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Abstract

For river crossing bridges, the vehicle-induced vibration can be transmitted to the bridge tower and foundation system. This vibration induced low frequency underwater noise radiation can cause great harm to aquatic organisms. A river crossing suspension bridge was selected to study the sound contribution and spatial distribution of the underwater noise. A bridge-sediment coupling finite element model was developed, and the vehicle-bridge-sediment interaction analysis was conducted to investigate the dynamic response of the coupling system. An acoustic finite element model was built to predict the underwater noise radiated from the tower and sediment, and the noise contribution of these two sound sources was compared. The research shows that the noise radiated from the bridge tower and the sediment is below 6.3 Hz, and the peak frequency is around 3.15 Hz. The noise radiated from bridge tower only has a larger contribution to the total noise level in its vicinity than the sediment, especially around the water surface. In other space, the noise generated through the sediment vibration plays a dominant role in the total noise. The radiated noise from the tower has lateral directivity, and the directivity of the sediment radiation is similar to the point sound source.

Keywords

Suspension bridge vehicle-induced vibration underwater noise sound contribution noise characteristics

Introduction

With the rapid growth of vehicle traffic in China, plenty of underwater tunnels and cross-river bridges have been constructed to decrease traffic congestion. However, when vehicles pass through cross-river bridges, the vehicle-induced vibration of the bridge deck can be transmitted to the bridge tower and foundation system, resulting in low frequency underwater noise radiation from both the tower and sediment.

The low frequency underwater noise radiated from river crossing structures induced by vehicles may be harmful to aquatic species, especially for endangered species such as Yangtze finless porpoise. On the one hand, many aquatic organisms have strong echolocation ability, and they rely on sonar for the communication between groups and the perception of the external environment. The underwater noise radiated from river crossing structures can interfere with the transmission and reception of the sonar signals of these organisms, thus affecting their perception of the external environment and the communication between the populations, and reducing their predation efficiency.^1–3 On the other hand, the excessive underwater noise such as pile driving noise⁴ can directly cause physical damage to the hearing sensitive aquatic organisms, especially for the newborn larvae.^5,6 In addition to directly interfering with and affecting the survival and reproduction of rare aquatic organisms, underwater noise can also endanger other related underwater species, destroy the diversity of the water area, and further deteriorate the associated ecological environment.^7,8 In order to evaluate the impact of underwater noise radiation on aquatic animals, the audiograms of some aquatic organisms were collected and compared with the measured underwater noise.^9–11 Due to the slow attenuation characteristics of low frequency noise radiated from river crossing structures, its influence range is larger than high-frequency noise. Thus, it is necessary to study the radiation mechanism and characteristics of such a low-frequency noise.

The influence of underwater noise caused by ships^12,13 and offshore wind farms on aquatic organisms¹⁴ have been studied in depth. From 2013 to 2017, dolphin's hearing sensitivity, hearing threshold, exposure sound pressure level limit standard and weight were systematically studied.^15–18 It was found that the pile driving noise can affect the vocal behavior of dolphins, hinder the migration of dolphins, and cause damage to their reproduction and hearing.^19–21 In order to evaluate the impact of underwater noise induced by construction on marine ecosystem, the pile driving noise¹⁴ during the construction of offshore wind farms was measured, and its spatial distribution under water was also investigated. However, the impact of underwater noise induced by vehicle vibration on aquatic species has been rarely studied. To investigate the influence of hydro-acoustic noise radiation on aquatic biodiversity, a field test²² was conducted to obtain the dynamic responses of an underwater tunnel structure during vehicle passing-by, and the underwater noise was also recorded. To the best knowledge of the authors, no research has been reported on the mechanism of underwater noise radiation of bridge structures.

