Prediction Of Sound Insulation Research Articles

Computational prediction of impact sound insulation of a full-scale timber floor applying a FEM simulation procedure

During the recent decades, simulation procedures involving the finite element method (FEM) have been developed to enable prediction of impact sound insulation of timber slabs and floors. FEM simulations have previously been applied for timber floors mainly in low frequencies despite their evident ability to operate over a wide frequency range. Additionally, the validation processes have involved calibrations and experimental modal analyses which can seldom be performed in product development tasks concerning full structures. The purpose of this research was to study the applicability of a FEM simulation procedure to predict normalised impact sound pressure levels Ln of a full-scale timber floor if material data provided by the product manufacturers is used. The floor was studied at three construction stages where the FEM simulations were performed for the bare floor and the rib slab, and the floor covering was considered in the post-processing stage in case of the full floor. The impact force excitation generated by the ISO standard tapping machine was described with the recently published procedure involving explicit dynamics analysis. To serve the purposes of this study, the FEM models were fully constructed before the measurements were carried out. According to the results, the 1/3-octave Ln of the full floor and the floor without covering was predicted with a 0 to 9 dB accuracy depending on the frequency band and the single-number quantities with a 0 to 4 dB accuracy. The single-number quantities of the bare rib slab were underestimated with the simulations by 4 to 5 dB. Probable causes for the discrepancies between the simulation and measurement results pointed mainly to the uncertain material properties but possibilities for modelling inaccuracies could not be excluded.

Uncertainty quantification of the diffuse sound field assumption in sound insulation predictions

The transmission loss of a partition depends on the sound fields in the adjoining rooms, which are often taken to be diffuse. A diffuse sound field is a random field, representing a conceptual ensemble of rooms with the same volume and reverberation time, but otherwise any possible arrangement of boundaries and small objects that have a wave scattering effect. Uncertainty due to random wave scattering is therefore inherently present in diffuse transmission loss values. In this work, closed-form expressions are presented for quantifying this uncertainty, such that it becomes possible to estimate by how much the transmission loss of a particular room-wall-room system may deviate from the nominal, ensemble average value which corresponds to omnidirectional incidence and halfspace radiation. The first expression is exact yet its evaluation requires knowledge of the dynamic stiffness of the partitioning structure and of the radiation impedances of the surrounding fluids. The second expression is approximate and depends on energetic quantities only, so it is also applicable in an experimental setting. The expressions are validated in a Monte-Carlo simulation study involving a single wall.

Impact sound insulation prediction and uncertainty quantification using a detailed source model in the modal Transfer Matrix Method

The main goal of this work is to provide an efficient and accurate prediction of the impact sound insulation of layered structures for the entire building acoustics frequency range (50-5000 Hz). To this end, the modal Transfer Matrix Method (mTMM) has been developed to predict the impact sound radiation from layered floors resulting from tapping machine impacts, while accounting for simply supported boundary conditions. A detailed source model is presented which accounts for both the impact locations of the individual hammers and the discrete 2 Hz force spectrum. It is also discussed how this detailed source model can be implemented into the mTMM. Monte Carlo simulations provide insight into the uncertainty of the radiated sound power and the impact sound insulation improvement for bare and layered floors, resulting from the impact force location. Numerical validation is provided by comparison to finite element models of various floors. Narrow-band sound pressure level measurements on a layered floor have been performed to validate the detailed source model and its use in the mTMM. A comparison of measured and predicted results indicates the importance of a detailed source approach, especially at low frequencies

Sound insulation prediction and band gap characteristics of four vibrators acoustic metamaterial with composite phononic crystal structure

Acoustic Metamaterial have been widely concerned because of their strong sound insulation characteristics for specific low-frequency bands. However, further optimization is still needed in terms of broadband sound insulation characteristics, and phononic crystals can generate multiple sound insulation bandwidths due to their unique bandgap characteristics. Therefore, a four vibrators acoustic Metamaterial structure with phononic crystals is proposed to broaden the sound insulation performance at medium and high frequencies while retaining the advantages of sound insulation at low frequencies. Firstly, a semi analytical method combining finite element analysis was proposed for the sound insulation performance of the structure. Afterwards, a bandgap theory based on the equivalent medium method was proposed to reveal the reasons for its characteristics. Finally, a cylindrical sleeve structure was designed for a certain rolling rotor compressor, and its sound insulation performance in the cylindrical state was verified through finite element simulation.

