 200 Hz, where sound insulation problems may arise. Obviously, these problems often come accompanied by complaints from the inhabitants, unsatisfied with the living environment. Therefore, in order to alleviate those sound insulation problems, gaining knowledge about the dynamic behaviour of lightweight timber buildings is of crucial importance.
The aforementioned poor insulation through the junctions, makes flanking transmis-sion an issue to be tackled in order to improve the comfort amid the occupants. To that end, elastomers are occasionally introduced in the junctions between floor and walls due to their sound and vibration insulating effects. However, still no reliable methods for predicting the vibratory and acoustic performance of a lightweight building before is constructed exist. Nowadays, product development is done on empirical basis, i.e. ob-servations and engineers’ experience [2]. Time and costs could be reduced by addressing flanking transmission issues during the design phase, for instance by using finite element (FE) simulations as prediction tools. Accurate and handy methods for characterization of lightweight timber buildings (materials, connections...) are thus needed in order to obtain reliable results.
The final goal of this project is to trustworthy predict the flanking transmission of a lightweight building as well as improve its vibratory performance by modifying certain design features. In a more general way, one could say that the objective is to create and develop a reliable FE prediction tool, or rather a method to set-up FE prediction tools, in order to unerringly predict the acoustic and vibratory performance of lightweight timber buildings during the design phase. In order to do so, many aspects must be taken care of as it will be hereupon described.
2
Project description
2.1
Timber Volume Elements (TVE)
In this still ongoing investigation, buildings made of Timber Volume Elements (TVE) were specifically investigated. For this types of buildings, the idea is to construct pre-fabricated modules containing floor, walls and ceiling together with electrical, heating, water sanitation and ventilation installations [2]. Those “boxes” are then transported to the construction site and stacked on top of each other with an elastomer in between. The flexible coupling permits that the only mechanical contact between two volumes in
the vertical direction is along the flanks by means of the elastic strip. With the proper design, it is believed that the flanking transmission can be significantly reduced [2]. In Figure 1, one can see a sketch of a TVE-based building, whereas in Figure 2 the change of vibration transmission path when introducing resilient strips in between with respect to a traditional construction is shown. As seen, the direct transmission is greatly reduced as there is an air gap between floor and ceiling, i.e. the waves travelling to the floor under are forced to pass through the elastomer and/or through the acoustic media (air).
Figure 1: Timber Volume Based building sketch [2].
Figure 2: Structural vibration transmission from one floor to another, for a traditional building (a) and TVE-based buildings (b) [2].
More specifically, the TVE-based buildings constructed for the project Brunnby Park in Upplands Väsby (Sweden) are being studied. The TVEs are manufactured by the company Lindbäcks Bygg AB. The reason for this choice was its widespread use in Sweden and also because of a feasible future comparison between finite element simulations and in-situ measurements, which have already been performed under the AkuLite project frame [3]. Two images corresponding to the drawings of the real building are shown in Figure 3.
Figure 3: Drawings of TVE junctions (Lindbäcks Bygg AB).
2.2
Method
After a reliable FE model is obtained by calibrating FE simulations and existent measure-ments, the influence of modifying the junctions of the TVEs will also be checked. Three cases are of interest as shown in Figure 4. Hence, as previously said, the working-method will be as follows:
• A FE model will be calibrated with existent measurements (the model will corre-spond to Figure 4a, as the measurements were performed in a building constructed in this fashion).
• Once this is done, the vibratory performance of configurations shown in Figure 4b and 4c will be checked by modifying parameters in the calibrated model to improve the TVE design. All cases will be modelled with load bearing beams placed length-and widthwise within the floor to check their influence in the flanking transmission.
• Ultimately, with the knowledge gained in this project, a method to set-up FE pre-diction tools, in order to predict the acoustic and vibratory performance of future lightweight timber buildings during the design phase, will be achieved.
Figure 4: Different configurations to be studied: (a) floor and ceiling installed between the walls and (b) floor installed upon walls, ceiling between and (c) floor and ceiling installed upon walls.
However, before reaching the final goal, many small investigations must be performed as it will be explained.
2.3
Literature review
Traditionally, in single-family timber houses, the different elements converging at the junctions were connected together using screws and/or nails, sometimes in combination
with glue. Since multi-storey timber buildings were authorized in Sweden in 1994, higher sound reduction requirements due to impact noise are demanded and thus new construc-tion techniques were developed ever since.
There are many existent methods to improve flanking transmission: addition of addi-tional wall plates with distances on the sending room and/or on the walls of the receiving room [4], hanging the ceiling on resilient channels [4], decoupled radiation isolated walls [4], roller bearings [5], addition of extra mass and damping to the floor through an extra board layer [2], the use of elastic glue between boards [2], and the utilization of a floating floor [2].
A more recent method, predominantly used in TVE-based buildings, is to place rub-ber insertions in between construction elements (e.g. floor, walls, the whole room). Even though this is a fairly new technique and still a lot of work must be done related to it; in the PhD thesis [6], elastomers are extensively studied. For instance, in [7], a comparison between measurements and finite element simulations of the same junction using elas-tomers was carried out. For the measurements, it was found that the insertion of rubber pieces is beneficial if one just looks at the vertical direction. However, when looking at the horizontal direction, i.e. a direction which can have a large contribution to the sound emission in the apartment below, the elastomer shows a positive influence up to 30 Hz and from 70 Hz, but within the span 30-70 Hz, the resilient strips actually increase the velocity levels. This finding correlated good with the finite element simulations of the same junction, which showed that acceleration levels were actually increased in the hor-izontal direction for frequencies between 40 and 70 Hz. This is believed to be caused by shear resonances at low frequencies, eliminating the isolation effect of the elastomer.
In [8], two full-scale mockups with difference junction configurations (screwed and using elastomers) were measured and compared in a laboratory environment. It was found that above approximately 70 Hz, the mean acceleration vibration level in the elastomer configuration was significantly lower than for the screwed configuration. Below 70 Hz, however, the mean vibration level for the elastomer configuration was overall significantly higher than for the screwed junction. The author highlighted that elastomers, used as in that study, could worsen e.g. footstep impact noise, although improving higher frequency acoustic performance. This concurs with the conclusions drawn in [2], where two volumes were stacked on top of each other without an elastomer in between, i.e., wood against wood. This resulted in improved sound insulation for frequencies from 80 Hz to 500 Hz, leading to 1 dB improvement of the index respect the construction using resilient blocks in between volumes.
