Sound diffraction by multiple wedges and thin screens

A theoretical formula that is based on the geometrical theory of diffraction (GTD) is proposed for computing sound diffraction by multiple wedges, barriers, and polygonal-like shapes. The formula can treat both convex and concave edges, where edges may or may not be inter-connected. Comparisons of theoretical predictions with other results done by the BEM or experiments for scaled model confirm the accuracy of the present formula. Numerical examples such as double wedges and doubly inclined barrier show that when there exist several diffraction paths for given source and receiver positions, the insertion loss is dominated by the diffraction associated with the shortest propagation path. It is also found that although the partially inclined barrier increases the shadow zone as compared to the simple screen type of the same total height, it does not necessarily increase the insertion loss at all heights.     

计入地面附加衰减的声屏障插入损失估算方法*

基于理论推导和计算,给出了公路声屏障声学设计中,在考虑地面附加衰减情况下计算插入损失的方法。该方法综合考虑了有限长线声源无限长声屏障绕射声衰减量、有限长线声源地面衰减量及遮蔽角对插入损失的影响。通过与《声屏障声学设计和测量规范》（HJ/T90-2004）的计算结果的对比,验证了本文所给方法的精确性及可行性,并对规范所给地面衰减修正量进行了商榷。最后,给出了当预测点位于有限长路段中央法线上时,通过计算线声源地面衰减量得到计算插入损失所需参数值,再计算插入损失的简便方法。本研究为存在地面附加衰减情况下有限长声屏障插入损失计算提供了一个新的参考方法。     

A boundary element method for the calculation of noise barrier insertion loss in the presence of atmospheric turbulence

Atmospheric turbulence is an important factor that limits the amount of attenuation a barrier can provide in the outdoor environment. It is therefore important to develop a reliable method to predict its effect on barrier performance. The boundary element method (BEM) has been shown to be a very effective technique for predicting barrier insertion loss in the absence of turbulence. This paper develops a simple and efficient modification of the BEM formulation to predict the insertion loss of a barrier in the presence of atmospheric turbulence. The modification is based on two alternative methods: (1) random realisations of log-amplitude and phase fluctuations of boundary sources and (2) de-correlation of source coherence using the mutual coherence function (MCF). An investigation into the behaviours of these two methods is carried out and simplified forms of the methods developed. Some systematic differences between the predictions from the methods are found. When incorporated into the BEM formulation, the method of random realisations and the method of MCF de-correlation provide predictions that agree well with predictions by the parabolic equation method and by the scattering cross-section method on a variety of thin barrier configurations.     

A parametric investigation of the performance of T-profiled highway noise barriers and the identification of a potential predictive approach

Although a considerable amount of research has been undertaken regarding the performance of T-profile noise barriers, the information available to the practicing highway engineer is confusing. For example, there is a widespread belief that the performance of a top edge, expressed as an insertion loss relative to that of the simple barrier on which it is mounted, is constant, irrespective of the relative locations of the source, barrier and receiver. In order to clarify the situation an investigation has been undertaken, using computer modelling, of the performance afforded by highway noise barriers with T-profile tops with different acoustic treatments. The relative insertion loss was found to increase systematically with increasing top width. Although the relative insertion loss afforded by a reflective T-top is small, significant attenuation can be obtained with an absorptive top. Examination of the effect on performance of the locations of source and receiver relative to that of the noise barrier indicated that, for source and receiver locations typical of those experienced for highway noise barriers, the relative insertion loss for a given width of T-top was a function of (a) the path difference between sound travelling to the receiver via the barrier top and direct sound from the source to the receiver and (b) the barrier height. Plots of relative insertion loss versus the path difference, normalised with respect to barrier heights, for a range of T-top widths and absorbent treatment, resulted in a collapse of data around well defined trend lines which offer the potential of being developed into a prediction method.     

预测声屏障插入损失的抛物方程法及其初始声场研究

Salomons建立的抛物方程(CNPE)方法可以预测非均匀环境中的声屏障插入损失。但是该方法在声屏障与声源距离较近时会产生较大误差。文中通过理论分析发现产生该问题的原因在于CNPE方法所使用的Gauss初始场仅适用于小仰角(10°以内)范围内的声波。为解决Gauss初始场引起的问题,推导了可以用于较大仰角声波的更高阶数的Gauss初始场。通过数值仿真对比了不同阶数的初始场在CNPE方法中的效果。结果表明:4阶初始场是最适合CNPE方法的初始场,将该初始场与CNPE方法相结合,可以准确预测当声屏障与声源距离较近时的插入损失.      

