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Abstract

To further investigate the bridge structural noise radiation characteristics when trains pass through continuous rigid frame box-girders and the influence of different bridge structural forms on the bridge structural noise radiation characteristics in urban elevated rail transit, the study conducted on the elevated rail transit lines in a Chinese city focused on the field testing of the vibration and noise of continuous rigid frame box-girders and simply supported box-girders. Through comparative testing results, the spectral characteristics of noise for the two types of box-girders were analyzed and compared. The finite element method and boundary element method were employed to establish numerical calculation models for vibration sound radiation of the two beam types, investigating and comparing the amplitude-frequency characteristics and spatial distribution patterns of noise for the two beam types. The research findings indicate that, within a range extending 120 m from the centerline of the bridge and 50 m above ground level, the difference in low-frequency structural noise radiated by the two types of box-girders is approximately −1.5 to 15 dB. The region beneath the bridge is where the continuous rigid frame box-girder demonstrates a significant advantage in low-frequency structural noise, reducing noise by 8 to 15 dB compared to the simply supported box-girder. Meanwhile, the low-frequency structural noise of the simply supported box-girder is only marginally lower than that of the continuous rigid frame box-girder in some areas under the sloped section of the bridge about 0 to 1.5 dB. Overall, the structural acoustic performance of the continuous rigid frame box-girder is superior to that of the simply supported box-girder.

Keywords

Rail transit continuous rigid frame box-girder bridge simply supported box-girder bridge bridge structural noise

Introduction

The research findings indicate that in recent years, urban rail transit has rapidly developed in China due to its advantages such as low pollution, high capacity, safety, and energy efficiency. As of December 31, 2023, mainland China has accumulated 59 cities with operational urban rail transit lines exceeding 11,000 km, reaching 11,232.65 km.¹ Elevated rail construction has gained widespread application in urban rail transit systems, given its low construction difficulty, fast construction speed, and cost only 1/4 to 1/3 of underground lines. Among these, box-girders, characterized by excellent mechanical properties, simple appearance, good esthetic effects, and high adaptability, have become the most widely used beam type in China’s urban elevated rail transit. However, the bridge structural noise caused by trains passing through urban rail transit box-girders has become a challenging problem for practitioners in the rail transit industry.

Extensive research has been conducted by scholars both domestically and internationally regarding the issue of bridge structural noise caused by trains passing through rail transit simply supported box-girders.^2–6 Ngai et al.⁷ verified the resonance frequencies of noise and vibration using Fourier transform and finite element method. Based on the measurement results of noise and vibration in elevated track bridges, they evaluated the transfer function and coherence relationship between noise and vibration. Kim et al.⁸ studied the vibration and noise of light rail bridges by analyzing the dynamic response of the light rail train’s movement as input data for noise analysis. Gao et al.⁹ measured the noise of the simply supported box-girder structure in the Capital Airport Express Rail Line and predicted the noise using the sound transmission vector method. Zhang et al.¹⁰ established a prediction model for the noise of rail transit simply supported box-girder structures based on the indirect boundary element method and validated it through experiments. Zhang et al.^11,12 predicted the sound radiation of rail transit elevated box-girder bridge structures using the hybrid finite element-boundary element method and investigated the sound radiation mechanism and characteristics of box-girder bridge structures in combination with resonance effects, modal sound radiation efficiency theory, and acoustic waveguide theory. Yin et al.¹³ predicted the noise radiation of box-girder bridges using the hybrid finite element-transient boundary element method and identified the bridge deck as the main noise radiation location. Wang¹⁴ conducted noise prediction for a 30 m simply supported box-girder structure in urban rail transit using the transient boundary element method and analyzed the sound pressure contributions of each plate component. Liu et al.¹⁵ conducted research on noise control in rail transit simply supported box-girder structures based on acoustic modal contribution analysis. To improve the efficiency of noise prediction for rail transit simply supported box-girder structures, Song¹⁶ established a noise prediction model for a 30 m simply supported box-girder structure in urban rail transit based on the hybrid waveguide finite element-two dimensional boundary element method and validated it through experiments. Li et al.^17,18 established a noise prediction model for a 30 m simply supported box-girder structure in urban rail transit based on statistical energy analysis and analyzed the influence of track structure forms on the noise of simply supported box-girder structures. Lin et al.¹⁹ taking a 24 m simply supported box-girder in rail transit as the research object, analyzed the impact of factors such as train speed, bridge stiffness, and web plate thickness on the noise of bridge structures.