If a general conclusion may be drawn from all the literature, is that when using resilient strips in between parts in lightweight buildings, it is of crucial importance to design and select the right stiffness for the material, because a higher load than the recommended one will compress the elastomer to a level where its isolating properties are greatly reduced. This was proved in [2] in a laboratory environment, where two volumes were stacked on top of each other, raising the top one with an overhead crane to a level where, ideally, both volumes would have mechanical contact just by means of the elastomer but where the upper volume would not transmit any static load to the lower volume. The tests showed that the impact sound pressure level was reduced by 2 dB. This confirmed what it was
previously shown in [9], where 31 nominally identical lightweight timber constructions using in all cases elastomer between load bearing walls and prefabricated floors were analyzed. It was found that the sound reduction was better higher up in the building. As said, both [2] and [9] proved that the static loads depending on the level within a building will influence the insulation performance. When two structures are brought together, their mechanical coupling will improve, compressing the elastomer and thus worsen the sound insulation.
All in all, it can be concluded that there is still a lack of knowledge about the vibra-tional performance of elastomers in lightweight buildings. In order to gain understanding about their performance, reliable material properties and accurate finite element models are needed. This is thus the intention of the investigation here presented.
3
“First steps”
The first steps of this investigation are described in detail in [10], although a summary with its main concepts and findings is also hereafter presented. In [10], a simplified massive wood finite element model was analysed. It must be pointed out that the relative differences between the modelled results were of greater importance than the absolute correlation between the model and the existent measurements. It was though that this would be a good first approach to gain an insight of the problem, understanding the model and thus allowing to eventually create a more refined model which could be calibrated with experimental results.
In order to do so, two halves of two TVEs attached to each other were considered. Its inner dimensions are 3.6 m width and 8.6 m long, whilst the height is 3 m. (1.5 m as only half the TVE is considered).
Just two different configurations were analysed (Figure 4a and 4b, henceforth denoted as case A and B respectively). In both cases, the beams comprising the floor and the ceiling were modelled along the shorter dimension, i.e. widthwise. Furthermore, for case A, the variation on the flanking transmission was also investigated when considering the beams along the lengthwise direction of the TVE. A parameter study varying the material properties for the Sylodyn was also carried out. Finally, an analysis of the same junction without Sylodyn was performed.
3.1
Finite element model
Modelling a junction is a very complicated task as it must be able to capture all phenomena occurring in reality. In this first approach, massive wood was considered all over the whole model with exception of the Sylodyn. This simplification will not disrupt the relative differences between the different cases studied. Furthermore and in order to reduce calculation time, the insulation was excluded and taken into account by increasing the damping of the other materials.
The elastomer used in the studied structure to reduce the noise and vibration trans-mission was Sylodyn NE, a mixed cellular polyurethane dampening material developed
by Getzner Werkstoffe GmbH. It is shaped as 100 x 95 x 25 mm3 blocks. The distance
c/c (centre-to-centre) between two blocks was set to 400 mm. A linear elastic material model was applied since the quasi-static tests shown in the data sheet provided by the manufacturer depict a fairly linear behaviour within the recommended operative range.
As the structure will only be exposed to loads and displacements with low magnitude, all non-linear behaviour was neglected and the wood was hence also modelled as linear elastic. The properties used for modelling the wood were provided by the manufacturers. All parts were individually created in Abaqus and assembled considering full coupling between them in all contact surfaces. This creates stiff connections, as it is believed to be in reality. Only 8-nodes brick elements were used (solid elements with linear interpolation of the acceleration field denoted in Abaqus as C3D8R) for the wood and the hybrid elements C3D8RH for the Sylodyn, yielding a FE-model with approximately 2 million degrees of freedom (DOF).
A 5 N harmonic concentrated force at the middle of the floor was considered and a frequency sweep was carried out from 10 to 100 Hz in steps of 1 Hz. Fixed boundary conditions were applied at the top and bottom of the walls. The model (for case A) can be seen in Figure 5. The blocks of Sylodyn are shown in grey, the floor in blue, the ceiling in red, the inner walls (apartment separating walls) in yellow and the outer (facade) walls in green.
For more theoretical background about the finite element method, see e.g. [11].
Figure 5: case A with beams oriented widthwise. On the left, the whole model is shown (apartments walls in one side removed). To the right, detail of the junction.
3.2
Results
The following results show the performance of the junctions regarding the flanking trans-mission as plots of acceleration versus frequency. Furthermore, the vertical transtrans-mission from the source, located on the middle of the floor, to the ceiling underneath through the long side of the room was investigated. Although more calculations were done, just the results corresponding to case A with load bearing beams placed widthwise as well as the ones for the junction without Sylodyn are hereafter presented. For more details, see [10]. The frequency dependent acceleration was evaluated at 6 nodes along the floor, apart-ment separating walls (upper and bottom TVE) and ceiling, all placed 0.2 m from the junction (see Figure 6 for the evaluation points). An average acceleration for the 6 nodes was calculated and plotted for the different elements composing the junction according to Equation (1), where mp is the number of measuring points and ai,f the simulated
accel-eration. Likewise, the complex acceleration magnitudes were also evaluated on top and bottom of the Sylodyn blocks to check the vibration reduction within them.
amean,f [m/s2] = 1 mp · mp X n=1 ai,f (1)
Figure 6: Acceleration magnitudes for case A. Acceleration levels at different locations (floor, ceiling and both upper and lower walls) (left) and acceleration levels at the top and bottom of the Sylodyn (right). The block of Sylodyn up to the right shown an example of reduction of the acceleration magnitudse in within a block for a given frequency (44 Hz). Red indicates high acceleration magnitudes whereas green shows low magnitudes. The sketch of the junction in the left plot shows the evaluation points as black dots.
As seen in Figure 6, for case A widthwise; the maximum complex acceleration magni-tudes occur between 35 and 60 Hz. One can also identify that Sylodyn dampens nearly all vibrations, as the acceleration levels evaluated on the ceiling and the wall underneath are very low.
The performance of the junction without Sylodyn was also investigated (wood-wood connections all over). The comparative results are shown in Figure 7. It is apparent that the complex acceleration magnitudes evaluated at the bottom room without the Sylodyn
Figure 7: Comparison between the acceleration magnitudes for the junction using Sylodyn (left) and without Sylodyn (right). case A widhwise was considered. The acceleration was evaluated on the floor, the ceiling and the both wall in the upper and lower floor
are much higher, which indicates the advantages of using an elastomer as a vibration insulator in the junction.
3.3
Conclusions
In [10], a preliminary investigation regarding the flanking transmission when introduc-ing an elastomer in between the components of a lightweight junction was carried out. As already stated, the relative differences between the modelled results were of greater importance than the absolute correlation between the model and existent measurements, in order to gain insight of the problem, understanding the model and thus allowing to eventually create a more refined model.
