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Abstract

The development of urban rail transit confronts numerous challenges such as vibration and noise. To mitigate the impact of environmental vibration, various damping measures have been implemented. The ladder sleeper damping track demonstrates excellent vibration reduction performance and is commonly deployed in vibration-sensitive areas to alleviate vehicle-induced vibration effects for the line foundation structure. However, this damping track exhibit amplified vibration noise phenomena for itself. This issue not only compromises passenger comfort but also adversely impacts the acoustic environment along rail transit corridors. This study systematically investigates the vehicle-induced vibration characteristics and noise generation mechanisms of the ladder sleeper damping tracks on concrete single-track box girder bridge. Furthermore, the influencing factors on sound radiation propagation of this track are examined comprehensively. The results demonstrate significant vehicle-induced low-frequency vibrations in ladder sleeper damping tracks, with primary vibrating components being sleepers and damping pads. The sleepers exhibit regular bending vibrations at lower frequency bands. Horizontally installed vertical damping pads show pronounced transverse and longitudinal vibrations due to compressive deformation. The track structure demonstrates substantial acoustic radiation capacity, generating intense sound waves across most areas within free acoustic fields. Deck reflection exerts considerable influence on the track’s acoustic radiation characteristics. And, the reflective effects of L-shaped supports similarly contribute substantially to sound radiation from components such as track slabs. The combined reflection effect of the L-type supports and the bridge deck renders the vibration propagation mechanism of the ladder sleeper damping track more complex.

Keywords

urban rail transit bridge line ladder sleeper damping track vehicle-induced vibration noise deck reflection

Introduction

Urban rail transit systems feature safety, comfort, speed, and convenience, which have significantly mitigated urban traffic congestion. It also demonstrates multiple advantages including low energy consumption, high efficiency and large transport capacity, prompting widespread construction for many cities. According to construction methods, urban rail transit systems are mainly classified into three types: underground lines, ground lines, and bridge lines. The environmental vibration issues induced during the operation of underground lines have become a key concern. The vibration problems caused in above-ground buildings within sensitive areas such as hospitals, museums, ancient structures, research institutes, and libraries have emerged as significant research topics.^1–4

However, the vehicle-induced vibration noise problems inside metro carriages are frequently overlooked. In addition to environmental vibrations, the noise generated during the operation of ground lines and bridge lines significantly impacts the living environment of residents along the routes. To address environmental vibration issues in vibration-sensitive areas, commonly adopted damping measures typically focus on track structures. Consequently, various damping track systems, including rail damping, fastener damping, sleeper damping, and ballast damping, have been implemented in urban rail transit to mitigate environmental vibrations.

Among sleeper damping technologies, the ladder sleeper damping track stands out as the most representative solution. Recent research findings that the vibration damping performance of this track is excellent. The ladder sleeper damping track is designed based on the longitudinal sleeper track theory. This track configuration addresses the shortcomings of conventional transverse sleeper tracks. Compared with transverse sleeper tracks, the ladder sleeper provides continuous support, thereby offering advantages in terms of stiffness which enhance its vertical load-bearing capacity. Furthermore, the horizontally arranged steel pipes forming a grid-like structure demonstrate significant superiority in lateral stability. Furthermore, the ladder sleeper damping track demonstrates advantages including a lightweight mass-spring system, superior vibration and noise reduction capabilities, and reduced maintenance costs. It enhances not only vibration and noise mitigation but also improves the dynamic characteristics of the vehicle-track interaction system while minimizing vibration load transmission within the track structure.^5–7 Consequently, this configuration has been widely implemented in urban rail transit systems.

However, with extensive engineering applications of vibration-damping tracks, adverse phenomena including rail corrugation^8–10 and aggravated self-excited vibration-noise from track structures have emerged during operation. While vibration-damping tracks demonstrate superior performance in mitigating environmental vibrations, the intensification of their inherent vibration-noise presents a contradictory deterioration effect, subsequently compromising both the service reliability of the tracks and the acoustic environments within vehicles and along adjacent areas.

Concerning the noise issues in rail transit, particular attention should be paid to bridge lines for three primary reasons. First, the bridge structure radiates low-frequency structural noise, resulting in higher noise levels along these lines. Second, compared to underground sections, the vehicle-induced vibration noise from trains operating on bridge lines significantly impacts the surrounding acoustic environment, especially in urban areas. Third, considering the common corridor sharing with other transport infrastructures in urban rail transit bridge lines and projected increases in operating speeds under future development plans, the noise problems caused by train operations are expected to become more severe.

