The 2.5-dimensional equivalent sources method for directly exposed and shielded urban canyons

Time-harmonic convention of exp(-iωt) can be preferable to exp(+iωt) (L)

Since (±i)² = -1, there are two time-harmonic conventions, namely, exp(+iωt) and exp(-iωt) with ω and t for angular frequency and time, respectively. Both conventions are mathematically valid. However, a question may still be asked whether a specific acoustic problem can favor one or the other convention. This letter reports one such example in which the use of exp(-iωt) can be preferable when the principal value of the square root of a complex number is considered as an argument of the Hankel functions in the context of 2.5-dimensional problems.

Simulation and Analysis of Road Traffic Noise among Urban Buildings Using Spatial Subdivision-Based Beam Tracing Method

In order to realize the simulation and evaluation of road traffic noise among urban buildings, a spatial subdivision-based beam-tracing method is proposed in this study. First, the road traffic source is divided into sets of point sources and described with the help of vehicle emission model. Next, for each pair of source and receiver, spatial subdivision-based beam-tracing method is used in noise paths generation. At last, noise distribution can be got by noise calculation of all receivers considering the complex transmission among urban buildings. A measurement experiment with a point source is carried out to validate the accuracy of the method; the 0.8 m height and 2.5-m height average errors are about 0.9 dB and 1.2 dB, respectively. Moreover, traffic noise analysis under different building layouts and heights are presented by case applications and conclusions can be reached: (1) Different patterns result in different noise distributions and patterns designed as self-protective can lead to an obvious noise abatement for rear buildings. Noise differences between the front and rear buildings are about 7–12 dB with different patterns. (2) Noise value might not show a linear variation along with the height as shielding of different layers is various in reality.

A numerical hybrid model for outdoor sound propagation in complex urban environments

Noise mapping in large and dense urban areas is computationally challenging, if not impossible, with the use of conventional numerical techniques. Recently, promising results have shown the potential of energy-based models to compete with conventional numerical techniques. In this paper, a hybrid full-wave/diffusion propagation model is proposed to address some of the flaws of the traditional diffusion model. The full-wave model is used for predicting sound propagation (i) near the source, where interactions between waves are important, and (ii) outside the cluttered environment, where free-field-like conditions apply. The diffusion model is used in regions where diffusion conditions are met.

A modified 3D algorithm for road traffic noise attenuation calculations in large urban areas

The primary objective of this study is the development and application of a 3D road traffic noise attenuation calculation algorithm. First, the traditional empirical method does not address problems caused by non-direct occlusion by buildings and the different building heights. In contrast, this study considers the volume ratio of the buildings and the area ratio of the projection of buildings adjacent to the road. The influence of the ground affection is analyzed. The insertion loss due to barriers (infinite length and finite barriers) is also synthesized in the algorithm. Second, the impact of different road segmentation is analyzed. Through the case of Pearl River New Town, it is recommended that 5° is the most appropriate scanning angle as the computational time is acceptable and the average error is approximately 3.1 dB. In addition, the algorithm requires only 1/17 of the time that the beam tracking method requires at the cost of more imprecise calculation results. Finally, the noise calculation for a large urban area with a high density of buildings shows the feasibility of the 3D noise attenuation calculation algorithm. The algorithm is expected to be applied in projects requiring large area noise simulations.

Evaluation of road traffic noise abatement by vegetation treatment in a 1:10 urban scale model

A 1:10 scale of a street canyon and courtyard was constructed to evaluate sound propagation when various vegetation treatments including trees, shrubs, vegetated facades, and green roofs were installed in the urban environment. Noise reductions in the street canyon and courtyard were measured for both single and combined vegetation treatments. Vegetated facades mitigated the overall noise level up to 1.6 dBA in the street canyon, and greening facades were effective to reduce low frequency noise levels below 1 kHz. Trees increased the noise level at high frequency bands to some extent in the street canyon, while the noise level over 1 kHz decreased in the courtyard after installing the street trees. This is because tree crowns diffused and reflected high frequency sounds into the street canyon. Green roofs offered significant noise abatement over 1 kHz in the courtyard, while the vegetated facade was effective to reduce noise levels at low frequencies. In terms of the integrated effects of vegetation treatments, a combined vegetation treatment was less effective than the sum of single treatments in the street canyon. The maximum noise reduction observed for all combinations of vegetation treatments provided 3.4 dBA of insertion loss in the courtyard.