It was shown for all cases studied (case A and case B ), regardless of the orientation of the load bearing beams in the floor and ceiling or the placement of the rubber foam material, that the reduction of acceleration magnitudes within the blocks is very effective. In addition, the performance of a junction with resilient blocks was compared to the same junction without the elastomer. It was observed that the vibrations transmitted are much higher in the latter than in the former case. Hence, using elastomers for this type of junction was proved to be advantageous, although further investigations are needed to confirm that at this stage.
Calculations not shown in this report (see [10] for further information) portrayed through a parameter study that a variation in the modulus of elasticity of the Sylodyn does not greatly influence the vibration transmission through the junction. Likewise, it was seen that case B may perform better than case A, although a more extensive study is needed in order to confirm this fact.
It was also shown that the linear elastic material model may not be accurate for the Sylodyn as its behaviour does not resemble the real one (in reality not all vibrations are dampened out). Furthermore, and looking at the low acceleration levels simulated, one could think that the model considered is too stiff, probably due to the connections used (full coupling in all contact surfaces). Moreover, a more detailed model was needed in
order to accurately mimic measurements performed in-situ.
To sum up, in [10]; an insight into the performance of this specific type of junction (although many on the market are similar) regarding flanking transmission has been gained. Ultimately, this will allow the creation of more refined models in order to correlate both experimental and simulation results, which could be used as a prediction tool during the design phase of the structures to improve their performance.
4
Improvements / Try-outs based on findings of [10]
From [10], it was concluded that a more detailed model was needed if the measurements performed in-situ are to be mimicked. Specifically, the use of a bigger model due to interactions in the building between volumes is strongly recommended. A new finite element model is being developed as we speak, and many improvements have been/are being taken into consideration, as described below. Note that the improvement of the model is just at the moment being performed for case A (see Figure 4) with the beams placed widthwise, which is the real case for contracted buildings. With all the findings for this configuration, i.e. once the model is calibrated, other configurations (case B and caseC ) will be ultimately analysed.
4.1
Modelling of the whole TVE
Instead of modelling two halves of adjoining rooms, a new modelling approach considering the whole TVE (inner dimensions 3.6 x 8.6 x 3 m3) was adopted instead. By doing so, one
could eventually assemble various modules to form the complete building. This statement is really important as the simulations are eventually to be compared with measurements and, in reality, interactions between different modules may influence the results. For instance, global modes of vibration of the whole building could contribute to the flanking transmission in one specific room. This will mostly affect the low frequency response, where most interest is focused in lightweight timber buildings.
However, later on when assembling the TVEs into the global model, the number of DOFs will quickly increase to exceed the limits of computer capacity, at least in a reasonable amount of time (e.g. one single TVE –for case A with beams placed widthwise– has approximately 4-5 millions of DOFs). Therefore, reduction methods, e.g. a component mode synthesis [12], which is already built-in in Abaqus, will be used in the simulations. In such manner, the finite element model of each volume element is reduced by retaining the interface degrees of freedom needed to connect the volume elements to other elements, together with internal degrees of freedom representing the dynamics of the full model. Using this approach, the calculations will be more time-efficient.
This new approach of modelling the whole TVE can be seen in Figure 8, where a single TVE is shown. Again, the floor is shown in blue, the ceiling in red, whereas the apartment separating walls are shown in yellow and the facade walls in green. Weather boards on the outside of the facade vertically embracing TVEs when stacked are shown in grey. In this new model, some of the real materials of the construction (Figure 3) were
introduced as well as a realistic damping ratio for the whole volume element extracted via measurements (see Section 4.2). The material properties used were either provided by the manufacturers or assessed via measurements, and can be seen in the Annex.
X Y Z X Y Z
Figure 8: Single TVE (left) and a section of the TVE (right).
Again, the elastomer used was Sylodyn NE and the blocks were shaped with dimen-sions 100 x 95 x 25 mm3. They were meshed with hybrid elements denoted in Abaqus as
C3D8RH. The distance c/c (centre-to-centre) between two blocks was set to 600 mm. The computational mesh for the Abaqus model was obtained using solid 3-D stress finite hexahedral elements (C3D20) with 20 nodes and quadratic spatial interpolation of the acceleration field. The element size was decided based on the wavelengths expected to occur in the model at the higher frequency of 200 Hz, (≈2M DOF each TVE).
Full coupling between all individuals parts within the TVE was considered. However, between floor, ceiling and surrounding walls just full tie at certain discrete surfaces was modelled (see Figure 9). This is believed to be the real case in constructed buildings, as discussed with the manufacturers. In all subsequent analyses, a unit harmonic concen-trated force placed at the middle of the floor was considered, carrying out a frequency sweep from 1 to 200 Hz in steps of 5 Hz.
X Y
Z
Figure 9: Discrete connections at certain surfaces (in pink colour) between floor, ceiling and surrounding walls (the surrounding walls were removed for showing the connections). The floor is shown in blue, the ceiling in red, the apartment walls in yellow and the Sylodyn blocks in white.
4.2
Damping
Due to the complexity when assessing damping and also due to the numerous different materials existent in the real structure, a global damping extracted from measured data was considered instead of considering individual damping for each material. It is believed that this approach will lead to more realistic results as there are less sources of error than when dealing with individual material damping ratios.
In [3], a Japanese ball was dropped from 1 m height on the middle of the room, measuring the vibrations created with two accelerometers, one of them placed parallel to the load bearing beams and the other one in the perpendicular direction, as shown in Figure 10. This measurement protocol was developed and used for all measurements performed within the AkuLite project.
The signals from both accelerometers were low-pass filtered and the resulted signal was then fitted exponentially in order to get the damping ratio by means of the envelope fitting method [14]. Having the damping ratio for both accelerometers, i.e. for both directions (see Figures 11 and 12), an average was carried out, resulting in a damping ratio of ζ = 5.77 %.
Figure 10: Layout used in [3] for measuring vibrations produced by the Japanese ball.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 −10 −5 0 5 10 15 Time [sec] Acceleration [m/s 2]
Exponential fitting of the filtered signal
Data Points Curve
Figure 11: Acceleration-time filtered signal and exponential fitting of the signal from the accelerometer placed in the direction parallel to the load bearing beams (ζ = 7.14 %).