Consequently, researchers worldwide have conducted extensive research on railway noise issues, primarily focusing on wheel-rail noise,^11–14 aerodynamic noise,^15–17 bridge-borne low-frequency structural noise,^18–24 and noise from ancillary structures such as sound barriers.^25–28 Furthermore, substantial studies have been devoted to vibration and noise reduction measures.^29–38 However, the track structure in bridge-line itself undergoes vibration and subsequent noise radiation during train passages.

Against the background of intensified wheel-rail interactions, the acoustic radiation characteristics of sleeper should be received significant attention, particularly in sections where vibration-damping track systems are implemented. Song investigated the vibroacoustic characteristics of a U-shaped girder bridge system equipped with ladder sleeper damping tracks.³⁵ The results demonstrate that although the damping track reduces bridge-borne noise, its own vibration amplification conversely emerges as a significant noise source. Feng et al. employed a wavenumber finite element-boundary element method to analyze the acoustic radiation properties of ballastless tracks in high-speed railways, revealing that track slabs exert substantial influence on the overall acoustic radiation of the track system.³⁹

Our preliminary studies have identified that steel spring floating slab tracks in bridge line exhibit pronounced acoustic radiation capabilities, being one of the dominant noise sources in railway systems. Furthermore, these earlier investigations established the theoretical foundation for developing acoustic prediction models of track structures on bridge lines.^40–42 Huang revealed that long-term fatigue effects can amplify track structure vibration.⁴³ Zhou investigated the causes and mitigation strategies for sudden train vibration amplification occurring at steel spring floating slab track transitions through field tests and numerical simulations.⁴⁴ This study provides theoretical guidance for optimizing steel spring floating slab design in noise control applications.

In summary, in order to characterize the noise signature of bridge lines accurately, the vibroacoustic properties of damping tracks themselves should not merely be disregarded but rather necessitate heightened attention in vibration and noise evaluations. When implementing track vibration mitigation measures for rail transit noise and vibration control, which must simultaneously minimize secondary environmental consequences while capitalizing on their inherent vibration damping capabilities. In this way, the vibration damping track can make the most of its strengths and enhance its service performance.

Therefore, this paper establishes a coupled dynamic model of the subway A-type vehicle, ladder sleeper damping tracks, and single-line box girder bridge based on the train-track-bridge interaction theory, along with an acoustic boundary element model for the ladder sleeper damping track by acoustic boundary element theory. It systematically analyzes the vehicle-induced vibration characteristics and acoustic properties of the ladder sleeper, while further investigating the bridge’s impact on the acoustic radiation of the ladder sleeper damping track. This research makes a significant contribution to the theoretical framework of acoustic studies in rail transit, thereby providing a theoretical basis for subsequent vibration and noise reduction designs.

The vehicle-ladder sleeper-box girder bridge interaction model

The acoustic radiation characteristics of foundation structure in rail transit lines can be effectively predicted based on the train-track-bridge interaction theory⁴⁵ and the acoustic boundary element theory.⁴⁶ This study investigates the ladder sleeper damping track installed on a single-track box-girder bridge line. The computational model comprises three subsystems: the Type A metro vehicle, the ladder sleeper damping track, and the single-track box-girder bridge. The Type A metro vehicle is modeled as a multi-rigid-body system with 35 degrees of freedom proposed by Zhai,⁴⁷ composed of four wheelsets, two bogie frames, and a carbody. Rigid components are interconnected through primary and secondary suspension systems. The primary dynamic parameters of the Type A metro vehicle are summarized in Table 1.

Table 1.

Dynamic parameters of Type A subway vehicle.⁴⁸.