In the past decades, a lot of research has been conducted to investigate the influence of vibration²³ and structure-borne noise radiation^24,25 from viaducts on human beings in the air. Analytical method^26,27 has been proposed to predict the noise radiation of simple structures. In order to improve simulation accuracy, finite element method (FEM) and boundary element method (BEM) are widely used to predict the noise radiation of complex structures in low to medium frequency range.²⁸ A finite element model of wheel rail sound barrier was developed, and BEM was used to evaluate the near rail noise characteristics and the acoustic performance of the sound barrier.²⁸ The finite element boundary element (FE-BEM) model of a U-shaped concrete subway girder was established, and the structural vibration and noise of the bridge was predicted by using the frequency domain method.²⁹ For high-frequency vibration and noise simulation, statistical energy analysis (SEA) method can be more efficient than FEM and BEM, especially for structures with high modal densities,³⁰ such as steel bridges, with the maximum frequency of interest of over 1000 Hz. More and more hybrid methods are applied to predict wide band range noise radiation of composite bridges. Based on the hybrid method of FEM-SEA, the noise characteristics of a steel-concrete composite bridge during train passing-by was analyzed,³¹ and the effectiveness of the method was verified by field measurements. In order to improve the computational efficiency of 3D bridge structures with large degrees of freedom, 2-D method,³² 2.5-D method³³ and fast multipole boundary element algorithm³⁴ have been used in noise simulations. Recently, the intensity characteristics of the near-field aerodynamic noise source of the train and the spatial distribution characteristics of the far-field aerodynamic noise around the bridge was studied,³⁵ based on the broadband noise sources method and acoustic analogy theory. The abovementioned research paid close attention to noise radiation of bridge structures in the air. For underwater noise radiation, most existing research focused on the sound pressure generated from ships,³⁶ marine propellers,³⁷ piling and tunnels. For ship structures, FEM, BEM, and SEA were combined to simulate the full band underwater noise radiation.³⁸ Based on a three-dimensional finite element model, the underwater noise radiation of a tunnel in the Yangtze River was simulated and compared with the measured results.²² However, the research on underwater noise of bridge structures is still deficient. It should be noted that the noise radiation of the elevated bridge is mainly induced by the vibration of the girder itself, while for cross-river bridges, the tower and foundation sediment are two major sound sources. The propagation mechanism and sound contribution of these two sound sources are still unclear.

In this study, a river crossing long-span suspension bridge was selected to investigate the low-frequency underwater noise characteristics and radiation mechanism of the bridge-sediment system. A bridge-sediment coupling finite element model was developed to calculate the natural frequencies and mode shapes of the system. Then, the dynamic response of the tower-sediment coupling system was obtained by using the vehicle-bridge interaction analysis. Finally, an acoustic finite element model was established and the underwater noise was predicted based on the modal acoustic transfer vector (MATV) method. The spatial distribution and noise contribution of both the tower and foundation sediment was analyzed.

Vehicle-induced structural vibration

The design plan of a three-tower four-span suspension bridge in Nanjing across Yangtze River was chosen in this study to investigate the associated radiation mechanism and characteristics of underwater noise induced by passing vehicles. The main tower is made of C50 reinforced concrete, and the heights of the three towers from south to north are 228.8 m, 205 m, and 192 m, respectively. Q420 low alloy high strength steel is selected for the stiffening beam, and the specific structure dimension is shown in Figure 1(a). The span arrangement is 460 m+1360 m+1420 m+520 m, and the elevation is shown in Figure 1(b).

Figure 1.

Layout of the bridge (unit: cm): (a) section of stiffening beam and (b) bridge span layout elevation.

The equations of motion for the vehicle-bridge interaction analysis can be expressed as, ${\begin{cases} {\ddot{q}}_{v} + 2 ξ_{v} ω_{v} {\dot{q}}_{v} + ω_{v}^{2} q_{v} = φ_{v}^{T} f_{v} \\ {\ddot{q}}_{b} + 2 ξ_{b} ω_{b} {\dot{q}}_{b} + ω_{b}^{2} θ_{b} = φ_{b}^{T} f_{b} \end{cases}$ (1)where $q$ is the modal coordinate vector; $ξ$ is the modal damping matrix; $ω$ is the angular frequency vector; $φ$ is the mode shape matrix; $f$ is the force vector; and the subscript $v$ and $b$ represent vehicles and bridges, respectively.