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 −8 −6 −4 −2 0 2 4 6 8 10 Time [sec] Acceleration [m/s 2]
Exponential Fitting of the Filtered Signal
Data Points Curve
Figure 12: Acceleration-time filtered signal and exponential fitting of the signal from the accelerometer placed in the direction perpendicular to the load bearing beams (ζ = 4.44 %).
In order to put this damping into Abaqus, the Rayleigh damping was used. This method considers the damping matrix as being a linear combination of the mass and stiffness matrices. For a more detailed description of Rayleigh damping, see for instance [13]. The coefficients obtained (input for Abaqus) were α = 17.37 and β = 9.77 · 10−5 (see Figure 13). 0 20 40 60 80 100 120 140 160 180 200 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Frequency [Hz] Damping ratio
4.3
Sylodyn linear viscoelastic model
Based on the previous results from [10], where almost total dissipation of vibrations within the block of Sylodyn was present (see Figure 6), a new material model was adopted for the elastomers. A linear viscoelastic model (with frequency dependent properties) instead of the linear elastic one previously used, was introduced in Abaqus. For further theoretical background about linear viscoelasticity, see e.g. chapter 9 of [15].
When looking at the data sheet of the manufacturers, one can see that those are bonded to structural effects such as shape factors and boundary conditions of the samples and tests, hindering the use of the material properties for an arbitrary size and/or shape. Hence, material parameters are of interest and can be determined from the manufacturer data sheet, static measurements and finite element simulations. After considering vari-ous models, a linear viscoelastic model was chosen due to the size of deformations (small deformations are assumed). The advantage of this choice is that it will yield a linear dynamic system for a structure containing elastomer in the junctions. Moreover, by using material parameters, elements of any size and shape can be included in the structural model for dynamic analysis (different construction types use different elastomer configu-rations). The extraction and characterization of the elastomer can be seen in [16] with more detail, although some explanations and key-points are hereafter given.
4.3.1 Static parameters
Isotropic linear elasticity is the base for the linear viscoelastic model and thus two pa-rameters define the static behaviour. Looking at Abaqus, material behaviour is defined in terms of a shear and a bulk modulus. This is a natural choice for a rubber-like material because the behaviour in shear is usually fairly linear even for quite large strains (say less than 100 % direct shear strain). Also, the bulk behaviour can be characterized by a constant with good accuracy.
Measurements: Preliminary static compression tests on Sylodyn samples between lu-bricated plates, giving a homogeneous state of stress and thus eliminating structural effects were performed in an uni-axial testing machine (MTS). The results yielded a static Young’s modulus E∞ = 3.2 MPa (using Abaqus notation). This will be the only mea-surements needed in order to extract all material parameters used as input for the finite element software.
Finite element calibration: In the data sheet of the Sylodyn NE [17], a compression modulus is defined and determined experimentally for different configurations (blocks, strip, surface) and shape factors of the elastomer (see Figure 14). Although this com-pression modulus is related to the Young’s modulus of the material, it is however not a material parameter. It depends on the shape and boundary conditions for the test piece used. This is often the case when manufacturers give data of their materials, hindering the use of the properties for an arbitrary size and/or shape.
Subsequently, FE simulations trying to calibrate the model by mimicking the tests performed in [17] were carried out. In order to do so, a block of Sylodyn with shape factor q = 6 –Equation (2)– was modelled, applying the same boundary conditions as the ones used for the tests shown in Figure 14. Likewise, the Young’s modulus obtained via measurements, i.e. E∞ = 3.2 MPa, and the density (measured simply as ρ = m/V in [kg/m3]) were assigned to the block of Sylodyn. The Poisson’s ratio, ν∞, was then varied in an iterative process until the simulated curve and the plot given in Figure 14 matched together. This was done for for all thicknesses stated in [17], i.e. t = 12.5, 25, 37.5, 50 mm. Once this calibration was carried through, the three obtained properties, namely ρ, E∞ and ν∞, were ascribed to the material and all the rest of the curves shown in Figure 14, i.e. blocks with q = 1.5, 3 as well as all thicknesses, were reproduced, portraying that the static parameters obtained give also a good match for the other plots and therefore yielding reliable linear static properties to be used henceforth. These parameters were E∞ = 3.25 MPa and Poissons ratio ν∞= 0.42.
Figure 14: Quasi-static load deflection curve measured at a velocity of deformation of 1% of the thickness per second; testing between flat steel-plates; recording of the 3rd loading; testing at room temperature
[17].
Linear elastic material model (basis for the linear viscoelastic model) was considered and the elastomer blocks were meshed with hexahedral 8-node elements, with reduced in-tegration and hybrid formulation (denoted in Abaqus as C3D8RH). For more information about the finite element method and Abaqus, see [11] and [29] respectively.
The Young’s modulus and the Poisson’s ratio need now to be converted to shear and bulk modulus using Equations (3).
q = loaded area
Figure 15: Shape factor parameters. G∞= E ∞ 2(1 + ν∞); K ∞ = E ∞ 3(1 − 2ν∞) (3)
Abaqus simulations and static measurements are consistent. Moreover, the value of the Poisson’s ratio seems reasonable considering that it is a compressible material. Using values from Abaqus simulations, it yields: G∞ = 1.14 MPa and K∞ = 6.8 MPa, which are the base for viscoelastic parameters considered next.
4.3.2 Dynamic parameters
The lightweight structures containing elastomers are to be analysed in steastate dy-namic analyses. In terms of linear dydy-namic analysis, this means solving for displacement amplitudes and phase lag in linear systems of equations containing complex numbers. Consequently, the material parameters are to be given in the form of complex numbers depending on the frequency.
Scaling method: The Sylodyn NE data sheet [17], yields a dynamic compression mod-ulus (Edyn
c ) and a loss angle (tan δ) for a case mixing in a structural dependence as
discussed, see Figure 16. The parameters Edyn
c (f ) and δ(f ), with f given in Hertz, can
be looked upon as the absolute value and phase angle of a complex quantity depending on frequency Ec∗ with:
Ecdyn = |Ec∗| δ = arg Ec∗ (4) Note that the subindex c denotes structural dependent properties.
Looking at Figure 16, one finds that Edyn
c is weakly dependent on the frequency with
a value of around 6 MPa. The dynamic modulus is always larger than the static modulus [15], and in this case, it is even higher due to structural effects. Thus, in order to find G∗ and K∗, being the dynamic complex shear and bulk modulus respectively, values have to be properly scaled with parameters, eliminating structural effects.
In [18], it was shown that losses represented by δ are not dependent much on the boundary conditions and can therefore be taken as the phase angle of the complex ma-terial parameters, i.e. they can be directly taken from the data sheet. Finding mama-terial parameters for input for FE simulations is thus a matter of doing the proper scaling of the dynamic stiffness given in the data sheet.