Vehicle component	Unit	Value
Mass of car body	t	34.69
Mass moment of inertia of car body around x-axis	t·m²	61
Mass moment of inertia of car body around y-axis		1835
Mass moment of inertia of car body around z-axis		1816
Mass of bogie	t	7.36
Mass moment of inertia of bogie around x-axis	t·m²	1.76
Mass moment of inertia of bogie around y-axis		2.18
Mass moment of inertia of bogie around z-axis		4.00
Mass of wheel set	t	1.90
Mass moment of inertia of wheel set around x-axis	t·m²	0.9
Mass moment of inertia of wheel set around z-axis	t·m²	0.9
Stiffness of longitudinal secondary suspension system	kN/m	194
Stiffness of lateral secondary suspension system		194
Stiffness of vertical secondary suspension system		268
Damping of vertical secondary suspension system	kN·s/m	80
Stiffness of longitudinal primary suspension system	kN/m	332
Stiffness of lateral primary suspension system		332
Stiffness of vertical primary suspension system		550
Damping of vertical primary suspension system	kN·s/m	6

The line foundation structure is primarily modeled using finite element methods. The finite element model of the ladder sleeper damping track explicitly incorporates all structural components, including rails, fastening systems, sleepers, L-shaped support brackets, connecting steel tubes, vibration damping pads of vertical, lateral, and longitudinal. A schematic diagram of the ladder sleeper damping track configuration and the finite element model of the bridge line system are shown in Figure 1. The finite element modeling parameters and dynamic properties of the line foundation structure are detailed in Table 2.

Figure 1.

Schematic diagram of the ladder sleeper damping track on the bridge.

Table 2.

Dynamic parameters of the ladder sleeper damping track on the bridge line.

Object	Finite element type	Parameter	Value
Rail	Beam188	Elastic modulus (Pa)	2.1 × 10¹¹
		Moment of inertia (m⁴)	3.215 × 10^-5
		Poisson’s ratio	0.3
		Density (kg·m⁻¹)	60.64
Fastener	Combin14	Rigidity (N·m⁻¹)	6 × 10⁷
		Damping (N·s·m⁻¹)	7.5 × 10⁴
		Span (m)	0.6
Sleeper	Solid45	Length (m)	6.0
		Width (m)	0.45
		Thickness (m)	0.18
		Elastic modulus (Pa)	3.3 × 10¹⁰
		Poisson’s ratio	0.2
		Density (kg·m⁻³)	2500
Connecting steel pipe	Beam188	Elastic modulus (Pa)	2.0 × 10¹¹
		Poisson’s ratio	0.3
		Density (kg·m⁻³)	7830
Damping pad	Solid45	Elastic modulus (Pa)	6.1 × 10⁵
		Poisson’s ratio	0.45
		Density (kg·m⁻³)	1600
L-concrete support	Solid45	Elastic modulus (Pa)	2.8 × 10¹⁰
		Poisson’s ratio	0.25
		Density (kg·m⁻³)	2300
Bridge	Shell63	Length (m)	24.3
		Top/bottom plate width (m)	4.65/1.5
		Top/web/bottom plate thickness (m)	0.2/0.15/0.25
		Elastic modulus (Pa)	2.8 × 10¹⁰
		Poisson’s ratio	0.25
		Density (kg/m³)	2300

Based on the train–track–bridge dynamic interaction theory, which has been verified by numerous field tests and widely applied to railway engineering practice, a spatial combined train–track–bridge dynamics model is established. Thus, the fundamental method and underlying logic of the model are briefly outlined. The proposed dynamic model comprises three subsystems: train, track, and box-girder bridge. Their motion equations can be written in matrix form as follows $M_{v} {\ddot{u}}_{v} + C_{v} {\dot{u}}_{v} + K_{v} u_{v} = F_{wr} (u_{v}, {\dot{u}}_{v}, u_{t}, {\dot{u}}_{t})$ (1) $M_{t} {\ddot{u}}_{t} + C_{t} {\dot{u}}_{t} + K_{t} u_{t} = F_{wr} (u_{v}, {\dot{u}}_{v}, u_{t}, {\dot{u}}_{t}) - F_{tb} (u_{t}, {\dot{u}}_{t}, u_{b}, {\dot{u}}_{b})$ (2) $M_{b} {\ddot{u}}_{b} + C_{b} {\dot{u}}_{b} + K_{b} u_{b} = F_{tb} (u_{t}, {\dot{u}}_{t}, u_{b}, {\dot{u}}_{b})$ (3)where M, C, and K represent the mass, damping, and stiffness matrices, respectively; u is the displacement vector; and the dot indicates a partial differential with respect to time. Subscripts v, t, and b denote the vehicle, track, and bridge subsystems, respectively; $F_{wr} (u_{v}, {\dot{u}}_{v}, u_{t}, {\dot{u}}_{t})$ is the load vector involving dynamic wheel–rail forces, which are deduced from the displacements and velocities of the train and rail; and $F_{tb} (u_{t}, {\dot{u}}_{t}, u_{b}, {\dot{u}}_{b})$ is the load vector composed of the dynamic track–bridge interaction forces, which are obtained from the displacements and velocities of the track slab and bridge.