In recent years, continuous rigid frame box-girders have gradually been applied in urban elevated rail transit due to their efficient load-bearing performance, good durability, and economic advantages. The Guangzhou Metro Line 6, which opened in 2013, was the first to extensively use continuous rigid frame box-girders in urban elevated rail transit projects. Subsequently, the Guangzhou Metro Line 14 and Line 21, which opened at the end of 2018, also adopted continuous rigid frame box-girders in urban elevated rail transit projects.²⁰ However, the radiation characteristics of bridge structural noise when trains pass through continuous rigid frame box-girders are not yet clear.

Compared to traditional steel box beams, concrete bridges offer lower cost, stronger economic viability, and wider engineering applications. Considering the suitability of concrete bridges in urban rail transit systems, this paper chooses concrete continuous rigid frame box-girders as the research subject. The study indicates that for concrete beam bridges, the frequency range of structural noise generation is between 20 Hz and 200 Hz.^7,21 Therefore, this paper focuses on analyzing vibration and noise within this frequency range.

This study selected the cross-sections of a concrete continuous rigid frame box-girder and a simply supported box-girder from a metro viaduct to conduct noise tests during train passage. By integrating numerical simulations, a comparison was made between the structural noise amplitude-frequency characteristics and spatial distribution patterns of the two types of bridges. The aim is to provide a theoretical basis for the design of vibration reduction and noise control beams for urban elevated rail transit systems. Throughout the text, unless specifically stated otherwise, “box beam” and “bridge” refer to concrete box beams and concrete bridges.

Field test

Field test information

Vibration and noise tests were conducted on selected sections of a 2 × 30 m concrete continuous rigid frame box-girder and a 30 m concrete simply supported box-girder in an urban rail transit system, as shown in Figure 1. The 2 × 30 m concrete continuous rigid frame box-girder section was subjected to the passage of a six-carriage B-type train, while the 30 m concrete simply supported box-girder section was subjected to a four-carriage L-type train. Both sections have no vibration reduction or noise control measures.

Figure 1.

Photographs of on-site vibration and noise testing: (a) continuous rigid frame box-girder section, (b) simply supported box-girder section.

In urban elevated rail bridges, bridge structural noise is generated by the vibrations of trains, the bridge structure itself, and other facilities on the bridge. The properties of structural noise, such as sound pressure amplitude and frequency spectrum characteristics, are closely related to the vibration characteristics.²² Therefore, in this test, microphones were placed 7.5 m from the centerline of the track, 1.2 m above the ground, and 3.5 m above the track at both cross-sections. Furthermore, vibration acceleration sensors were positioned at three locations on the inner and outer rail bottoms and the center of the bridge deck at the mid-span of both continuous rigid frame and simply supported box-girders to better understand the radiation characteristics of bridge structural noise. Detailed information on the layout of vibration and noise measurement points can be found in Table 1, Figure 2, and Figure 3.

Table 1.

Number and location of vibration and noise measurement points.

Sensor type	Number	Location
Vibration sensor	V1	Bottom of left rail
	V2	Bottom of right rail
	V3	Top plate center
Noise sensor	N1	7.5 m away from track centerline, 1.2 m above the ground
Noise sensor	N2	7.5 m away from track centerline, 3.5 m above the rail surface

Figure 2.

Schematic of vibration measurement point arrangement: (a) continuous rigid frame box-girder section, (b) simply supported box-girder section.

Figure 3.

Schematic of noise measurement point arrangement.

Test results

The vibration acceleration spectra at the inner, outer rail bottoms, and center of the bridge deck were measured when a six-carriage B-type train passed through the continuous rigid frame box-girder section at a speed of 93 km/h, and when a four-carriage L-type train passed through the simply supported box-girder section at a speed of 74 km/h. The spectra are shown in Figure 4.