Figure 16: DMA-tests; mastercurve with a reference temperature of 21◦C; tests within the linear area of the load deflection curve, at low specific loads [17].
The following scaling will be explained for the complex shear modulus, G∗, although the same procedure applies to the complex bulk modulus, K∗. Because of linear viscoelas-ticity, one can state, for the same elastomer test sample, the following equalities:
αc(f ) = Edyn c (f ) E∞ c = E dyn(f ) E∞ = Gdyn c (f ) G∞ c = G dyn(f ) G∞ (5)
being E the Young’s modulus of the material, and G the shear modulus. Note that the subscript “c” denotes structural dependent properties whereas the superscripts “∞” and “dyn” indicate static and dynamic properties respectively.
By working out our parameters of interest in the equations, it can be stated:
Gdyn(f ) = αc(f ) · G∞=
Ecdyn(f ) E∞
c
· G∞ (6)
where Ecdyn(f ) can be taken directly from Figure 16 for each frequency of interest, and Ec∞ from Figure 17. The parameter Ec∞, has a value, for the lowest shape factor (q = 1.5) fairly constant (≈ 6 MPa) if the preload is less than about 0.6 MPa, which should be the operating range for the material. The static shear modulus G∞ in Equation 6 was determined in Equation 3 by using the results obtained in the MTS measurements.
Hence, material parameters can be obtained directly from static parameters by scal-ing them with a frequency-structural dependent parameter αc(f ), determined for each
frequency directly from the data sheet [17].
The loss angle is, as mentioned, not affected by boundary conditions and structural effects [18], giving that the phase angle for G∗(f ) is taken directly from the data sheet (Figure 16), i.e.:
arg G∗(f ) = δ(f ) (7) The parameters determined give the complex shear modulus in polar form. Abaqus re-quires G∗ and K∗ in a rectangular form, i.e. G∗ = Gs+ iGl, with Gs and Gl being the
Figure 17: Static modulus of elasticity as a tangent modulus taken from the load deflection curve; dynamic modulus of elasticity due to sinusoidal excitation with a velocity level of 100 dBv re. 5·10−8m/s; test according to DIN 53513 [17].
storage and loss modulus respectively. The conversion may be done by applying simple trigonometry, according to:
Gs= Gdyncos δ
Gl = Gdynsin δ
(8)
Turning to the complex bulk modulus, the same procedure applies, i.e.:
Kdyn(f ) = αc(f ) · K∞ = Edyn c (f ) E∞ c · K∞ (9)
where αc(f ) has the same values and thus is obtained in the same way as for the dynamic
shear modulus. Again, the phase angle for K∗(f ) is taken directly from the data sheet (Figure 16).
4.4
New comparison Sylodyn / No Sylodyn
After considering the new material model for the elastomer and the new damping, two full TVEs were stacked on top of each other –the lower one clamped at the bottom– (Figure 18), carrying out another comparison between the differences when using and not using elastomers in between volumes (Figure 19). The results are shown in Figures 20 and 21, where it can be seen that, as advanced in [10], the use of elastomer in the junctions reduces, overall, the complex acceleration magnitudes in the level under. The evaluation points are those shown in Figure 22, and they will be used henceforth unless stated otherwise. Note that they are not the same as the measurement points in [3] as no calibration is done at this stage yet (just comparisons between models).
X Y
Z
Figure 18: Model with two TVEs stacked.
X Y Z X Y Z
Figure 19: Detail of the FE models without (left) and with Sylodyn (right) in between.
Figure 20: Results of the model without Sylodyn. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
Figure 21: Results of the model with Sylodyn. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
4.5
Influence of evaluation points
Even though the measurements in-situ were done according to the AkuLite protocol and thus the measuring points, i.e. the position of the accelerometers, is known with a fairly good accuracy, this investigation was carried out in order to point out the importance of the evaluation points of the simulations being placed in the exact same spot as the accelerometer’s position. In here, two difference placements for the evaluation points were evaluated, see Figures 22 and 23. If one compares Figure 24 with Figure 21, one can see that the selection of the evaluation points does influence to a great extent the resultant acceleration complex magnitudes. If the accelerometers were not placed in the exact same spot as the evaluation points in the FE model, differences in amplitudes up to a factor of 10 can be found (if for instance the evaluation point is in between two beams instead on top of one).
Step: FreqSweep Increment 48: Frequency = 200.0 Deformed Var: not set Deformation Scale Factor: not set
ODB: CaseAwideStructure2TVEFreqSweep.odb Abaqus/Standard 6.11−3 Thu Jan 17 19:57:30 W. Europe Standard Time 2013
X Y
Z
Figure 22: First evaluation points layout (5 evaluation points –in red– in just one half of the floor). Results from this 1 N frequency sweep placed at the middle of the floor are seen in Figure 21.
Step: FreqSweep Increment 48: Frequency = 200.0 Deformed Var: not set Deformation Scale Factor: not set
ODB: CaseAwideStructure2TVEFreqSweep.odb Abaqus/Standard 6.11−3 Thu Jan 17 19:57:30 W. Europe Standard Time 2013
X Y
Z
Figure 23: Second evaluation points layout (5 evaluation points –in red– along the whole floor). Results from this 1 N frequency sweep placed at the middle of the floor are seen in Figure 24.
Figure 24: Results of the model with different evaluation points (layout 2, Figure 23). Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
4.6
Connections
It was thought that the influence of the connections between floor, ceiling and surrounding walls should also be checked. Two tried outs were examined in addition to the one shown in Figure 9.
In first instance, the all the surfaces of the floor were fully tied to the surrounding walls, whereas the ceiling was let as before, i.e. fully coupled at discrete surfaces. Furthermore, a new approach was tried, where all surfaces of both floor and ceiling were fully connected to the surrounding walls, as shown in Figure 27.
X Y
Z X
Y
Z
Figure 25: Floor fully tied to the surrounding walls (left) and floor and ceiling fully tied to surrounding walls (right). The connecting surfaces in each case are highlighted in pink colour.
As depicted in Figures 26 and 27, differences are present when changing connections within the junctions (compare with Figure 20). As previously said, modelling a junction is a very complicated task, and the connections are the key points. Nevertheless, the first type of connection shown in Figure 9 is believed to be the one who correlates at best with the real behaviour of the building, as discussed with the manufacturers.