The equations of motion of the vehicle-bridge coupling system can be solved to obtain the dynamic responses of the bridge tower and the sediment by using mode superposition method in the time domain. Finite element model was used to simulate the bridge subsystem. Multiple rigid body models were used to simulate the vehicle subsystem, and the first and second suspension system was modeled by spring and dashpot elements.³⁹

Four vehicle models with good mass difference and strong representation were selected in this study, including five-axle truck, two-axle truck, two-axle passenger car and two-axle car, with the weight of 70 tons, 27 tons, 6 tons, and 2 tons, respectively.

Three types of random traffic flow models were selected in the numerical simulation: (1) Free flow. The vehicle runs smoothly, with high running speed and low flow rate, and the road utilization rate is low; (2) Dense flow. The vehicle runs relatively smoothly and is in the car-following state, with high running speed, high flow, and high road utilization. (3) Congested flow. The traffic is crowded with intensive following vehicles, which corresponds to a lower running speed and higher flow.

With consideration of traffic statistics, the traffic-flow ratio, speed ratio, and vehicle spacing in each lane can be determined.²² The random traffic-flow models with three simulated conditions are shown in Figure 2.

Figure 2.

Random traffic flow: (a)free flow; (b)dense flow and (c)congested flow.

Natural vibration characteristics of the bridge-sediment structure

A three-dimensional beam element model and a hybrid finite element model were established, respectively. In the beam element model, the girder, tower, bearing platform and pile foundation were all simulated by beam elements. The main cable and hanger structures were simulated by tension only truss elements. The foundation system, including the bearing platform, piles, and sediment, were not directly simulated in the 3D beam element model. Spring elements were used to model the restraint action of the foundation. In the hybrid model, the south tower and the associated foundation system were simulated by using solid elements, and the rest of the components were simulated by beam elements and truss elements.

Considering the computer capacity and calculation accuracy comprehensively, the sediment in a certain range near the bridge tower was included in the numerical model. According to previous research, the sediment model size should meet the following conditions, namely, the minimum distance L from the vibration source to the truncated boundary should be greater than the maximum half wavelength of the medium, $L > λ_{tru} = \frac{C_{S}}{2 f_{\min}}$ (2)where $C_{S}$ is the shear wave velocity of the soil layer; and $f_{\min}$ is the minimum frequency of interest.

The shear wave velocity of the first layer of soil was 120 m/s, and the minimum analysis frequency was set as 2 Hz. Thus, and the minimum distance L was 30 m according to equation (2). Considering the actual situation of bridge soil, the soil model size (length × wide × high) was finally determined as (100 m × 60 m × 97 m). The full bridge hybrid model, main tower and sediment solid model are shown in Figures 3 and 4, with the associated parameters listed in Table 1.

Figure 3.

Full bridge hybrid model.

Figure 4.

(a) Sediment model and (b) main tower model.

Table 1.

Parameters of the hybrid model.

Element number	Model size (m)	C_s (m/s)	L (m)	f_min (Hz)
69,135	100 × 60 × 97	120	30	2

Based on the two finite element models, the natural frequencies of the bridge tower-sediment system were obtained (Table 2) and the related vibration mode diagrams of the two models are shown in Figure 5. It can be seen from Table 2 that due to the large span length of the suspension bridge, the natural frequency of the entire bridge-sediment system is very low. The first-order natural frequency is only 0.06 Hz, and the subsequent order frequencies are very close. The difference of the natural frequencies between two types of models are insignificant, and the same order mode shapes are consistent, which verifies the accuracy of the numerical model.

Table 2.

The first six order natural frequency and mode shape.