Figure 4.

Vibration acceleration spectra at each measurement point: (a) V1, (b) V2, and (c) V3.

From Figure 4, it can be observed that under the conditions where both sections lacked vibration reduction measures, the vibration of the steel rail caused by the train passing through the continuous rigid frame box-girder section at a speed of 93 km/h was significantly higher in the frequency range of 20 to 1000 Hz compared to the vibration caused by the train passing through the simply supported box-girder section at a speed of 74 km/h. However, the peak vibration amplitude at the center of the bridge deck caused by the train passing through the continuous rigid frame box-girder section at a speed of 93 km/h was lower than that caused by the train passing through the simply supported box-girder section at a speed of 74 km/h.

Figure 5 illustrates the A-weighted sound pressure level spectra at measurement points N1 and N2, along with the corresponding bar chart of the overall sound pressure levels. These measurements were taken when a six-carriage B-type train passed through the continuous rigid frame box-girder section at a speed of 93 km/h and when a four-carriage L-type train passed through the simply supported box-girder section at a speed of 74 km/h.

Figure 5.

A-weighted sound pressure level spectra—overall sound pressure level bar chart at each measurement point: (a) N1, (b) N2.

From Figure 5, it can be observed that despite the train passing through the continuous rigid frame box-girder section at a speed 19 km/h higher than that of the train passing through the simply supported box-girder section, the overall sound pressure level at measurement point N1 is approximately the same. This is because the measurement point N1 is located 7.5 m from the centerline of the track and 1.2 m above the ground, where the beam structure provides some shielding against wheel-rail noise. Moreover, the low-frequency secondary structural noise radiated by the continuous rigid frame box-girder is significantly lower than that radiated by the simply supported box-girder.

On the other hand, measurement point N2, located 7.5 m from the centerline of the track and 3.5 m above the rail surface, is influenced by both wheel-rail noise and bridge structural noise. Therefore, when the train passes through the continuous rigid frame section at a higher speed, the overall sound pressure level at N2 is greater. However, the spectral curve still indicates that the low-frequency secondary structural noise generated by the train passing through the simply supported box-girder section is higher at measurement point N2.

Although the experimental results above indicate that the structural-acoustic performance of the continuous rigid frame box-girder is superior to that of the simply supported box-girder, it cannot be directly concluded that the structural-acoustic performance of the continuous rigid frame box-girder is better than that of the simply supported box-girder due to the diverse factors affecting the cross-sections of the two girders in this test. In the subsequent numerical simulations, the influences of factors such as train type and speed on the simulation results are eliminated to enhance the significance of comparing the two bridge structural forms.

Simulation model

In the aforementioned experiments, there were certain differences in terms of train type, speed, and track structure between the two test sections. To further compare the structural noise characteristics of the two beam types, this section establishes vibration and noise prediction models for both the continuous rigid frame and simply supported box-girders. These models are used to calculate the structural noise radiation of the two beam types under the same conditions of train type, speed, and track structure.

Modeling principles

When establishing the two box beam models, the uniform load in the second phase is equivalent to the self-weight uniformly applied to the bridge deck. The formula for the equivalent density of the continuous rigid frame box-girder top plate is $ρ_{e q} = β \times ρ_{r} + \frac{p - p_{t} - p_{b} - p_{s}}{A}$ (1)

In the formula: ρ_eq and ρ_r represent the equivalent density and density of the top plate, respectively; p, p_t, p_b, and p_s denote the mass of second-phase permanent load, track slab mass, bridge parapet mass, and rail mass, with p set at $\frac{90 k N / m}{9.8 N / k g} = 9184 k g / m$ ;²³ β is the structural amplification factor, assumed as 1 in this study; A denotes the cross-sectional area of the top plate.