The vehicle and track subsystems are coupled based on the spatial wheel-rail contact model proposed by Zhai.⁴⁷ The American Federal Railroad Administration (FRA) Class 6 Track Irregularity Spectrum with wavelength ranges of 0.1–100 m is applied as the external excitation input to the system. The train-track subsystem and bridge subsystem are governed by the explicit Zhai algorithm and implicit Newmark-β method, respectively,^45,49 with time steps specifically set at 10^-4 s and 10^-3 s to ensure numerical convergence.

The vibration response of the ladder sleeper damping track serves as the acoustic boundary condition for subsequent sound field computations. The acoustic boundary element method (BEM) was employed to calculate the acoustic characteristics of the ladder sleeper damping track. Since our previous investigations revealed significant acoustic coupling effects between adjacent track sections on bridge structures,⁴² the established acoustic BEM model explicitly incorporates all ladder sleeper damping track units within a single bridge span to accurately capture their collective sound radiation behavior. The BEM has been extensively validated for structural acoustic radiation prediction, particularly demonstrating superior accuracy in low-frequency domain.²⁰ The computational framework implemented in this study builds upon our established methodology detailed in previous investigations.^19,23,49 For comprehensive implementation schematic, readers are directed to these foundational works. The schematic diagram of acoustic numerical simulation prediction procedure for ladder sleeper damping track can be seen Figure 2.

Figure 2.

Schematic diagram of acoustic numerical simulation prediction procedure for ladder sleeper damping track.

Vibration and acoustic characteristics of the ladder sleeper damping track

Vibration characteristics of the ladder sleeper damping track

This study takes the ladder sleeper damping track on a 24m single-track box girder bridge as the research object. The acoustic-vibration characteristics of each component in the ladder sleeper damping track are analyzed. The vibration acceleration frequency spectrum curves of the ladder sleeper damping track system presented in Figure 3.

Figure 3.

Vibration acceleration of each component of the ladder sleeper damping track (a) Vibration acceleration analysis points of sleeper, (b) Vertical vibration acceleration of sleeper at different positions, (c) Vibration acceleration of vertical damping pad, and (d) Vibration acceleration of L-concrete support).

As shown in Figure 3, significant vibration differences exist among components of the ladder sleeper damping track during train passage. The main vibration characteristics can be summarized as follows:

First, the vibration characteristics of concrete sleepers are primarily concentrated in frequencies below 500 Hz, with the 200–250 Hz range emerging as the dominant frequency band. Small-amplitude vibrations densely distribute in the 0–150 Hz range, while sleeper installed with vertical damping pads exhibit strong vibrations within this band. This phenomenon indicates that vibration energy accumulates in sleepers while the damping pads perform their vibration reduction function.

Second, among all track components, the sleepers and damping pads demonstrate the most intense vibrations, significantly exceeding those of L-shaped supports. The vibration frequency of L-shaped supports mainly concentrates in 0–150 Hz, showing substantial attenuation in the 200–250 Hz range. This phenomenon indicates the damping pads effectively weaken vibration energy transmission and provide excellent attenuation for principal vibration frequencies.

Third, the vertical damping pads installed beneath sleepers exhibit stronger lateral and longitudinal vibrations compared to vertical vibrations, with lateral vibrations demonstrating the highest intensity. The vertical damping pad performs vertical vibration damping whilst being subjected to vertical compression forces, thus resulting in marked lateral and longitudinal vibration manifestations.

Figure 4 shows the vertical vibration acceleration contour map of the ladder sleeper damping track at 215.2 Hz. Within the predominant vibration frequency band, a marked concentration of vibration energy is observed in the vertical damping pad. Concurrently, the sleepers exhibit pronounced vibrational characteristics, whereas the L-shaped supports demonstrate relatively weaker vibrations. This phenomenon indicated that components which have excellent damping performance will be amplified self-vibration due to energy accumulation significantly. In this background, the subsequent analysis will focus on investigating the acoustic radiation characteristics of the ladder sleeper damping track system.

Figure 4.

The vibration of the vertical damping pad at 215.2 Hz (unit: m/s²).