A study of sound intensity control for active noise barriers

Active noise control systems have been applied to increase the insertion loss of noise barriers where the squared sound pressure or the total acoustic energy density is used as the cost function in previous works. The absolute value of the mean active sound intensity is chosen as the cost function to obtain extra sound insertion loss in the dark area of a hybrid active noise barrier system in this note. The strategy of minimizing the near-field sound intensity at discrete locations along the edge of the passive barrier is shown to be able to provide better far-field noise reduction than that of minimizing the squared sound pressure control. Both numerical simulations and off-line experiments are carried out with a three-channel demonstration system, where the locations of the secondary sources and the error sensors are optimized and comparisons are made between the extra sound pressure attenuation of the sound intensity control and that of the squared sound pressure control.     

The predicted barrier effects in the proximity of tall buildings

A ray model is developed and validated for the prediction of the insertion loss of barriers that are placed in front of a tall building in high-rise cities. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model, as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and barrier. Comparisons of the ray model with indoor experimental data and wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Case studies are also presented that highlight the significance of positioning the barrier relative to the noise-sensitive receivers in order to achieve improved shielding efficiency of the barrier.     

Combined effects of admittance optimisation on both barrier and ground

The focus of this paper is on the problem of finite impedances on both ground and barrier. Using a boundary element approach the surface treatment of the barrier and finite parts of the ground have been optimised to yield maximum insertion loss at multiple frequencies simultaneously. A 1 m high T-shaped barrier optimised in this way gives up to 8 dB higher insertion loss than a rigid barrier of equal shape. Optimisation of the acoustical properties of the ground below the source as well as those of the barrier improves the insertion loss dramatically for all receiver heights. The ground close to the source is the part of the ground that influences the insertion loss most, and in such a way that the radiation properties of the source are altered, and the radiated sound power is reduced. Having an optimised admittance only on the ground close to the barrier gives only a minor effect. A barrier-ground combination with specialised treatment on the ground close to the source and on the barrier top gives an increase in insertion loss that is comparable to the optimised results. The main conclusion of this paper is that specialised surface treatments provide largest effect if they are used on the ground surface.     

A ray model for hard parallel noise barriers in high-rise cities

A ray model is developed and validated for prediction of the insertion loss of hard parallel noise barriers placed in an urban environment either in front of a row of tall buildings or in a street canyon. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the ground, barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and the near-side barrier. Comparisons of the ray model with a wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Results of scale model experimental studies are also presented. It is demonstrated that the ray model agrees tolerably well with the scale model experimental data.     

NUMERICAL MODELLING OF MEDIAN ROAD TRAFFIC NOISE BARRIERS

Outdoor sound propagation from road traffic is modelled by solving a boundary integral equation formulation of the wave equation using boundary element techniques in two dimensions. In the first model, the source representing a traffic stream can be considered as a coherent line source of sound. The results can then be transformed to derive a pseudo-three dimensional solution to the problem. In the second model the line source is incoherent. For receivers near the ground, the second model predicted significantly higher values of ground attenuation than the first. The first model generally produced better agreement with ground attenuation results obtained using the U.K. traffic noise prediction model. For conditions when a noise barrier was present and the ground was absorbent, the incoherent line source model generally predicted significantly higher values of attenuation than those from the barrier and ground attenuation calculated separately. Over a range of receiver positions and barrier heights a similar, but less marked effect was observed when the coherent line source model was used. On dual carriageway roads, it is possible to incorporate barriers on the central reservation as a noise control measure. These are “median” noise barriers. The incoherent line source model is used to assess the performance of median barriers in reducing noise when installed alone and also with associated roadside barriers. A sound absorbent median noise barrier 1m in height produced consistent values of insertion loss of between 1 and 2dB over the range of receiver positions and ground conditions considered. When the median barrier was used in conjunction with a roadside barrier it produced a consistent improvement in insertion loss of between 1 and 2 dB over the range of conditions considered.     