Modal order	Natural frequency (beam model)/Hz	Natural frequency (hybrid model)/Hz	Mode shape	Relative error (%)
1	0.06013	0.06001	Lateral side bending of main beam	-0.20
2	0.06464	0.06481	Lateral side bending of main beam	0.26
3	0.07421	0.07680	Vertical deflection of main beam	3.36
4	0.10044	0.09986	Vertical deflection of main beam	-0.58
5	0.10408	0.10425	Vertical deflection of main beam	0.16
6	0.11141	0.11205	Vertical deflection of main beam	0.57

Figure 5.

Mode diagram: (a) beam element model (the third stage); (b) hybrid model (the third stage); (c) beam element model (the fourth stage); and (d) hybrid model (the fourth stage).

Vehicle-induced structural vibration response

Structure-borne noise is mainly induced by the vibration in outer normal direction of the structure surface. Thus, the horizontal and longitudinal vibration response of the bridge tower and the vertical dynamic response of the sediment were mainly concerned. Two points were chosen here to show the dynamic responses of the coupling system in post-processing analysis, where No.1 was at the bridge tower node near the lower beam, and No.2 was on the sediment surface near the tower support (Figure 6).

Figure 6.

Post treatment points of the bridge.

Figure 7 shows the time history of the lateral acceleration of the bridge tower and vertical acceleration of the sediment induced by three different traffic flow models. It can be found that the dynamic response of the structure induced by the dense flow is the largest, followed by the congested flow, and the vibration generated by the free flow is the smallest. Thus, the traffic flow with higher operating speed and higher flow rate can induce larger vibrations. The dynamic response of the structure with the congested flow is relatively stable due to the closely arranged vehicles. While for the free flow model, there are multiple obvious peaks in the dynamic response of the structure, which correspond to the vibration induced by heavy vehicles. Figure 8 also shows that the amplitude of the acceleration time history of the sediment is smaller than that of the bridge tower, which illustrates the vibration energy loss during the transmission from the bridge superstructure to the foundation system.

Figure 7.

Acceleration time history: (a) free flow, tower; (b) free flow, sediment; (c) dense flow, tower; (d) dense flow, sediment; (e) congested flow, tower and (f) congested flow, sediment.

Figure 8.

Acceleration level spectrum: (a) dense flow, tower and (b) dense flow, sediment.

The one-third octave band acceleration level spectrum can be obtained by using fast Fourier transform (FFT). Figure 8 shows the acceleration spectrum of bridge tower and sediment under dense flow condition, respectively. The dynamic responses of both bridge tower and soil reach their peak values around 3 to 4 Hz, and the vibration gradually decreases after 4 Hz.

Characteristics and mechanism of underwater noise radiation

In this paper, the modal acoustic transfer vector method was used to predict the radiated sound pressure of the bridge tower and sediment, by combining the structural vibration in the time domain and the acoustic calculation in the frequency domain. ${\begin{cases} P (ω) = M A T V {(ω)}^{T} Q (ω), \\ M A T V {(ω)}^{T} = j ω A T V {(ω)}^{T} T_{n} Φ_{n}, \end{cases}$ (3)where $P (ω)$ is the sound pressure; $M A T V (ω)$ is the modal acoustic transfer vector; $Q (ω)$ is the frequency spectrum of bridge modal coordinate; $A T V (ω)$ is the acoustic transfer vector; $Φ_{n}$ is the structural mode projected to the outer normal direction of the structural surface; and $j$ is the imaginary number.

The acoustic transfer can be obtained by solving the acoustic wave equation, assuming that the acoustic medium is an ideal fluid with no viscosity and heat change. The frequency domain Helmholtz equation can be expressed as follows: $\nabla^{2} p_{f} + k^{2} p_{f} = 0$ (4) $k = \frac{ω}{c_{0}} = \frac{2 π f}{c_{0}}$ (5)where $\nabla^{2}$ is Laplacian operator; $p_{f}$ is the frequency domain sound pressure; $k$ is the wave number; $f$ is the frequency; $c_{0}$ is the sound velocity; and $ω$ is the angular frequency.