The formula for calculating the equivalent density of the simply supported box-girder top plate is $ρ_{e q} = β \times ρ_{r} + \frac{p}{A}$ (2)

When employing the finite element method for structural vibration analysis, it is crucial to ensure the accuracy of the computational results. To achieve this, the maximum element size in the finite element model of the structure should be less than one-sixth of the minimum wavelength of vibration. The bending wave speed c_b for plate structures can be expressed as²⁴ $c_{b} = {(\frac{E h^{2}}{12 ρ (1 - μ^{2})})}^{0.25} \sqrt{ω}$ (3)where E represents the elastic modulus of the structure; ρ denotes the density of the structure; μ signifies the Poisson’s ratio of the structure; h stands for the thickness of the plate structure, and ω indicates the angular frequency.

The relevant parameters of the two types of box-girders are shown in Table 2.

Table 2.

Bridge parameters for calculation models.

Parameters	Continuous rigid frame box-girder	Simply supported box-girder
Bridge elastic modulus (N·mm⁻²)	3.65 × 10¹⁰	3.45 × 10¹⁰
Bridge top plate and top structure density/(kg·m⁻³)	3120	4800
Bridge web and bottom plate density/(kg·m⁻³)	2500	2400
Bridge Poisson’s ratio	0.2	0.2
Bridge roof thickness (m)	0.25	0.25
Bridge web thickness (m)	0.3	0.29
Bridge floor thickness (m)	0.3	0.25

When a train crosses a bridge, the low-frequency structural noise predominantly occurs in the frequency range below 200 Hz. Accordingly, 200 Hz is selected as the cutoff frequency for the analysis. Based on equation (1) and the parameters provided in Table 2, the minimum wavelengths of the bending wave in the continuous rigid frame box-girder and the simply supported box-girder bridge decks are approximately 2.81 m and 2.49 m, respectively. Consequently, the maximum element size for the finite element models of the two box-girders should be less than 0.47 m and 0.42 m, respectively.

When conducting vibro-acoustic analysis using the boundary element method, the principle of the maximum element size being less than 1/6 of the minimum sound wave wavelength should also be followed.²⁵ To ensure the accuracy of the finite element-boundary element co-simulation, the element size on the outer surface of the structural finite element model needs to be smaller than 1/6 of the minimum sound wave wavelength. Assuming the analysis cutoff frequency is 200 Hz, the minimum sound wave wavelength is 344/200 = 1.72 m. Therefore, the maximum element size on the outer surface of the finite element model and the boundary element model should be less than 0.287 m.

Model establishment

As trains travel on rails, the interaction between the wheels and rails generates wheel-rail forces due to the influence of track roughness. To model this wheel-rail interaction, a dynamic flexibility method²⁶ is employed. The standardized ISO 3095 (2005) track roughness is used as the input excitation (as shown in Figure 6) to establish the wheel-rail interaction model. By solving for the wheel-rail forces, the forces transmitted to the bridge can be determined. The specific parameters are shown in Table 3.

Figure 6.

Rail roughness spectrum.

Table 3.

Parameters for the wheel-rail interaction model calculation.

Structure	Parameters	Continuous rigid frame box-girder	Simply supported box-girder
Train	Bogie mass/t	3.52	2.43
	Wheelset mass/t	1.539	1.744
	Primary suspension stiffness/(kN·m⁻¹)	1700	1252
	Length between bogie centers/mm	12600	15700
	Bogie wheelbase/mm	2200	2500
Steel rail	Cross-sectional area of steel rail/mm²	7745	7745
	Steel rail density/(kg·mm³)	7850	7850
	Steel rail elastic modulus (N·mm⁻²)	2.06 × 10¹¹	2.06 × 10¹¹
	Steel rail Poisson’s ratio	0.3	0.3
	Steel rail damping factor	0.01	0.01
	Fastener stiffness/(MN·m⁻¹)	40	40
	Fastener spacing/m	0.625	0.625
	Fastener damping/(N·m/s)	0.25	0.25

This article is based on the hybrid finite element-boundary element method to establish numerical models for the vibration and acoustic radiation of two types of box beams. Firstly, the vibration numerical models for both box beams are developed using the finite element analysis software. When establishing the finite element model of the continuous rigid frame box-girder, the boundary conditions are set as shown in Figure 7. The constraint forms depicted in Figure 7 are applied to the model nodes within the four dashed surfaces to simulate the constrained state of the continuous rigid frame box-girder in reality.