Acoustic radiation characteristics of the ladder sleeper damping track

This study employs sound power and sound pressure at field points to evaluate the acoustic radiation characteristics of the ladder sleeper damping track. The sound power characterizes the structural acoustic radiation capacity of the track. The sound pressure at field points reflects the acoustic characteristics of structural radiated waves transmitted to receiving positions, while also indicating variations during wave propagation processes.

Figure 5 illustrates the sound power curves of the ladder sleeper damping track. The ladder sleeper track exhibits strong acoustic radiation capability in the mid-to-low frequency band below 500 Hz. Within the frequency band of 0∼500 Hz, the ladder sleeper damping track has the strongest sound radiation capacity in the intense vibration frequency band of 200∼500 Hz. In other frequency bands, the ladder sleeper damping track has stronger sound radiation capacity with small vibrations, but it is significantly weaker than that in the intense vibration frequency band. Consequently, the impact of its structure-borne noise radiation on the acoustic environment along bridge lines must not be overlooked, and it should be paid more attention and required systematic mitigation measures.

Figure 5.

The sound power curves of the ladder sleeper damping track.

To further investigate the sound pressure characteristics of the ladder sleeper damping track in different acoustic zones, the sound field points shown in Figure 6 were selected for analysis. Figure 7 presents linear sound pressure levels at various field points. The results demonstrate that:

(a) Within all studied acoustic frequency bands, the track exhibits significantly higher sound pressure levels in intense vibration frequency bands.

(b) Near 450 Hz, all measured sound pressures exceed values observed in the 0–200 Hz range.

Figure 6.

Schematic diagram of the measurement points arrangement in the free-field.

Figure 7.

Sound pressure frequency spectrum curves of the ladder sleeper damping track in different sound fields.

Based on the above analysis, it can be concluded that the ladder sleeper damping track demonstrates strong sound radiation capacity under vehicle-induced vibration excitation. This structural configuration demonstrates pronounced acoustic energy emission across all measured sound fields, accompanied by broadband radiation characteristics. Consequently, while the track system provides effective vibration attenuation, its vehicle-induced structure-borne noise by requires high attention.

Vibration and acoustic radiation patterns of the ladder sleeper damping track

To analyze the overall vibration characteristics and acoustic radiation patterns of the ladder sleeper damping track, Figure 8 presents the contour maps of the overall vibration acceleration and the acoustic radiation patterns of the transverse sound field at mid-span. The results indicate that the overall vibration of the L-shaped supports in the ladder sleeper is minimal, with vibrations primarily concentrated in the sleeper and damping pad components. At lower frequencies, the vibration of the sleeper exhibits a regular pattern, manifesting as vertical bending vibrations. Notably, the transverse vibration of the damping pad is particularly prominent.

Figure 8.

The contour maps of vibration and acoustic radiation of the ladder sleeper damping track (Units: Left column – m/s²; Right column – dB/L).

The vehicle-induced vibration noise radiation characteristics of the ladder sleeper damping track can be summarized as follows:

(a) The sleeper exhibits vertical bending vibrations below 250 Hz, with minor vibrations of the L-shaped supports concentrated below 150 Hz. Consequently, the acoustic radiation patterns of the ladder sleeper damping track remain relatively regular in this frequency band, as illustrated in Figures 8(a)–(d).

(b) In the frequency bands of intense vibration of the ladder sleeper damping track, the L-shaped supports exhibit a shielding effect on the overall acoustic radiation of the track. However, the pronounced vibrations of the sleeper and damping pad result in more concentrated acoustic radiation in localized areas directly above the track. It can therefore be inferred that the acoustic radiation of the ladder sleeper damping track in these frequency bands will significantly impact the internal cabin noise environment, as shown in Figures 8(e)–(g).

(c) Near 450 Hz, minor vibrations occur in the sleeper, but the vibrational behavior becomes highly complex. The sleeper primarily displays intricate local vibration characteristics, and no distinct patterns are observable in the acoustic radiation of the ladder sleeper, as demonstrated in Figures 8(h)–(k).

(d) The contour maps of the acoustic for radiation damping pad have concentrated regions that is small spatial ranges. This indicates that the rubber damping pad can generate significant noise even under intense vibration. Positioned between the L-shaped supports and the sleeper, the vertical damping pad is subject to acoustic shielding effects from both components. Consequently, intense vibrations of the damping pad only induce concentrated acoustic radiation within a limited spatial range near the track structure, as depicted in Figures 8(a) and (b).