Sound-insulation prediction model and multi-parameter optimisation design of the composite floor of a high-speed train based on machine learning

Designing a sound-insulation scheme for a composite structure efficiently and accurately for noise control in equipment is essential. However, traditional simulation and experimental methods for obtaining an optimal solution are not only time-consuming but also difficult to implement. In this paper, a sound insulation optimisation design method based on machine learning is proposed. The method is applied to design a complex composite floor structure of a high-speed train. By testing numerous practical schemes in the acoustics laboratory to obtain a sample set, a machine learning model for predicting the sound insulation performance of a composite floor of a high-speed train is trained and verified. Subsequently, an efficient and accurate multi-parameter sound insulation optimisation design of the composite floor structure based on the machine learning model is implemented. First, the original data samples required for model training are analysed and sorted. Second, the target feature subset is selected through the main influencing factor analysis, correlation-redundancy analysis, and mRMR feature selection calculation. Then, based on the SVR method, the standardised feature data are used to train and verify the sound-insulation prediction model of the composite floor structure of a high-speed train. Finally, two embodiments are presented to verify the advantages of the model in the multi-parameter optimisation design of the sound-insulation model of the composite floor structure of a high-speed train. The results show that the optimal sound insulation is 51.69 dB when the thickness and surface density of the composite floor are given. Similarly, the minimum surface density is 89.42 kg/m2 when the thickness and sound insulation limit are given.

Study on Sound Transmission across a Floating Floor in a Residential Building by Using SEA

For the purpose of reducing the impact noise transmission across floating floors in residential buildings, two main sound transmission paths in the floating floor structure are considered: the stud path and the cavity path. The sound transmission of each path is analysed separately: the sound transmission through the cavity and the stud are predicted by statistical energy analysis (SEA). Then, the sound insulation prediction model of the floating floor is established. There is reasonable agreement between the theoretical prediction and measurement, and the results show that a resilient layer with low stiffness can attenuate the sound bridge effect, resulting in higher impact noise insulation. Then, the influences of the floor covering, the resilient layer and the floor plate on the impact sound insulation are investigated to achieve the optimised structure of the floating floor based on the sound insulation.

Effect of the Laying Order of Core Layer Materials on the Sound-Insulation Performance of High-Speed Train Carbody.

The design of sound-insulation schemes requires the development of new materials and structures while also paying attention to their laying order. If the sound-insulation performance of the whole structure can be improved by simply changing the laying order of materials or structures, it will bring great advantages to the implementation of the scheme and cost control. This paper studies this problem. First, taking a simple sandwich composite plate as an example, a sound-insulation prediction model for composite structures was established. The influence of different material laying schemes on the overall sound-insulation characteristics was calculated and analyzed. Then, sound-insulation tests were conducted on different samples in the acoustic laboratory. The accuracy of the simulation model was verified through a comparative analysis of experimental results. Finally, based on the sound-insulation influence law of the sandwich panel core layer materials obtained from simulation analysis, the sound-insulation optimization design of the composite floor of a high-speed train was carried out. The results show that when the sound absorption material is concentrated in the middle, and the sound-insulation material is sandwiched from both sides of the laying scheme, it represents a better effect on medium-frequency sound-insulation performance. When this method is applied to the sound-insulation optimization of a high-speed train carbody, the sound-insulation performance of the middle and low-frequency band of 125-315 Hz can be improved by 1-3 dB, and the overall weighted sound reduction index can be improved by 0.9 dB without changing the type, thickness or weight of the core layer materials.