A 2.5-dimensional method for the prediction of structure-borne low-frequency noise from concrete rail transit bridges

Predicting structure-borne noise from bridges subjected to moving trains using the three-dimensional (3D) boundary element method (BEM) is a time consuming process. This paper presents a two-and-a-half dimensional (2.5D) BEM-based procedure for simulating bridge-borne low-frequency noise with higher efficiency, yet no loss of accuracy. The two-dimensional (2D) BEM of a bridge with a constant cross section along the track direction is adopted to calculate the spatial modal acoustic transfer vectors (MATVs) of the bridge using the space-wave number transforms of its 3D modal shapes. The MATVs calculated using the 2.5D method are then validated by those computed using the 3D BEM. The bridge-borne noise is finally obtained through the MATVs and modal coordinate responses of the bridge, considering time-varying vehicle-track-bridge dynamic interaction. The presented procedure is applied to predict the sound pressure radiating from a U-shaped concrete bridge, and the computed results are compared with those obtained from field tests on Shanghai rail transit line 8. The numerical results match well with the measured results in both time and frequency domains at near-field points. Nevertheless, the computed results are smaller than the measured ones for far-field points, mainly due to the sound radiation from adjacent spans neglected in the current model.

Energy-based method for near-real time modeling of sound field in complex urban environments

Prediction of the sound field in large urban environments has been limited thus far by the heavy computational requirements of conventional numerical methods such as boundary element (BE) or finite-difference time-domain (FDTD) methods. Recently, a considerable amount of work has been devoted to developing energy-based methods for this application, and results have shown the potential to compete with conventional methods. However, these developments have been limited to two-dimensional (2-D) studies (along street axes), and no real description of the phenomena at issue has been exposed. Here the mathematical theory of diffusion is used to predict the sound field in 3-D complex urban environments. A 3-D diffusion equation is implemented by means of a simple finite-difference scheme and applied to two different types of urban configurations. This modeling approach is validated against FDTD and geometrical acoustic (GA) solutions, showing a good overall agreement. The role played by diffraction near buildings edges close to the source is discussed, and suggestions are made on the possibility to predict accurately the sound field in complex urban environments, in near real time simulations.

A coupled modal-finite element method for the wave propagation modeling in irregular open waveguides

In modeling the wave propagation within a street canyon, particular attention must be paid to the description of both the multiple reflections of the wave on the building facades and the radiation in the free space above the street. The street canyon being considered as an open waveguide with a discontinuously varying cross-section, a coupled modal-finite element formulation is proposed to solve the three-dimensional wave equation within. The originally open configuration-the street canyon open in the sky above-is artificially turned into a close waveguiding structure by using perfectly matched layers that truncate the infinite sky without introducing numerical reflection. Then the eigenmodes of the resulting waveguide are determined by a finite element method computation in the cross-section. The eigensolutions can finally be used in a multimodal formulation of the wave propagation along the canyon, given its geometry and the end conditions at its extremities: initial field condition at the entrance and radiation condition at the output.

Engineering modeling of traffic noise in shielded areas in cities

A computational study of road traffic noise in cities is presented. Based on numerical boundary-element calculations of canyon-to-canyon propagation, an efficient engineering algorithm is developed to calculate the effect of multiple reflections in street canyons. The algorithm is supported by a room-acoustical analysis of the reverberant sound fields in the source and receiver canyons. Using the algorithm, a simple model for traffic noise in cities is developed. Noise maps and exposure distributions of the city of Amsterdam are calculated with the model, and for comparison also with an engineering model that is currently used for traffic noise impact assessments in cities. Considerable differences between the two model predictions are found for shielded buildings with day-evening-night levels of 40-60 dB at the facades. Further, an analysis is presented of level differences between the most and the least exposed facades of buildings. Large level differences are found for buildings directly exposed to traffic noise from nearby roads. It is shown that by a redistribution of traffic flow around these buildings, one can achieve low sound levels at quiet sides and a corresponding reduction in the percentage of highly annoyed inhabitants from typically 23% to 18%.