Effect of the bridge deck on the acoustic radiation characteristics of the ladder sleeper damping track

Given the substantial rigidity of concrete box girder bridge decks, the propagation of sound waves radiated from the ladder sleeper damping track on the bridge downwards is significantly impeded. To accurately characterize the sound radiation propagation behavior of the ladder sleeper damping track, the bridge deck was considered as a fully reflective rigid panel when analyzing the influence of deck reflection on the acoustic radiation characteristics of the ladder sleeper damping track system.

This study selects field points in the far-field and directly above the track structure as the focus of research. By comparing the linear sound pressure at different points and analyzing the sound radiation patterns above the bridge, the study investigates the effect of the bridge on the sound radiation of the trapezoidal sleeper damping track. The significance of this research lies in considering the reflection effect of the bridge deck, which makes the theoretical study of track structure sound radiation more aligned with actual conditions.

The selection of the acoustic field points is shown in Figure 9. Here, $S F_{i} (i = 1, 2, 3 . . .)$ represents the acoustic field points in the free sound field, and ${S F}_{i_{'}}^{'} (i^{'} = 1, 2, 3 . . .)$ represents the acoustic field points in the semi-free sound field incorporating box-girder bridge reflections. Although deck reflection effects are excluded in the current methodology, this configuration enables more precise characterization of the intrinsic acoustic radiation properties of the ladder sleeper damping track. These findings establish a foundational framework for subsequent noise reduction strategies. Specifically, by weakening the acoustic radiation capability of ladder sleeper damping tracks at the vibration source can their noise reduction designs become more targeted. Consequently, the inclusion of deck reflection effects in track structure analyses should be judiciously determined based on specific research objectives.

Figure 9.

The selection of the acoustic field points.

Figure 10 illustrates the influence of deck reflection on linear sound pressure characteristics at field points in the acoustic field of ladder sleeper damping track systems. The deck reflection predominantly affects acoustic radiation characteristics of ladder sleepers within the 0–200 Hz frequency band. The sound pressure level in the far-field acoustic field shows significant amplification. In the vertical acoustic field directly above the track, sound pressure exhibits both reduction and amplification segments within 0–200 Hz, while the horizontal acoustic field demonstrates broader frequency bands with pressure increases. Notably, deck reflection displays negligible effects on acoustic radiation in the predominant vibration frequency bands of ladder sleepers.

Figure 10.

Effect of bridge deck reflection on acoustic radiation characteristics of ladder sleeper damping track.

The comparative analysis of overall averaged sound pressure levels in Figure 10(h) reveals that deck reflection substantially enhances sound pressure in far-field regions, but its impact on vertical acoustic fields follows irregular patterns. In vertical field regions, deck reflection slightly increases total sound pressure only at near-proximity field points (SF8) adjacent to ladder sleepers, while reducing overall pressure at other monitoring positions. This analysis confirms that L-shaped support brackets significantly influence acoustic radiation from track components. The combined interaction between L-shaped supports and bridge deck induces complex acoustic propagation mechanisms for ladder sleeper systems.

To comparatively analyze the influence of deck reflection on the acoustic radiation characteristics of ladder sleeper damping tracks, the sound radiation patterns were investigated under both considered and neglected deck reflection conditions. For enhanced comparability, the color scale ranges of sound pressure contour plots were uniformly calibrated to evaluate the holistic impact of deck reflection on the sound field distribution above the ladder sleeper damping track system, as illustrated in Figure 11.

Figure 11.

Effect of deck reflection on acoustic radiation characteristics of ladder sleeper damping track (Left column: deck reflection neglected, Right column: deck reflection considered, Unit: dB/L).

In lower frequency bands, the deck reflection effect effectively extended the acoustic radiation domain of ladder sleepers and significantly augmented the radiation characteristics in the far-field zone above bridge structures. The combined interactions between the deck and L-shaped support bearings substantially altered the sound radiation mechanisms of ladder sleepers, with these modifications showing increased prominence at elevated frequencies. As demonstrated in Figure 11(g), both the shielding effect of L-shaped bearings and the deck reflection phenomenon have profoundly modified the propagation characteristics of acoustic radiation from the ladder sleeper damping track system.