Figure 7.

Illustration of boundary constraints for continuous rigid frame box-girder (two-span bridge model).

When establishing the finite element model of a simply supported box-girder, the boundary conditions are set as shown in Figure 8. Different constraint methods depicted in the figure are applied to nodes at different positions to simulate the constrained state of the simply supported box-girder in reality.

Figure 8.

Illustration of boundary constraints for simply supported box-girder (single-span bridge model).

In the process of establishing finite element models, solid elements and shell elements are commonly used for bridge modeling. The solid45 element can effectively simulate solid structures, providing comprehensive stress and deformation information suitable for bending vibration analysis of bridges. The shell63 element can be used to simulate thin-walled structures, assuming rigidity in the thickness direction, making it suitable for bending vibration analysis of plate-like structures. Both types of elements can simulate bridge vibration responses well, and when using these two element types to solve the vibration response of the model, the error between the vibration response results is generally acceptable and negligible. In this study, the continuous rigid frame box-girder is simulated using solid45 elements, while the simply supported box-girder is simulated using shell63 elements, as shown in Figure 9. The calculation parameters of the finite element models for the two bridge structures are presented in Table 4 (Note: The rail mass in the simply supported box-girder model has been equated to the bridge deck, so the relevant parameters of the rail in that model are not listed).

Figure 9.

Two numerical computational models for box beam vibration analysis: (a) numerical computational model for vibration analysis of continuous rigid frame box-girders, (b) numerical computational model for vibration analysis of simply supported box-girders.

Table 4.

Finite element model calculation parameters for bridges.

Structure	Parameters	Continuous rigid frame box-girder	Simply supported box-girder
Steel rail	Rail type	60 kg/m rail track	-
	Rail type/(kg·mm³)	7850	-
	Rail elastic modulus (N·mm⁻²)	2.06 × 10¹¹	-
	Rail Poisson’s ratio	0.3	-
Bridge	Box beam height/m	2	1.7
	Bridge deck width/m	10.22	9.274
	Bridge bottom width/m	2.4	4
	Bridge top plate and top structure density/(kg·m⁻³)	3120	4800
	Bridge web and bottom plate density/(kg·m⁻³)	2500	2400
	Bridge elastic modulus (N·mm⁻²)	3.65 × 10¹⁰	3.45 × 10¹⁰
	Bridge Poisson’s ratio	0.2	0.2

The developed finite element model for the continuous rigid frame box-girder consists of a two-span box-girder model with 75,842 elements and 102,403 nodes. The simply supported box-girder is modeled as a single-span structure, comprising 6912 elements and 6976 nodes. The maximum element size for both models does not exceed 0.28 m, meeting the requirements for subsequent analysis of vibration response and acoustic radiation characteristics.

In the established finite element numerical model, the first natural frequency of the continuous rigid frame box-girder is 4.3 Hz, the corresponding mode can be described as the transverse roll of the beam. Additionally, the frequency corresponding to the first-order vertical bending mode of the continuous rigid frame box-girder is 7.42 Hz, and it is the third-order mode of the continuous rigid frame box-girder. The first-order vertical bending mode is shown in Figure 10. And its static stiffness under a mid-span axial load is 318 kN/mm, as shown in Figure 11. For the simply supported box-girder model, the first natural frequency is 3.94 Hz, the corresponding mode is the first order vertical bending mode, as shown in Figure 12. And its static stiffness under a mid-span axial load is 154 kN/mm, as shown in Figure 13. These results indicate that the first natural frequencies of the two types of box-girders are relatively close. However, the static stiffness of the continuous rigid frame box-girder is significantly greater than that of the simply supported box-girder under the same mid-span axial load. This suggests that the continuous rigid frame box-girder has a higher resistance to deformation under static loads than the simply supported box-girder.

Figure 10.