In order to investigate the noise characteristics and contribution of the tower and sediment, the associated modal acoustic transfer vectors were calculated separately. The acoustic finite element model was developed to simulate both the air above the water surface and the water above the sediment. The adaptive matched layer (AML) was used at the truncated boundary to simulate the no-reflection condition of the sound propagation. The air density and sound speed were set as 1.225 kg/m³ and 340 m/s, respectively. The water density and the associated sound speed was set as 103 kg/m³ and 1500 m/s, respectively. The grid size followed the principle that each wavelength includes at least 6 elements, with the minimum element size of 1 m. The acoustic model is shown in Figure 9.

Figure 9.

Acoustic model.

The vibration of bridge tower and sediment are two major sound sources of the underwater noise. For the bridge tower, both the upper part in the air and the lower part in the water can generate noise radiation due to the vehicle-induced vibration. To investigate the contribution of these different sound sources to the total noise level, multiple sound field points were set in the acoustic model under the water surface, and the acoustic contribution factor was calculated based on the sound pressure of the bridge tower and sediment at each field point as: $D_{c} = Re \frac{p_{c} p^{*}}{{| p |}^{2}}$ (6)where $p$ is the total sound pressure; $p^{*}$ is the conjugate complex of the total sound pressure; $p_{c}$ is the sound pressure induced by each single vibration source; and Re represents the real value of the results.

Analysis of underwater noise contribution

In order to investigate the sound contribution of the upper and lower parts of the tower, a total of 10 sound field points were arranged along the centerline of the bridge tower directly from the soil to the water surface with an interval of 1 m. The specific numbers and positions are shown in Figure 10.

Figure 10.

Site layout.

The sound pressure generated by the tower above the water surface and below the water at different field points are shown in Figure 11. The sound contribution factors of these two parts are shown in the Table 3.

Figure 11.

Spectrum curve of bridge tower above and below water surface and total sound pressure: (a) sound field point 1; (b) sound field point 4; (c) sound field point 7; and (d) sound field point 10.

Table 3.

Sound contribution factor of the bridge towers above and below the water surface.

Frequency/D_c (Hz)	Field point 1	Field point 4	Field point 7	Field point 10
Frequency/D_c (Hz)	Below/Above	Below/Above	Below/Above	Below/Above
2	0.916/0.084	0.859/0.141	0.749/0.251	0.300/0.700
3.15	1.005/-0.005	1.009/-0.009	1.031/-0.031	0.347/0.653
6.3	0.965/0.035	0.961/0.039	0.941/0.059	0.705/0.295

It can be found from Figure 11 that for field points 1, 4 and 7, the spectrum curve of the total sound pressure level almost coincides with the curve of the underwater bridge tower, showing that the underwater noise radiation of the tower is basically provided by the structure below water surface. Table 3 also verifies that the acoustic contribution factor of the bridge tower below water surface is much larger than that of the upper bridge tower. However, the contribution of sound pressure radiated from the bridge tower above water surface increases gradually with the distance away from the sediment surface. For field point 10, which is close to the water surface, the spectrum curve of the total sound pressure is in good agreement with the curve of the lower bridge tower in the low frequency band (0 Hz-1 Hz). However, the spectrum curve of the total sound pressure agrees better with that of the upper bridge tower near the peak frequency point, and the sound contribution factor of the upper bridge tower is also larger than that of the lower bridge tower. Thus, the radiation noise at the field points near water surface is mainly induced by the vibration of the bridge tower above the water surface.

In order to investigate the contribution of structure-borne noise radiated from the tower and sediment to the total noise, plane field points in the horizontal and longitudinal directions of the bridge were established in the acoustic model. The sound field points were arranged between the water surface and the sediment, and the distance between adjacent field points was 2 m. The horizontal plane field points were arranged on the two inner sides of the bridge tower, with a total of 19 columns and 5 rows (Figure 12(a)). The longitudinal plane field points were arranged close to the tower, with a total of 6 columns and 5 rows (Figure 12(b)).

Figure 12.

Plane field points: (a) horizontal plane field points and (b) longitudinal plane field points.