A Mathematical Approach for Sound Insulation Characteristics and Cost Optimization of Double-Layer Composite Structures

The compressor is the primary source of noise in a refrigeration system. Most compressors are wrapped with multi-layer sound insulation cotton for noise reduction and sound insulation. We explore the sound insulation law of different polyvinyl chloride thicknesses and non-woven fibers. Polyvinyl chloride with varying thicknesses and non-woven fibers are then combined by bonding to study the sound insulation characteristics of a two-layer composite structure. A sound insulation prediction model is established using the multi-parameter nonlinear regression method. An optimal cost mathematical model is established based on experimental and mathematical methods that can quickly determine the optimal cost scheme for different designs with the same effect.

Calculating the equivalent elastic moduli and their influence on modelling the sound insulation of softwood cross laminated timber (CLT)

There are characteristics unique to natural materials such as timber that must be dealt with carefully to develop successful sound insulation prediction models. Timber has low internal losses typical of low-density building materials but with material properties that vary according to growth conditions. To study these factors in cross laminated timber (CLT) products, orthotropic thin plate and isotropic thick plate models are investigated. Equivalent elastic moduli are obtained using two methods from values and limits provided in the timber standards and literature, or by the manufacturer. The equivalent moduli are used to calculate the sound insulation of three- and five-layer CLT plates. Appropriate upper and lower limits are calculated from the combined material parameters and compared with sound insulation results measured in accredited laboratories for the first time. EN ISO 10140 test standards require that surface density of the sample be documented in the laboratory; additional precision information such as the fifth percentile of the material density is not required. However, considering the limits on the internal loss factors and elastic moduli only in the thin plate sound insulation model, gives a poor overall prediction performance (23.6% within the upper and lower limits). In this paper we combine the limits on elastic moduli, internal loss factors, and density. With these combined parameters the prediction is improved; less than half of the measured sound insulation values fall within the upper and lower limits of a typical thin plate model (44.0%). The single figure sound reduction index values are underestimated in seven out of nine cases. The prediction is further improved when a thick plate model is considered. There are several layers of complexity in the measurement and modelling conditions that must be carefully considered. The contributions from these compounding factors are discussed, and additional moduli and density parameters are proposed for inclusion in the literature and standards.

Low-frequency sound insulation optimisation design of membrane-type acoustic metamaterials based on Kriging surrogate model

Low frequency is a difficult problem in noise control. How to design new lightweight materials or structures to achieve low-frequency noise reduction is of utmost importance. This study presents a multi-parameter optimisation design procedure for a specific sound insulation frequency and bandwidth of a lightweight acoustic metamaterial. First, a sound insulation model of membrane-type acoustic metamaterials (MAMs) was established based on the finite element method, and the predicted results are validated with results from previous studies. Subsequently, the bandgap characteristics and generation mechanism of the sound insulation peak are analysed. Second, the influences of both material and structural parameters of the membrane and mass block, on the sound insulation characteristics of the MAMs are systematically investigated. They are discussed by first using a single variable control method and then considering the multi-parameter coupling effect. Finally, a Kriging surrogate model for sound insulation prediction of MAMs is established. Aiming at a specific sound insulation frequency and bandwidth, the multi-parameter optimisation design of the MAMs is performed. According to the results, during multi-parameter coupling, the influence law of a single variable on the sound insulation peak of MAMs is unchanged; however, the influence magnitude differs. The Kriging surrogate model can effectively design acoustic metamaterials with a specific sound insulation frequency and bandwidth.