Figure 26: Results with full tie connection on the floor. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
Figure 27: Results with full tie connections on the floor and ceiling. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
4.7
Tie plates
In the real construction, metallic tie plates embrace volumes vertically on the exterior part in order to provide stability to the building. Therefore, their contribrution to flanking transmission was checked by modelling them as shown in Figure 28. The dimensions of each plate are 1.33 m long and 50 mm wide (two of those plates are attached forming a framing square).
The results are presented in Figure 29. If one compares them with the ones in Figure 21 (same model without tie plates), one can see that the tie plates do not change much the behaviour of the structure regarding flanking transmission as both the shapes and the magnitudes of the curves remain the same in both cases. Therefore, it can be concluded that they can be eventually disregarded in future larger models.
X Y Z X Y Z
Figure 29: Results with tie plates. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
4.8
Metal studs
As stated in [2], in order to ensure that the volumes are positioned correctly relative to each other during assembling at the building yard, a number from two to four solid metal studs (diameter 30 mm), are installed in centered drilled holes between every two volumes in vertical direction, as shown in Figure 30. This investigation was done after a meeting the authors had with Lindbäcks Bygg, where it was pointed out that the metal studs are not always removed and they are sometimes left in between volumes. Therefore, the potential influence of those studs was checked by modelling them as shown in Figure 31.
Figure 30: Centering metal studs between every two volumes on top of each other [2].
As illustrated in Figure 32, if one compares the model without studs (Figure 21) with the same model with studs, the contribution of the studs to the flanking transmission is negligible. It can be concluded from these simulations that they can be eventually disregarded in future models.
X Y Z X Y Z
Figure 31: Model with four metal studs included. A centering stud is shown in black color on the right picture.
Figure 32: Results with metal studs. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
4.9
Modelling of various TVEs
The fact that the acceleration magnitudes transmitted to the lower TVE within the low frequency range are barely not noticeable, could be, as aforesaid, due to the fact that global modes of the building are not caught. Along those lines, the influence of placing a third TVE on top of the two already analyzed was checked, as shown in Figure 33.
The results shown in Figure 34 portray that still not much is happening in the low frequencies. More TVEs both vertically and horizontally should be assembled in order to inspect this hypothesis, but this will require the use of reduction methods since the three TVEs are in the limit of what the supercomputers at our disposal are able to handle in a reasonable amount of time (≈1.5 week this 3TVE-simulation). Before assembling more TVEs, two other hypothesis will be tried to see if they influence the low frequency behaviour (Sections 4.10 and 6.2).
X Y Z X Y Z
Figure 33: Modelling of three stacked TVEs.
Figure 34: Results with 3 TVEs. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
4.10
Air influence
Accurately modelling the flanking transmission between two adjoining rooms can be a really complicated and daunting task. Many factors come into play making more difficult the creation of a realistic model that captures all phenomena occurring in reality.
X Y Z X Y Z
Figure 35: Model with air inclusions (light blue colour).
Hence, air cavities are now included between some parts of the construction since they may influence the sound transmission to a great extent, especially in the low frequency range. This investigation was, as for the improvements described above, carried out for case A with beams placed widthwise.
Figure 36: Results with air inclusions. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in (note that for clarity, the scale in the right plot is different than in the other graphs as the magnitudes are larger).
The model used for this investigation is shown in Figures 35. Air cavities in the TVE can be observed in light blue whereas the other parts are shown in the same colours as in Figure 8. Acoustic hexahedral elements (AC3D20 in Abaqus) with 20 nodes were utilized for meshing the air, whose properties are shown in the Annex.
5
Discussion and conclusions
In this still ongoing investigation, an extensive insight of timber based volume buildings has being gained. The influence on flanking transmission of different structural features such as: different types of connections, the modelling of air between construction elements, material parameters, connectors (tie plates, metal studs), evaluation points, etc. has been checked. The findings stated here together with the ones to come from this still ongoing investigation will allow the creation of a finite element model prediction tool (by calibrating simulated and measured results) in order to check the vibratory and acoustic performance of these types of buildings during the design phase. In order to achieve the latter, still several things left to do, as it will be explained in Section 6.
6
Future work
To unerringly predict the real behaviour of the type of construction under study and calibrate FE results with measurements, still more construction features must be looked into:
6.1
Assembly of more TVEs
As advanced in Section 4.9, it is our belief that by assembling many TVEs both in the vertical and horizontal direction, to form the complete building, global modes of vibra-tion could caught, contributing to the flanking transmission in one specific room. This would affect overall the low frequency range, where most interest is focused in lightweight buildings.
As previously said, when assembling the volume elements into the global model, the number of DOFs will quickly increase to exceed the limits of computer capacity, at least in a reasonable amount of time. Therefore, reduction methods, e.g. a component mode synthesis [12], will be adopted. In such manner, the finite element model of each volume element is reduced by retaining the interface degrees of freedom needed to connect the volume elements to other elements together with internal degrees of freedom representing the dynamics of the full model. The calculations will be more time-efficient using this approach.
6.1.1 Simplification of the elastomer blocks
A simplified approach is to treat the elastomer as a discrete spring and dashpot system. This is a more suitable and efficient approach for time-consuming FE simulations,
effec-tively allowing the use of substructuring reduction techniques, when eventually assembling parts into an entire building. So far, elastomers have been sometimes dimensioned as a vertical single degree of freedom point loaded mass-spring-dashpot system (see [7], [19]); although they in practice also act as shearing isolators in the horizontal plane and that they are not strictly point loaded [4]. Along those lines, in [19], it was advised to also model the rotational stiffness and damping of an elastomer in order to match experiments and FE simulations. Therefore, this is currently being studied by the authors. These properties and/or simplified spring-dashpot systems will ultimately serve as an input for FE commercial softwares. This will ultimately allow the assemblage of TVEs into a finite element model of an entire building.
6.2
Scaling input force with source spectra
If one looks at [3], one can see that the low frequency range is still not mimicked properly as barely any vibrations are seen traveling through the junction. It is our belief that another reason why the low frequency vibrations are not properly caught is because of the input force. In the models, an unit harmonic force is considered for all frequencies when carrying out a frequency sweep. However, when performing the measurements, a Japanese ball was used (heavy soft impact source). This source effectively excites low frequency sound. Therefore, in order to correctly reproduce the measurements’ scenario, the input force should be eventually scaled. Some references where the Japanese ball force spectra is presented, both empirically and analytically are e.g. [20] and [21]. Those will be used for the forthcoming scaling.
6.3
Insulation
It must be pointed out that the results given in Section 4.10, could be slightly overes-timating the flanking transmission. In reality, if one looks at Figure 3, it can be seen that right under the floor surface, insulation is placed, as well as in the ceiling cavities. Therefore, the insulation is being right now considered in the latest models.