Noise attenuation by a hard wedge-shaped barrier

This paper is concerned with the problem of sound screening by a wedge-like barrier. The sound source is assumed to be point like, and the receiver is located in the shadow of the source sound field, so that according to geometrical optics only the field diffracted by the edge of the barrier is considered. First, for the hard wedge in space, three models are used for calculating the amplitude of the edge-diffracted field. These are the uniform theory of diffraction (UTD), the Hadden-Pierce model, both in the frequency domain, and the Biot-Tolstoy theory of diffraction which is a time domain formulation. It is first shown that even at relatively low frequencies, the frequency domain models perform quite satisfactorily as compared to the exact time domain theory. Hence, and due to its relative simplicity the UTD is proposed as an accurate calculation scheme for solving problems with edge diffraction by hard wedges. It is also proved from theoretical calculations that the amplitude of the edge-diffracted field increases for an increasing angle of the wedge, and consequently the hard half-plane gives the lowest field amplitude in the shadow zone. Some applications are then considered for evaluating the performance of a barrier on a flat ground, either completely hard or with mixed homogeneous boundary conditions. An improvement of the scheme for calculating the sound field in the all-hard case is achieved through considering the multiple diffraction, in this case only to the second order, between the top of the wedge barrier and its base. The results show that for usually occurring situations, increasing the angle of the hard wedge barrier affects negatively its efficiency through diminishing its insertion loss. These conclusions are also supported by the results of some experimental measurements conducted at a scale-model level.     

Sound transmission in pipes with porous walls

Pipes with porous (permeable) walls have received the attention of several authors as a noise control element in automotive intake systems; however, a closed theory of sound transmission including the effect of the coupling of the internal and external acoustic fields and the presence of mean flow does not appear to be available. The present paper proposes an integro-differential system for the propagation of plane sound waves in pipes with porous walls, and presents its general numerical solution, as well as an approximate analytical solution. The predicted effect of the coupling between the internal and external acoustic fields in a circular pipe made of reinforced woven fabric walls is shown, and the transmission loss predictions are compared with the existing experimental data in the literature.     

A correction to Maekawa's curve for the insertion loss behind barriers.

Maekawa's curve is one of the most established methods for predicting the insertion loss (IL) behind barriers. For the simple case of a barrier modeled as a half plane, the IL is given versus a single parameter, the Fresnel number (N1). Predictions obtained by Maekawa's curve deviate largely from experimental data, and from predictions obtained by analytical solutions, when the receiver is either close to the barrier or at the boundary separating the illuminated from the shadow zone. It is shown that if a second Fresnel number (N2) is appropriately defined, the IL obtained by the existing analytical solutions can be expressed versus N1 and N2 for several types of incident radiation (plane, cylindrical, and spherical). Accordingly, the single curve in Maekawa's chart can be replaced by a family of curves. Each curve corresponds to a different N2 and provides the IL versus N1 . The Kurze-Anderson formula (a mathematical expression of Maekawa's curve) is also modified to describe this set of curves. Besides providing increased accuracy in the areas where Maekawa's curve does not, the graph proposed here addresses the more general problem of combining the simplicity of empirical models like Maekawa's with the accuracy of sophisticated mathematical models.     

Traffic noise reduction by means of surface wave exclusion above parallel grooves in the roadside

A new method to reduce traffic noise by means of an ‘invisible’ wall has been investigated both theoretically and experimentally. A formula was derived for the frequency dependent impedance of an infinite structure of parallel ribs on an impedance boundary. From the definition of surface waves it followed that these waves can only exist for certain combinations of frequencies, heights of ribs and phases of the complex reflection coefficient of the underlying surface. Upon making this surface softer, more low frequency sound is absorbed. Outdoor experiments above an array of 16 or 21 low brick walls showed a considerable absorption of sound. Attenuations occurred up to 20 dB in the one-third octave bands from 125 to 400 Hz and amplifications up to 12 dB in the range of 400–1000 Hz. It was possible to explain these measurements qualitatively by the theory of surface waves. The wall structure caused an insertion loss of approximately 4 dB(A) in the total sound pressure level of the A-weighted one-third octave bands from 100 to 12,500 Hz.     