Prediction of Sound Insulation Using Artificial Neural Networks—Part II: Lightweight Wooden Façade Structures

A prediction model based on artificial neural networks is adapted to forecast the acoustic performance of airborne sound insulation of various lightweight wooden façade walls. A total of 100 insulation curves were used to develop the prediction model. The data are laboratory measurements of façade walls in one-third-octave bands (50 Hz–5 kHz). For each façade wall, geometric and physical information (material type, dimensions, thicknesses, densities, and more) are used as input parameters. The model shows a satisfactory predictive capability for airborne sound reduction. A higher accuracy is obtained at middle frequencies (250 Hz–1 kHz), while lower and higher frequency ranges often show higher deviations. The weighted airborne sound reduction index (Rw) of façades can be estimated with a maximum difference of 3 dB. Sometimes, the model shows high variations within fundamental and critical frequencies that influence the predictive precision. A sensitivity analysis is implemented to investigate the significance of parameters in insulation estimations. The material density (i.e., cross-laminated timber panel, gypsum board), thickness of the insulation materials, thickness and spacing between interior studs and the total density of façades are factors of significant weight on predictions. The results also emphasize the importance of façade thickness and the total density of the clustered exterior layers.

Sound insulation prediction method for single and spot laminated multilayer panels

Single-leaf panels made from homogeneous and isotropic materials are commonly used in buildings. However, it is often necessary to add various layers of the same or different materials in order to increase the acoustic insulation. This article presents a prediction method for the calculation of the sound reduction index that comprises single panels and multilayer panels joined together using spot techniques, such as by screws. The method is based on previous single-leaf panel models extended to multilayer structures. The predicted values are compared with panel measurements obtained according to ISO 140-3. The sound reduction index R in third octave bands, the weighted sound reduction index Rw, and the spectral adaptation terms ( C, Ctr) are examined. In addition, predictions from two commercial software tools are evaluated and compared. Statistically, the results show that the proposed method gives values that agree well with the measurements, both for single and multilayer panels.

Prediction of Sound Insulation Using Artificial Neural Networks—Part I: Lightweight Wooden Floor Structures

The artificial neural networks approach is applied to estimate the acoustic performance for airborne and impact sound insulation curves of different lightweight wooden floors. The prediction model is developed based on 252 standardized laboratory measurement curves in one-third octave bands (50–5000 Hz). Physical and geometric characteristics of each floor structure (materials, thickness, density, dimensions, mass and more) are utilized as network parameters. The predictive capability is satisfactory, and the model can estimate airborne sound better than impact sound cases especially in the middle-frequency range (250–1000 Hz), while higher frequency bands often show high errors. The forecast of the weighted airborne sound reduction index Rw was calculated with a maximum error of 2 dB. However, the error increased up to 5 dB in the worse case prediction of the weighted normalized impact sound pressure level Ln,w. The model showed high variations near the fundamental and critical frequency areas which affect the accuracy. A feature attribution analysis explored the essential parameters on estimation of sound insulation. The thickness of the insulation materials, the density of cross-laminated timber slab and the concrete floating floors and the total density of floor structures seem to affect predictions the most. A comparison between wet and dry floor solution systems indicated the importance of the upper part of floors to estimate airborne and impact sound in low frequencies.

Acoustic design tools for estimation of sound insulation performance of wood wall and floor assemblies

The National Building Code of Canada 2015 stipulates the minimum requirements of the airborne sound insulation transmission through common interior walls and ceiling/floor assemblies. The required minimum Apparent Sound Transmission Class (ASTC) is 47 in Canada, whereas the Impact Insulation Class (IIC) for floors is recommended to be higher than 55. For many years, significant efforts were made to develop sound insulation prediction models or tools to predict the sound insulation performance of wall and floor/ceiling assemblies at the design phase in order to meet the requirements and the recommendations made by codes. However, today few models can provide a reliable acoustics design tool. In this document, three prediction tools thought to be practically useful are presented and evaluated. Between these three prediction tools, one is an analytical model of the Insul software while the other two are empirical models developed by the National Research Council of Canada and the American Wood Council. This paper compared the STC and IIC ratings of wood wall and floor assemblies estimated by these three models and verified them by the measured STC and IIC ratings. This work aims at providing an idea for readers to choose a suitable design tool to proceed with their acoustic designs.