Some preliminary results can be seen in Figure 37. One can already state by simply looking at the results that indeed the consideration of just air in the cavity between floor and ceiling overestimates the wave propagation as the amplitudes are higher than when including insulation.
The insulation was so far only modelled using the Craggs method [23], which is built-in built-in Abaqus. More empirical as well as theoretical methods, e.g. [25], [26], [27], [28], for modelling insulation are at the moment being tried in order to check the differences between them.
6.3.1 Local and global influence
To sum up the latter, the inclusion of air and insulation has a local influence in the vibration propagation from floor to ceiling, although the insulation should always be considered, as just including the air would overestimate the transmission. It is our belief
Figure 37: Results with air inclusions and insulation. Acceleration complex magnitudes evaluated on the floor (blue line), ceiling (red line) and bottom walls (green). On the left, all curves are shown, whereas on the right, the curves correspondent to the ceiling and walls were zoomed in.
that the insulation and air will only affect locally, i.e. in the cavity directly in contact with the excitation force, although the inclusion of acoustic media (air) in other parts not directly in contact to the excitation force, i.e. surrounding walls, will also be looked into.
6.4
Boundary conditions
The influence of boundary conditions of the building when assembling several TVEs will be also examined.
6.5
TVE configurations
Once the accurate finite element model is achieved and calibrated, modifications will be done and new TVE configurations, i.e. case B and case C (see Figure 4) will be checked regarding flanking transmission performance.
6.6
Isolator properties
Likewise, improvement of elastomer properties for this specific application could eventu-ally be proposed.
References
[1] J. Forssén, W. Kropp, J. Brunskog, S. Ljunggren, D. Bard, G. Sandberg, F. Ljung-gren, A. ÅLjung-gren, O. Hallström, H. Dybro, K. Larsson, K. Tillberg, L-G. Sjökvist, B. Östman, K. Hagberg, Å. Bolmsvik, A. Olsson, C-G. Ekstrand, M. Johansson: Acous-tics in wooden buildings. State of the art 2008. Vinnova project 2007-01653, Report 2008:16, SP Trätek (Technical Research Institute of Sweden), Stockholm, 2008.
[2] F. Ljunggren, A. Ågren: Potential solutions to improved sound performance of vol-ume based lightweight multistory timber buildings. Applied Acoustics 72 (2011) 231– 240.
[3] AkuLite Mättaport 100526 Brunnby Park, Upplands Väsby, Sweden, 2012.
[4] A. Ågren, F. Ljunggren, Å. Bolmsvik: Flanking transmission in light weight timber houses with elastic flanking isolators. Proceedings of Internoise, New York, USA, 2012.
[5] S. Ljunggren: Measurement of the performance of noise controlling devices in build-ings of massive wood. Working Report 2001:42001. Department of Civil and Archi-tectural Engineering, Division of Building Technology, KTH, Stockholm, Sweden, 2001.
[6] Å. Bolmsvik: Structural-acoustic vibrations in wooden assemblies – Experimental modal analysis and finite element modelling. PhD thesis. Linnaeus University, Växjö, Sweden, 2012.
[7] Å. Bolmsvik, A. Linderholt, K. Jarnerö: FE modeling of a lightweight structure with different junctions. Proceedings of Euronoise, Prague, Czech Republic, 2012.
[8] Å. Bolmsvik, A. Brandt: Damping assessment of light wooden assembly with and without damping material. Engineering Structures 49 (2013) 434–447.
[9] R. Ökvist, F. Ljunggren, A. Ågren: Variations in sound insulation in nominal iden-tical prefabricated lightweight timber constructions. Journal of building acoustics, 17(2) 2009, 91–103.
[10] J. Negreira, A. Sjöström, D. Bard: Investigation of the vibration transmission through a lightweight junction with elastic layer using the finite element method. Proceedings of Internoise 2012, New York, USA, 2012.
[11] K.J. Bathe: Finite Element Procedures, Prentice Hall, New York, United States, 1996.
[12] R. R. Craig: Structural Dynamics; An Introduction to Computer Methods, John Wiley & sons Inc., New York, United States, 1981.
[14] N. Labonnote: Damping in timber structures. PhD thesis. Norwegian University of Science and Technology, Trondheim, Norway, June 2012.
[15] P-E. Austrell: Modeling of elasticity and damping for filled elastomers. PhD thesis, Division of Structural Mechanics, Lund University, Sweden, 1997.
[16] J. Negreira, P-E. Austrell, O. Flodén, D. Bard: Characterization of an elastomer for noise and vibration isolation in lightweight timber buildings – Part I: obtaining material properties from laboratory testing, material modelling, and finite element simulations. In preparation process. To be submitted to a Jounal, June 2013.
[17] Getzner Werkstoffe GmbH (2004). Data sheet of the Sylodyn NE.
[18] A. K. Olsson, P-E. Austrell: Finite element analysis of a rubber bushing considering rate and amplitude dependence effects. Proceedings of 3rd European Conference on Constitutive Models for Rubber (ECCMR), London, UK, 2003.
[19] Å. Bolmsvik, A. Linderholt, A. Brandt, T. Ekevid: FE Modelling of Light Wooden Assemblies. Submitted to Engineering Structures, January 2013.
[20] S. Schoenwald, B. Zeitler: Floor excitation with the heavy soft impact source. Pro-ceedings of Forum Acusticum 2011, Aalborg, Denmark, 2011.
[21] J. Y. Jeon, J. K. Ryu, J. Jeong: Review of the Impact Ball in Evaluating Floor Impact Sound. Acta Acustica united with Acustica 92(5) (2006), 777–786.
[22] L. Cremer, M. Heckl, B. A. T. Petersson: Structure-borne sound. Springer. Berlin, Germany, 2004.
[23] A. Craggs: A finite element model for rigid porous absorbing materials. Journal of Sound and Vibration 61 (1978), 101–111.
[24] P. Davidsson: Structure-acoustic analysis; finite element modelling and reduction methods. PhD thesis. Division of Structural Mechanics, Lund Univesity, Sweden, 2004.
[25] M. E. Delany, E. N. Bazley: Acoustical properties of fibrous absorbent materials. Applied Acoustics 3 (1970), 105–116.
[26] M. A. Biot: Theory of propagation of elastic waves in fluid-saturated porous solids. i. low frequency range. The Journal of the Acoustic Society of America 28(2) (1956), 168–178.
[27] Y. Miki: Acoustical properties of porous materials – Modifications of Delany-Bazley models. Journal of the Acoustical Society of Japan 11(1) (1990), 19–24.