For the horizontal plane field points, 4 field points were chosen here to investigate the associated sound pressure spectrum (Figure 13), including No. 1, No. 5, No. 51 and No. 55. No. 1 and No. 5 are close to the tower, and No. 51 and No. 55 are far away from the tower support. The sound contribution factors of these field points are listed in Table 4.

Figure 13.

Sound pressure spectrum curve of plane field points in horizontal direction of bridge: (a) field point 1; (b) field point 5; (c) field point 51; and (d) field point 55.

Table 4.

Tower/sediment sound contribution factor.

Frequency/D_c (Hz)	Field point 1	Field point 5	Field point 51	Field point 55
Frequency/D_c (Hz)	Sediment/Tower	Sediment/Tower	Sediment/Tower	Sediment/Tower
2	0.966/0.034	0.685/0.315	0.999/0.001	0.999/0.001
3.15	0.849/0.151	0.352/0.648	0.997/0.003	0.997/0.003
6.3	0.511/0.489	0.099/0.901	0.997/0.003	0.998/0.002

It can be seen from Figure 13 that the peak frequency of sound pressure at each field point is about 3.15 Hz. For field points 1, 51 and 55, the spectrum curve of the total sound pressure is basically consistent with that of the sediment, showing that the acoustic contribution of the sediment at each frequency point is significantly larger than that of the tower. For field point 5, which is near the tower and the water surface, the sound pressure spectrum of the sediment is closer to that of the tower in the dominant frequency range. Table 4 further validates that the sound contribution factor of the tower at field point 5 is larger than that of the sediment at 3.15 Hz.

Similarly, for the longitudinal plane field points, the sound pressure spectrum curves can also be obtained, and the sound contribution factors were calculated. The associated conclusion is similar to that of horizontal plane field points. Related results are not shown here to avoid repetition.

In order to consider the influence of the total sound pressure level difference of the radiated noise between the sediment and bridge tower, the contour map of the corresponding sound pressure level difference of these two sound sources is shown in Figure 14. The origin is set at field point 1 (Figure 12), which is near the junction of tower and sediment. It can be found from Figure 14 that for underwater noise, the noise radiation from bridge tower is comparable with that of the sediment only in the space around the bridge tower and close to the water surface. When the distance away from the tower increases, the sound pressure level difference between the two major sound sources increases rapidly. When the horizontal distance away from the tower exceeds 5 m and the vertical distance exceeds 2 m, the sound pressure level difference can be over 10 dB, and the sound contribution of the tower is negligible. Thus, it can be concluded that in most of the area, the noise generated by sediment vibration is dominant for the underwater noise.

Figure 14.

Contour map of sound pressure difference between sediment and bridge tower radiated noise: (a) horizontal bridge direction and (b) longitudinal bridge direction.

Spatial distribution of underwater noise

Based on the simulated results of the plane field points in the previous section, taking the field points with the same height from the sediment (the same row) as a group of points (Figure 12), the sound pressure variation with the horizontal distance (H1 to H5, L1 to L5) is illustrated in Figure 15.

Figure 15.

Variation curve of sound pressure with horizontal distance: (a) tower, lateral distance; (b) tower, longitudinal distance; (c) sediment, lateral distance and (d) sediment, longitudinal distance.

It can be seen from Figure 15 that with the increase of the distance away from the tower, the sound pressure-distance curve of the tower shows a linear downward trend, and the slope is large. Thus, the noise radiation of the tower decays linearly, and the decay rate is relatively larger than that of the sediment. The sound pressure-distance curve of the sediment is relatively flat. With the increase of the distance from the tower, the attenuation of the radiated noise of the sediment is very slow and almost unchanged.

Taking the field points with the same distance from the tower support as a group of points, and the sound pressure level of these field points (V1 to V5) are shown in Figure 16. It can be seen from Figure 16 that with the increase of the height from the sediment, the sound pressure-distance curve induced by the bridge tower shows a slow downward trend, while the sound pressure-distance curve by the sediment decreases rapidly. This shows that with the increase of the vertical distance, the sound pressure radiated from the tower attenuates slower, and the decay rate of the noise radiated from the sediment is larger.