A Sound Insulation Prediction Model for Floor Structures in Wooden Buildings Using Neural Networks Approach

Recently, machine learning and its applications have gained a large attraction in different fields. Accurate predictions in building acoustics is vital especially in the design stage. This paper presents a sound insulation prediction model based on Artificial Neural Networks (ANNs) to estimate acoustic performance for airborne and impact sound insulation of floor structures. At an initial stage, the prediction model was developed and tested for a small amount of data, specifically 67 measurement curves in one third octave bands. The results indicate that the model can predict the weighted airborne sound insulation for various floors with an error around 1 dB, while the accuracy decreases for the impact sound especially for complex floor configurations due to large error deviations in high frequency bands between the real and estimated values. The model also shows a very good accuracy in predicting the airborne and impact sound insulation curves in the low frequencies, which are of higher interest usually in building acoustics. Keywords: building acoustics, airborne sound, impact sound, prediction model, neural networks

Shape optimization of studs in double-leaf plasterboard walls for maximal broadband sound insulation and minimal material use

The cross-sectional shape of the metal studs in a double-leaf wall has a significant influence on its sound insulation. In a recent study, a numerical optimization of the stud shape resulted in designs that offer a significant increase in broadband airborne sound insulation, both when compared to conventional C-shaped studs and commercially available acoustic studs, but at the expense of a much higher material use. In the present work, a multi-objective optimization of the stud shape is aimed at, so as to find an optimized trade-off between the stud material cost and the sound insulation of the overall system across the entire building acoustics frequency range. This is achieved by combining a computationally efficient, iterative multi-objective optimization scheme with a computationally efficient numerical sound insulation prediction model of sufficient accuracy. Pareto fronts, which represent the set of optimal combinations of sound insulation and stud material use, are computed for a range of plasterboard wall systems that differ in cavity depth, number of sheets of plasterboard and stud type (symmetric or point-symmetric). For nearly all walls with symmetric studs, the Pareto fronts show that the introduction of a single deep indentation in the stud results in a high increase in sound insulation at a limited increase in material cost compared to simple C-shaped studs while two or three deep indentations result in a higher material cost with a performance close to that of a wall with decoupled leafs. For nearly all walls with point-symmetric studs, the Pareto fronts show that the introduction of two deep indentations results in a high increase in sound insulation at a limited increase in material cost compared to Z-shaped studs while four deep indentations result in a higher material cost with a performance close to that of a wall with decoupled leafs. It is shown that often, the acoustic performance of commercially available acoustic stud shapes can be further improved with less material used to produce the stud and sometimes even a shallower cavity.

Airborne sound insulation prediction of masonry walls using artificial neural networks

In this paper, an alternative method for the calculation of masonry walls sound insulation is investigated. Thirty-four simple monolithic brick walls were examined. For the considered walls, the measurements made by accredited laboratories in compliance with ISO 10140 standard were collected. For each building element, the experimental measurements and all the information concerning the geometric and physical characteristics of all the components (material, dimensions, mass, density, Young’s modulus, Poisson’s module, hole content, etc.) were classified. Then, from the collection of measurements obtained in the standard laboratories and the division of them into homogeneous groups, a statistical sensitivity analysis to determine the most statistically significant parameter for the sound insulation of building walls was carried out. This analysis was a useful tool for selecting parameters to be used in forecast models and for calculating statistical effects. Finally, an alternative method based on the use of artificial neural networks (ANN) was proposed. This paper discusses the results obtained by applying the models to a specific kind of construction: the masonry walls. The results will show a good correlation of the values obtained on this first type of building construction. This encourages the extension of the method explained in this work to other types of walls.