The first order vertical bending mode of numerical model of continuous rigid frame box-girder.

Figure 11.

Static stiffness of continuous rigid frame box-girder.

Figure 12.

The first order vertical bending mode of numerical model of simply supported box-girder.

Figure 13.

Static stiffness of simply supported box-girder.

Next, the forces obtained from the wheel-rail interaction model, which are transferred to the bridge, are applied to the finite element model of the box beam to calculate the vehicle-induced vibration response. Subsequently, acoustic boundary element numerical models for the two types of box beams are separately established using the boundary element analysis software, as depicted in Figure 14. The vibration response of the box beams obtained from the finite element models is used as acoustic boundary conditions input into the acoustic boundary element models. The indirect boundary element method is then employed to calculate the sound pressure in the frequency range of 20 to 200 Hz at various field points and surfaces, thereby solving the structural noise radiation of the two types of box beams.

Figure 14.

Two numerical computational models of acoustic boundary element method for box beams: (a) numerical computational model of acoustic boundary element method for continuous rigid frame box-girders, (b) numerical computational model of acoustic boundary element method for simply supported box-girders.

Model validation

In order to verify the accuracy of the two numerical computational models developed for box beams, measured results from N1 and N2 sensors located at a 7.5 m lateral distance from the centerline of the outer track, 1.2 m above the ground and 3.5 m above the track surface, were compared with the corresponding calculated results. The comparison and validation are illustrated in Figures 15 and 16.

Figure 15.

Comparison of measured and calculated results for noise in continuous rigid frame box-girder structures: (a) N1, (b) N2.

Figure 16.

Comparison of measured and calculated results for noise in simply supported box-girder structures: (a) N1, (b) N2.

From Figures 15 and 16, it can be observed that the measured results agree well with the calculated results. This indicates that the two numerical computational models established in this study are capable of accurately predicting the noise radiation characteristics of the box beam structures. However, there are still some discrepancies between the measured and calculated results in certain frequency ranges. These differences can be attributed to unavoidable disparities between the chosen model parameters, boundary conditions, and the actual circumstances.

Comparison of noise characteristics

Bridge vibration response

To make a reasonable comparison of the vibration responses and structural noise characteristics of the two types of box-girders, the following numerical simulations will standardize parameters such as train type and speed: The wheel-rail interaction model will uniformly use the parameters corresponding to the continuous rigid frame box-girder in Table 2, and the train operating speed will be set uniformly at 90 km/h.

After adjusting the parameters, we re-solved the wheel-rail interaction model to obtain the excitation under the corresponding conditions. This excitation was then input into the finite element model established in the previous section to obtain the bridge’s vibration response. Due to some differences in the model establishment process: the continuous rigid frame finite element model included a portion of the bridge top structure, including the steel rail, while the simply supported box-girder treated it as part of the secondary permanent load and equivalently applied it as the uniform self-weight on the bridge deck. This makes the comparison at the steel rail measuring point less meaningful. Therefore, only the vibration response spectrum at the center of the top slab is provided here. Figure 17 shows the 1/3 octave frequency spectrum of the vibration acceleration at the center of the top slabs of the two box-girders.

Figure 17.

Comparison chart of 1/3 octave frequency spectrum simulation results for vibration response at the top slab center.

From Figure 17, it can be observed that under the same train type and speed conditions, in the frequency range of 4 to 20 Hz, the vibration acceleration levels at the top plate of the simply supported box-girder exhibit a significant peak at 4 Hz, while the vibration acceleration levels of the continuous rigid frame box-girder are significantly greater than those of the simply supported box-girder in the frequency range of 8 to 10 Hz. These phenomena are related to the first-order vertical bending modes of the box-girders. In the frequency range of 20 to 200 Hz, the vibration acceleration levels at the top slab of the simply supported box-girder are higher than those of the continuous rigid frame box-girder in the range of 20 to 160 Hz, only falling below the continuous rigid frame box-girder at 200 Hz. Both the continuous rigid frame box-girder and the simply supported box-girder exhibit peak vibration responses at 63 Hz.

