# Acoustic Radiation Prediction Model Rationality and Mechanism of Steel-Spring Floating-Slab Tracks on Bridges

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## Abstract

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## 1. Introduction

## 2. Prediction Model of Acoustic Radiation from SSSFSTs on a Bridge

## 3. Theoretical Model Verification

#### 3.1. Comparative Verification of Dynamic Calculation Models

#### 3.2. Discussion of the Vibration Reduction Track Noise Test Problem and the Verification of Theoretical Methods

## 4. Rationalization of the Acoustic Radiation Model of a Track on a Bridge

## 5. Discussion

## 6. Conclusions

- (1)
- The acoustic radiation characteristics obtained from the acoustic models with different numbers of floating-slabs were significantly different. With an increased number of floating-slabs in the acoustic model, the acoustic radiation capacity of the SSSFSTs and the sound pressure radiated to the outside were enhanced. However, this did not occur in simple linear increments.
- (2)
- The vibration characteristics of each floating-slab on the one-span bridge were different, and the acoustic input conditions of different numbers of floating-slabs in the acoustic models used for acoustic analysis led to significant differences in the acoustic analysis results.
- (3)
- With the same number of floating-slabs in the acoustic model, there were obvious differences in different floating-slab acoustic contributions at the same sound point. Using acoustic models with different floating-slab numbers, the acoustic contribution of the same floating-slab showed amplified or weakened contributions at the same sound point. Therefore, the number of sound sources in the acoustic model directly affects the acoustic calculation results because the sound waves of each floating-slab can cause acoustic effects during the propagation process.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Dynamics model of UM dynamic simulation software and solution process diagram: (

**a**) UM vehicle-track-bridge dynamics model; (

**b**) vehicle-track-bridge dynamics calculation process in UM.

**Figure 5.**Comparison of calculation results of two models: (

**a**) The model calculation results of this paper; (

**b**) The calculation results of UM software.

**Figure 6.**The research points to the selection of the track acoustic characteristics in the free sound field.

**Figure 9.**Comparison of the acoustic power of different numbers floating on slabs: (

**a**) The sound power spectrum of different numbers of floating-slabs; (

**b**) The average sound power of different numbers of floating-slabs.

**Figure 10.**Comparison of linear sound pressure at different sound field points for different numbers of floating-slabs: (

**a**) Comparison of linear sound pressure at SF1 for different numbers of floating-slabs; (

**b**) Comparison of linear sound pressure at SF4 for different numbers of floating-slabs; (

**c**) Comparison of linear sound pressure at SF8 for different numbers of floating-slabs.

**Figure 11.**Acoustic radiation contribution of floating-slabs to different sound field points at 215.2 Hz: (

**a**) Contribution of acoustic radiation to the field point SF1; (

**b**) Contribution of acoustic radiation to the field point SF2. (

**c**) Contribution of acoustic radiation to the field point SF4. (

**d**) Contribution of acoustic radiation to the field point SF8.

**Figure 12.**Acoustic radiation contribution of floating-slabs to different sound field points at 64.4 Hz: (

**a**) Contribution of acoustic radiation to the field point SF1; (

**b**) Contribution of acoustic radiation to the field point SF2; (

**c**) Contribution of acoustic radiation to the field point SF4; (

**d**) Contribution of acoustic radiation to the field point SF8.

**Figure 13.**The vibration acceleration and the mid-span sound field sound radiation pattern of different numbers floating-slabs at 64.4 Hz (Unit: left column—m/s

^{2}; right column—dB/L): (

**a**) Vibration acceleration cloud picture of a single floating-slab at 64.4 Hz; (

**b**) Acoustic radiation pattern of a single floating-slab at 64.4 Hz; (

**c**) Vibration acceleration cloud picture of two floating-slabs at 64.4 Hz; (

**d**) Acoustic radiation pattern of two floating-slabs at 64.4 Hz; (

**e**) Vibration acceleration cloud picture of four floating-slabs at 64.4 Hz; (

**f**) Vibration acceleration cloud picture of four floating-slabs at 64.4 Hz.

**Figure 14.**The vibration acceleration and the mid-span sound field sound radiation pattern of different numbers floating-slabs at 215.2 Hz (Unit: left column—m/s

^{2}; right column—dB/L): (

**a**) Vibration acceleration cloud picture of a single floating-slab at 215.2 Hz; (

**b**) Acoustic radiation pattern of a single floating-slab at 215.2 Hz; (

**c**) Vibration acceleration cloud picture of two floating-slabs at 215.2 Hz; (

**d**) Acoustic radiation pattern of two floating-slabs at 215.2 Hz; (

**e**) Vibration acceleration cloud picture of four floating-slabs at 215.2 Hz; (

**f**) Vibration acceleration cloud picture of four floating-slabs at 215.2 Hz.

Track Component | Unit Type | Dynamical Parameters | Value |
---|---|---|---|

Rail | Beam188 | Elastic modulus (GPa) | 210 |

Poisson ratio | 0.3 | ||

Density (kg/m^{3}) | 7830 | ||

Fastener | Combin14 | Stiffness (kN/mm) | 60 |

Damping (Ns/m) | 7500 | ||

Distance (m) | 0.625 | ||

Floating-slab | Solid45 | Slab length (m) | 6.3 |

Slab width (m) | 2.7 | ||

Slab thickness (m) | 0.25 | ||

Elastic modulus (GPa) | 40 | ||

Poisson ratio | 0.167 | ||

Density (kg/m^{3}) | 2500 | ||

Steel-spring | Combin14 | Stiffness (kN/mm) | 2.0 |

Damping (Ns/m) | 25000 | ||

Distance (m) | 0.625 | ||

Bridge | Shell63 | Elastic modulus (GPa) | 38 |

Poisson ratio | 0.2 | ||

Density (kg/m^{3}) | 2500 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, X.; Zhang, X.; Xu, J.; Yang, L.; Song, G.
Acoustic Radiation Prediction Model Rationality and Mechanism of Steel-Spring Floating-Slab Tracks on Bridges. *Appl. Sci.* **2023**, *13*, 11073.
https://doi.org/10.3390/app131911073

**AMA Style**

Zhang X, Zhang X, Xu J, Yang L, Song G.
Acoustic Radiation Prediction Model Rationality and Mechanism of Steel-Spring Floating-Slab Tracks on Bridges. *Applied Sciences*. 2023; 13(19):11073.
https://doi.org/10.3390/app131911073

**Chicago/Turabian Style**

Zhang, Xiaoyun, Xiaoan Zhang, Jiangang Xu, Li Yang, and Gao Song.
2023. "Acoustic Radiation Prediction Model Rationality and Mechanism of Steel-Spring Floating-Slab Tracks on Bridges" *Applied Sciences* 13, no. 19: 11073.
https://doi.org/10.3390/app131911073