[28] Y. Miki: Acoustical properties of porous materials – Generalizations of empirical models. Journal of the Acoustical Society of Japan 11(1) (1990), 25–28.
[29] Dassault Systèmes: Abaqus theory manual, Version 6.11, 2012.
[30] F. Ljunggren: Using elastic layers to improve sound insulation in volume based multistory lightweight buildings. Proceedings of Internoise, Ottawa, Canada, 2009.
[31] A. Ågren: Acoustic highlights in Nordic light weight building tradition – focus on ongoing development in Sweden. Proceedings of BNAM, Bergen, Norway, 2010.
[32] M. Meyers, K. Chawla: Mechanical Behavior of Materials. Cambridge University Press, New York, USA, 2009.
[33] K. Jarnerö, Å. Bolmsvik, A. Brandt, A. Olsson: Effects of flexible supports on vibra-tion performance of floors. Proceedings of Euronoise 2012, Prague, Czech Republic, 2012.
[34] Å. Bolmsvik, T. Ekevid: Flanking transmission in a timber-framed building – A comparison of structural vibrations in measurements and FE analyses, Submitted to The International Journal of Acoustics and Vibration, January 2013.
[35] Å. Bolmsvik, T. Ekevid: FE modeling of wooden building assemblies. Proceedings of Internoise 2010, Lisbon, Portugal, 2010.
[36] F. Ljunggren: Long-term effects of elastic glue in lightweight timber constructions. Proceedings of Forum Acusticum. Aalborg, Denmark, 2011.
Annex
Structure material properties
Table 1: Material properties.
Air Particle board Plasterboard Plywood Wood Air Insulation
E1 [Pa] - 3.9 · 109 2 · 109 12.4 · 108 8.5 · 108 - -E2 [Pa] - - - - 3.5 · 107 - -E3 [Pa] - - - - 3.5 · 107 - -ν12[-] - 0.3 0.2 0.3 0.2 - -ν13[-] - - - - 0.2 - -ν13[-] - - - - 0.3 - -G12[Pa] - - - - 7 · 108 - -G13[Pa] - - - - 7 · 108 - -G23[Pa] - - - - 5 · 107 - -ζ[%] - 5.55 5.55 5.55 5.55 - -ρ [kg/m3] 1.2 767 692.3 710 - - -Ka[Pa] 141360 - - - -Ω [-] - - - 0.96 R [Ns/m4] - - - - - - 32000 Ks [-] - - - 1.7
E is the modulus of elasticity of the materials, ν the Poisson’s ratio, G the shear modulus, ζ the damping ratio (leading to Rayleigh coefficients as explained in the report of α = 17.3730 and β = 9.7792 · 10−5), ρ the density, and Ka the bulk modulus of the air. For
the porous material, Ω is the porosity, R the resistivity and Ks the structure factor, i.e.
tortuosity, for the insulation material. Those properties were taken for this first try-out from [24]. Another realistic materials will be eventually tried. Those parameters allow to get the needed parameters for Abaqus simulations using the Craggs method [23], according to (see Abaqus manual for more information [29]):
ρ = ρfKsΩ = 1.9747 kg/m3
Volumetric drag = RΩ = 30720 Ns/m4 Bulk modulus = ρfc2f = 142355
(10)
Sylodyn properties
Table 2: Sylodyn NE linear elastic properties.
ρ [kg/m3] E [Pa] ν [-]
Table 3: Sylodyn NE viscoelastic properties.
Complex shear modulus Complex bulk modulus
Freq. [Hz] Gs [MPa] Gl [MPa] Ks [MPa] Kl [MPa]
1 1.25243 0.06267 7.47065 0.37384 2 1.25174 0.07519 7.46654 0.44853 3 1.25155 0.07832 7.46540 0.46720 4 1.25135 0.08145 7.46420 0.48586 5 1.25093 0.08771 7.46168 0.52317 6 1.25047 0.09396 7.45897 0.56047 7 1.24999 0.10021 7.45608 0.59776 8 1.24973 0.10334 7.45456 0.61640 9 1.24947 0.10646 7.45299 0.63503 10 1.24892 0.10646 7.44973 0.67229 15 1.28244 0.01282 7.61178 0.76373 20 1.27328 0.15353 7.59499 0.91580 25 1.27475 0.14079 7.60376 0.83980 30 1.29994 0.16995 7.75401 1.01374 35 1.29906 0.17645 7.74875 1.05248 40 1.29817 0.18294 7.74349 1.09123 45 1.29621 0.19590 7.73180 1.16855 50 1.29425 0.20887 7.72012 1.24587 55 1.29318 0.21533 7.71370 1.28444 60 1.29210 0.22180 7.70727 1.32301 65 1.29096 0.22825 7.70047 1.36151 70 1.28982 0.23471 7.69366 1.40001 75 1.28861 0.24115 7.68647 1.43844 80 1.28741 0.24759 7.67927 1.47688 85 1.28614 0.25402 7.67170 1.51524 90 1.28487 0.26046 7.66412 1.55360 95 1.31141 0.27281 7.82243 1.62731 100 1.33795 0.28517 7.98073 1.70103 105 1.33660 0.29100 7.97268 1.73581 110 1.33525 0.29683 7.96463 1.77059 115 1.33390 0.30266 7.95658 1.80537 120 1.33255 0.30850 7.94853 1.84015 125 1.33120 0.31433 7.94047 1.87492 130 1.32985 0.32016 7.93242 1.90970 135 1.32917 0.32307 7.92840 1.92709 140 1.32850 0.32599 7.92437 1.94448 145 1.32782 0.32890 7.92035 1.96187 150 1.32715 0.33182 7.91632 1.97926 155 1.32606 0.33595 7.90983 2.00392 160 1.32497 0.34008 7.90333 2.02858 165 1.32388 0.34422 7.89684 2.05324 170 1.32279 0.34835 7.89035 2.07789 175 1.32170 0.35249 7.88385 2.10255 180 1.32062 0.35662 7.87736 2.12721 185 1.32007 0.35869 7.87411 2.13954 190 1.31953 0.36075 7.87086 2.15187 195 1.31898 0.36282 7.86762 2.16420 200 1.31844 0.36489 7.86437 2.17653
Finite Element Modelling of
a Timber Volume Element
Based Building with Elastic
Layer Isolators
As part of developing reliable tools for predictions of the acoustic and vibratory performance of light-weight timber buildings during the design phase, a timber volume building using elastic layers in the junctions was analyzed by means of the finite ele-ment method.
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