Amplitude-frequency characteristics

The structure of a bridge can block the wheel-rail noise, allowing the area directly beneath the bridge to be influenced mainly by the structural noise. Studying the structural noise directly below the bridge often holds significant practical importance. Therefore, when simulating low-frequency structural noise, it is crucial to focus on the structural noise directly below the bridge. Thus, we proceeded to compute the structural noise radiation at specified locations when a train passes through two types of beams at a speed of 90 km/h. These locations include the mid-span section of the beams, positioned 30 cm below the beam, 7.5 m from the outer edge of the beam’s centerline, 1.2 m above the ground, and 3.5 m above the track surface. Comparative analyses were conducted at these locations for both types of beams.

From Figure 18, it can be observed that at 30 cm below the mid-span section, the simply supported box-girder exhibits higher peak values of structural noise, with frequency peaks reaching around 103 dB. Moreover, the overall structural noise of the continuous rigid frame box-girder is lower than that of the simply supported box-girder. At the N1 and N2 measurement points located at a lateral distance of 7.5 m from the centerline of the outer track, 1.2 m above the ground, and 3.5 m above the rail surface, the continuous rigid frame box-girder still demonstrates significantly lower low-frequency structural noise radiation compared to the simply supported box-girder. The structural noise of the continuous rigid frame box-girder reaches frequency peaks at around 50 Hz at both N1 and N2 measurement points, with noise levels reaching approximately 85 dB. On the other hand, the structural noise of the simply supported box-girder reaches frequency peaks at around 63 Hz at both N1 and N2 measurement points, with noise levels reaching approximately 91 dB.

Figure 18.

Structural noise spectra at each measurement point: (a) 30 cm below the mid-span section, (b) N1, (c) N2.

By comparing Figures 17 and 18, it can be observed that the vibration response and structural noise radiation characteristics of the continuous rigid frame box-girder and the simply supported box-girder exhibit a clear correlation. Their spectral graphs show similar numerical trends, with peak frequencies at either 50 Hz or 63 Hz.

Spatial distribution

To further investigate and compare the spatial distribution patterns of noise in the two box beam structures, numerical calculations were carried out using experimentally validated computational models. These calculations involved determining the structural noise of both box beam configurations within a range of 50 m above the ground and a lateral distance of 120 m from the centerline of the bridge while a train passed by at a constant speed of 90 km/h. Subsequently, linear sound pressure level contour maps and noise difference contour maps were generated for both box beam systems to illustrate the spatial distribution patterns of structural noise. The contour maps are presented in Figures 19 and 20, respectively.

Figure 19.

Spatial distribution of noise in two box beam structures (Unit: dB(L)): (a) spatial distribution of noise in continuous rigid frame box-girder structures, (b) spatial distribution of noise in simply supported box-girder structures.

Figure 20.

Contour maps of noise difference between simply supported and continuous rigid frame box-girders (Unit: dB).

From Figure 19, it can be observed that the spatial distribution patterns of structural noise in both types of box beams are generally consistent. The structural noise is higher near the beam and decreases as the distance increases, with higher noise levels directly above and diagonally above the beam. However, there are slight differences in the calculated values of structural noise between the two box beam types. Specifically, the continuous rigid frame box-girder exhibits a lower peak structural noise (97 dB) directly above and below the beam than the simply supported box-girder (106 dB). At a distance of 120 m from the centerline of the bridge, the structural noise of the continuous rigid frame box-girder attenuates to around 68 dB, while the simply supported box-girder attenuates to around 72 dB.

Figure 20 demonstrates that the difference in low-frequency structural noise radiation between the two box beams ranges from −1.5 dB to 15 dB. Notably, the continuous rigid frame box-girder exhibits lower structural noise compared to the simply supported box-girder directly above and below the beam, with noise differences ranging from 0.9 dB to 15 dB. The noise difference reaches around 5 to 15 dB directly below the bridge. Within a range of 1.2 m above the ground, primarily influenced by the bridge structural noise, the noise difference ranges from 0 dB to 15 dB, indicating that the continuous rigid frame box-girder has lower low-frequency structural noise radiation. Overall, the acoustic performance of the continuous rigid frame box-girder is superior to that of the simply supported box-girder. We posit that the observed differences in acoustic performance between continuous rigid-frame box-girders and simply supported box-girders likely stem from variations in their differences in stiffness.