In conclusion, the inherent rigidity of concrete bridge structures confers significant constraints on the propagation pathways of acoustic radiation from track systems. To investigate the acoustic radiation characteristics of track structures under real-world operating conditions, it is essential to comprehensively consider this acoustic boundary condition.

Conclusions

This study employs vehicle-track-bridge interaction theory and acoustic boundary element theory to systematically investigate the vehicle-induced vibration noise characteristics of ladder sleeper damping tracks. The acoustic radiation capacity and acoustic characteristics of this track system in free sound fields are thoroughly analyzed. Furthermore, we systematically explore the influence of concrete bridges with high rigidity on the acoustic radiation properties of ladder sleeper damping tracks. The principal findings are summarized as follows:

(1) The ladder sleeper damping track exhibits prominent low-frequency vibrations under track irregularity excitation. Intensive small-amplitude oscillations are observed in the 0–150 Hz range, with the most severe vibrations occurring within 200–250 Hz. Vibrations are primarily concentrated in the sleepers and damping pads. Regular bending vibrations manifest in the sleepers at lower frequency bands. The damping pads play a crucial role in vibration attenuation, where the horizontally installed vertical damping pads experience significant transverse and longitudinal vibrations due to compressive deformation. Localized vibrations of the track structure become increasingly pronounced with ascending frequency.

(2) The ladder sleeper damping track demonstrates substantial acoustic radiation capacity. It radiates intensive acoustic waves in most regions of free sound fields. The acoustic radiation pattern of this track system in free-field conditions is significantly influenced by its L-shaped supports, which exhibit notable shielding effects on sound wave propagation. The shielding effect of the L-shaped support in ladder sleeper is closely related to the propagation mechanism of vibration-damping tracks. It affects the sound radiation patterns of vibration-damping tracks and the sound pressure at different field points in the sound field.

(3) The reflection effect of the rigid deck can be considered as equivalent to a virtual sound source existing at the symmetric position of the real sound source relative to the deck surface, which simultaneously radiates sound waves. This results in the combined effect of a real sound source and its virtual counterpart. Consequently, the sound radiation in both the vertical direction above the track structure and the horizontal sound field is significantly enhanced. The deck reflection exerts notable influence on sound wave propagation, thereby modifying the acoustic radiation characteristics of the track system.

(4) The deck reflection predominantly influences acoustic radiation of ladder sleepers within 0–200 Hz frequency band. The far-field sound pressure demonstrates significant amplification, while the vertical acoustic field directly above the track exhibits both reduction and enhancement zones within this frequency band. This reflection effect shows limited impact on the primary vibration frequency band of ladder sleepers. Notably, the L-shaped support exerts substantial influence on acoustic radiation characteristics from track components. The collaborative interaction between L-shaped supports and deck reflections results in a complex propagation mechanism emerging within the ladder sleeper system.

In summary, the ladder sleeper damping track, while demonstrating effective vibration attenuation capabilities, exhibits pronounced vehicle-induced vibration characteristics. Moreover, the cumulative build-up of vibrational energy significantly amplifies its dynamic characteristics. Subjected to vehicle-induced vibrations, this track system demonstrates pronounced acoustic radiation capabilities. The propagation of acoustic waves is further influenced by its structural components, particularly the L-shaped support brackets and bridge line interaction. Such vehicle-induced vibro-acoustic emissions not only adversely impact the ambient acoustic environment along the rail corridor but may also exacerbate low-frequency noise levels within passenger compartments. Therefore, the vibro-acoustic characteristics of ladder sleeper damping tracks warrant heightened attention and require effective mitigation measures, particularly considering potential resonance effects with foundation structures and deck reflection phenomenon

Footnotes

ORCID iD

Xiaoyun Zhang

Consent to participate

All the authors listed have approved the manuscript that is enclosed.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (NSFC) (No. 52362049), the Science and Technology Research and Development Project of CHINA RAILWAY (No. L2024G008), the Joint Innovation Fund Project of Lanzhou Jiaotong University and Corresponding Supporting University (No. LH2023016), the Natural Science Foundation of Gansu Province (No. 25JRRA158), the Science and Technology Research and Development Program Project of China railway group limited (No. 2025-Special-03), and the Youth Fund Project of Lanzhou Jiaotong University (No. 2021014).

Declaration of conflicting interests

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

Data Availability Statement

The datasets generated or analyzed during this study are included in this article. Raw data can be provided by the corresponding author upon reasonable request.*

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