Thick barrier noise-reduction in the presence of atmospheric turbulence: measurements and numerical modelling

Atmospheric turbulence causes scattering of sound, which can reduce the performance of sound barriers. This is an important inclusion in prediction models to obtain a correct picture of the sound reduction at higher frequencies. Here a prediction method is applied that uses the strengths of the wind and temperature turbulence to estimate the scattered power into the shadow zone of a barrier. The predictions are compared to full-scale measurements on a thick barrier, where both acoustic and meteorological data were recorded simultaneously under both calm and windy conditions. Comparison between the measurements and the predictions indicate that the method gives reasonably accurate results for mid to high frequencies and a slight overestimation at very high frequencies.     

A mathematical model for a single screen barrier in open-plan offices

In open-plan offices, single screen barriers are widely used to separate individual workplaces as a means of improving acoustical privacy. In this paper, a general model for calculating the insertion loss of a single screen barrier in the presence of a floor and a ceiling is developed using the image source technique. In addition to the acoustical properties of the floor and ceiling, this model also takes the sound absorption of the screen, the sound transmission through the screen and the interference between the sound waves into account. This model is able to separate the contribution of reflected sound and diffracted sound from the total sound pressure level at the receiving point, which can help indicate how best to improve the acoustical design of an open office. The mean differences between the predicted 1/3 octave band insertion loss values behind the screen and the corresponding measured results are within 2 dB.     

Reduction of surface transport noise by ground roughness

Measured insertion losses due to the ground effects associated with low configurations of loosely stacked household bricks on a car park are reported. A particularly successful design has the form of a two brick high square lattice which is found to offer a similar insertion loss to regularly-spaced parallel wall arrays of the same height but twice the total width. Part of the insertion loss due to the roughness configurations is the result of transfer of incident sound energy to surface waves which can be reduced by introducing wall absorption or material absorption in the form, for example, of shallow gravel layer. Predicted finite length effects have been explored using a Pseudo-Spectral Time Domain Method, which models the complete 3D roughness profile. It is concluded from measurements and predictions that the lattice design has less dependence on azimuthal source-receiver angle than parallel wall configurations. These predictions are supported by measurements of level difference spectra as a function of azimuthal angle. A 2D Boundary Element Method gives predictions that agree well with data for parallel wall arrays up to 16 m long and it is used to investigate the potential insertion loss of longer configurations up to 0.3 m high. It has been found possible also to make predictions of the insertion loss due to infinitely long 3D lattices using the 2D BEM with the lattice represented by the surface impedance derived from fitting short range data with a slit-pore impedance model. The insertion losses of recessed configurations are predicted to be approximately 3 dB less than those of embossed configurations of the same size. Outdoor experiments also show that pathways can be made through such roughness configurations without significantly affecting their insertion loss. It is concluded that artificial roughness configurations could achieve substantial noise reduction along surface transport corridors without breaking line of sight between source and receiver, thereby proving useful alternatives to noise barriers.     

Studies of parallel barrier performance by acoustical modeling

An investigation is presented into the performance of parallel barrier configurations, using acoustical scale modeling. A realistic geometry is investigated, with the source being positioned over a paved roadway and the receiver over grass-covered ground. The grass-covered ground surface was properly modeled in terms of its impedance. Results were obtained for a range of barrier types, and demonstrate that frequency dependent effects are evident in barrier insertion loss data. In most cases, the barrier on the far side of the source did not significantly affect sound levels at the receiver. The most effective barrier design was found to be that of a gradual grass-covered slope up to an upright, thin barrier.     

An analytical model to estimate the performance of an indoor barrier at low-medium frequencies

Indoor barriers are now widely used for sound insulation. This paper examines the performance of indoor barriers in the low-medium frequency range and analyses the interaction between different natural modes of a room-barrier-room system. Morse proposed a theoretical model to calculate the sound field in a coupled-room, but this model neglects the surface integral of the boundary values of sound pressure. To estimate the performance of a barrier in an indoor environment, an analytical model is proposed that modifies the Green’s function for a non-rigid boundary enclosure and approximates the surface integral by a pre-estimated sound pressure based on Morse’s model. An additional approximation has been made in the proposed model to neglect the coupling area in the calculation of the surface integral. The proposed model used to predict the insertion loss of the barrier is verified by the experimental results using a 1:5 scale model. The predicted results agree well with the measured results at lower frequencies.