Conclusions and outlook

This study focuses on the investigation of vibrations and noise generated by a 2 × 30 m continuous rigid-frame concrete box beam and a 30 m simply supported concrete box beam in an urban rail transit system. Tests were conducted during train passage to obtain acoustic characteristics such as acceleration level, sound pressure level spectra, and noise attenuation patterns at various measurement points. Additionally, predictive models for vibration and noise were developed for both types of box-girders. The accuracy of these models was validated by comparing them with field test results. Furthermore, based on the models, the structural noise amplitude-frequency characteristics and spatial distribution patterns of the two beam configurations were compared under the same conditions. The main conclusions of this study are as follows:

(1) The peak vibration level induced by a train passing over the section of the continuous rigid frame box-girder at a speed of 93 km/h is lower than that induced by a train passing over the simply supported box-girder section at a speed of 74 km/h. Meanwhile, at a lateral distance of 7.5 m from the centerline of the outer track and 3.5 m above the rail surface, the low-frequency structural noise generated by a train passing over the simply supported box-girder section is greater than that generated by a train passing over the continuous rigid frame box-girder section.

(2) When a Type B train passes through the two types of box-girder sections at a speed of 90 km/h, the peak frequency of structural noise generated by the continuous rigid frame box-girder is around 50 Hz, while for the simply supported box-girder, it is around 63 Hz. The peak structural noise level of the simply supported box-girder section is approximately 6 dB higher than that of the continuous rigid frame box-girder section. Both types of box-girders exhibit a clear correlation between vibration response and structural noise characteristics.

(3) Within a range of 120 m from the centerline of the bridge and at a height of 50 m above the ground, the structural noise from the continuous rigid frame box-girder section attenuates to around 68 dB, while that from the simply supported box-girder section attenuates to around 72 dB. The difference in low-frequency structural noise between the two types of beams ranges from −1.5 to 15 dB.

(4) The area directly below the bridge is the dominant area of the acoustic performance of the continuous rigid frame box-girder, and the noise difference between it and the area directly below the simply supported box-girder can reach 5 to 15 dB.

The low-frequency structural noise issues of the continuous rigid frame box-girder and simply supported box-girder studied in this paper represent just a small aspect within the field of bridge structural noise problems. In the present and foreseeable future, low-frequency structural noise in urban rail transit bridges will continue to be a focal area of interest. Currently, there are limited effective means for addressing low-frequency structural noise in urban rail transit bridges. It is necessary to explore new avenues for controlling bridge structural noise, such as delving deeper into the mechanisms of noise generation, developing innovative structural noise control technologies, promoting interdisciplinary integrated research, and further enhancing the noise reduction capabilities of existing structural noise control methods.

Footnotes

Acknowledgements

The authors would like to thank Dr He Wei from China University of Geosciences for his assistance and support during the paper revision process.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was financially supported by the National Natural Science Foundation of China (52378450,52008169,52372328,52272348),the China Postdoctoral Science Foundation (2023T160214,2023M731077),the Natural Science Foundation of Jiangxi Province (20224BAB214074,20232BAB204087),the Technology Research and Development Program of China Railway Corporation (P2022Z003-2),the open funding project of the State Key Laboratory of Performance Monitoring and Protecting of Rail Transit Infrastructure (HJGZ2021105),and the Postgraduate Innovation Special Foundation of Jiangxi Province (YC2023-S541).

ORCID iD

Quanmin Liu

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Comparative study on structural noise characteristics of continuous rigid frame and simply supported box-girder bridges in rail transits

Abstract

Keywords

Introduction

Field test

Field test information

Test results

Simulation model

Modeling principles

Model establishment

Model validation

Comparison of noise characteristics

Bridge vibration response

Amplitude-frequency characteristics

Spatial distribution

Conclusions and outlook

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References