Numerical investigation of the sound-insulation effect of a suspended ceiling structure with arrayed Helmholtz resonators by the finite-difference time-domain method

In order to develop a numerical simulation of floor impact sound transmission via a floor structure that includes sound absorption materials, floor impact sound transmission via a composite floor structure composed of concrete slab, suspended ceiling plate, and an array of Helmholtz resonators inside a sandwiched air layer is modeled by the discrete wave-based numerical method of the vibroacoustic finite-difference time-domain (FDTD). As a preliminary study, the reverberant sound absorption coefficients of absorbers that contain arrayed resonators are simulated and compared to empirically measured values. The accuracy of the estimated sound absorption coefficient is found to depend largely on the diffuseness of the sound field in the simulated sound field as well as in reality. Thereafter, the floor impact sound generated by a floor structure that contains an array of resonators inside a sandwiched air layer between the floor slab and the ceiling plate is simulated, and relatively good agreement between the calculated and measured results for the improvement of the impact sound pressure levels caused by the installation of the resonators was confirmed. This suggests the applicability of the vibroacoustic FDTD method to sound-insulation prediction of the floor impact sound.

Broadband acoustic shape optimization of studs in double-leaf walls

Design optimization of vibro-acoustic systems over a wide frequency band is challenging. It does not only require a computationally efficient numerical prediction model of sufficient accuracy, but the optimization scheme itself should also be computationally efficient and the design space should be limited by all relevant manufacturing and performance constraints. In this paper, a methodology is presented for the shape optimization of components in a complex wall system, with the aim of achieving an optimized sound insulation of the overall system across the entire building acoustics frequency range. As an example, the cross-sectional shape of studs in a double-leaf wall is first parameterized and subsequently optimized for broadband sound insulation with a gradient-based optimization scheme. A recently developed sound insulation prediction model that has the required balance between accuracy and computational efficiency is adopted and validated for a range of plasterboard walls with acoustic studs. The model is further complemented with a novel sensitivity analysis, such that the sensitivities of the predicted sound insulation to the cross-sectional stud shape parameters can be obtained in a semi-analytic way. This approach reduces the computation cost related to broadband acoustic design optimization significantly. Furthermore, inequality constraints that are necessary for obtaining a feasible design in terms of material usage and manufacturing limitations are identified and incorporated in the optimization procedure. The relevant constraints related to strength and stiffness of the wall are very mild and therefore verified after optimization. As an example of the proposed methodology, the cross-sectional shape of flexible metal studs in double-leaf plasterboard walls is optimized for the overall A-weighted sound reduction under pink noise excitation. A range of combinations in stud depths and number of sheets is analyzed. Walls containing the optimized studs have an airborne sound insulation that is close to that of walls with fully decoupled leafs. Their sound insulation is on average 11.8 dB higher than when they would contain conventional C-shaped studs, and 5.1 dB higher than when they would contain acoustic studs that are presently available.

Prediction of sound insulation of flexible panels in low frequencies with dynamics and volume relations

The problem of sound insulation in the low-frequency region (up to 100 Hz) is relevant, but little has been studied theoretically and practically has not been investigated experimentally due to the lack of the necessary experimental base. Especially important is the solution of the problem for local isolation of low-frequency mechanisms by perspective mesh-plate flexible panels (MPP) for various configurations of isolated and protected volumes and at low first natural frequencies. The purpose of this study is to evaluate the effect of forced vibration panel and room volume ratio of the source of the perturbation and the protected volume. The objective is to develop a mathematical model, which can verify the adequacy of the experimental results obtained at frequencies above 30 Hz and acoustic reverberation chambers interferometer. As a result, a formula for calculating the sound insulation has been received, allowing taking into account the volume ratio of the shared spaces and the transition through resonance. The results of the research can be used in the design of direct soundproofing of low-speed mechanisms or for the organization of the first stage of soundproofing and modernization of the design of the MPP in relation to specific conditions and requirements for sound insulation.