Figure 16.

Variation curve of sound pressure with vertical distance: (a) tower induced and (b) sediment induced.

In order to assess the impact of noise radiation caused by bridge structures on aquatic animals, audiograms of the following animals were collected: Fin whale,¹⁰ Carassius auratus,¹¹ and Gadus morrua.¹² Figure 17 shows the simulate sound pressure level and the hearing threshold curves of the related underwater species. It can be found from Figure 17 that the frequency range of audiograms of these species is greater than 10 Hz, and very limited frequency overlap can be observed between the simulated SPL and hearing threshold curves. Thus, it is difficult to evaluate the impact of ultralow frequency (less than 10Hz) noise on these organisms by only using the hearing threshold curves. Previous research has shown that infrasound source can generate near-field particle motion, which can influence the migration of European silver eels.⁴⁰ However, very few research on the effect of infrasound on various underwater organisms has been reported. Thus, more research should be conducted to investigate the influence of infrasound on the related underwater species.

Figure 17.

Simulated SPL with threshold of underwater species.

Directivity analysis of underwater noise

Arc sound field points surrounding the tower and the sediment (Figure 18) were arranged in the acoustic model to analyze the directivity of the structure-borne noise radiated from the bridge tower and sediment structure.

Figure 18.

Arc sound field point arrangement: (a) tower; (b) sediment.

The sound pressure levels of each field point shown in Figure 18(a) generated by the tower was calculated to investigate the associated noise directivity. Meanwhile, the noise radiation of the sediment at each field point shown in Figure 18(b) was simulated. The corresponding noise rose diagram at 2 Hz, 3.15 Hz, and 6 Hz is illustrated in Figure 19.

Figure 19.

Radiated noise rose diagram: (a) tower and (b) sediment.

It can be seen from Figure 19 that the radiated noise rose diagram of the bridge tower has good overall symmetry, and it is an ellipse with a short concave axis in the middle. The radiation noise of the tower is laterally directional, the noise radiation on the east and west sides of the tower branch is the largest, and the noise radiation at the centerline of the two tower branches is the smallest. The radiated noise rose diagram of sediment is a regular semi-ellipse, and the radiated noise of sediment has obvious horizontal directivity. The whole sediment can be approximately regarded as a point-like sound source located in the center, and the vibration of such points is transmitted by the tower located in the center.

Conclusion

In this study, a long-span suspension bridge spanning a river was chosen to investigate the underwater noise radiation. The bridge-sediment coupling finite element model was developed to simulate the vehicle-induced vibration. The acoustic finite element model was used to predict the noise radiation from the tower and the sediment. The sound contribution and spatial distribution of these two major sources were studied.

The vehicle-induced vibration and associated noise radiation of the suspension bridge is from 2 Hz to 6.3 Hz, with the peak frequency of 3.15 Hz. The radiated infrasound is not within the hearing threshold of most underwater creatures. The influence of particle motions induced by such infrasound should be further investigated. The contribution of the tower to the total underwater noise attenuates rapidly around the junction of the bridge tower and the water surface. The structure-borne noise from the bridge tower only plays an important role in its vicinity, especially at the water surface. For field points in other areas, the noise radiated from the sediment is dominant. The underwater noise radiation from the sediment is the major source in most of the area.

The spatial distribution of underwater radiated noise shows a trend of attenuation from the bottom of the tower to the surrounding area. The noise radiated from tower structure decays rapidly with the horizontal distance away from the tower. However, the decay rate of noise radiated from sediment in horizontal direction is much smaller. The radiated noise of the tower has lateral directivity, and the radiated noise of sediment has horizontal directivity. The sediment can be approximately regarded as a point-like sound source located in the center.

Footnotes

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 research was supported by National Natural Science Foundation of China (No. 51608116),the Natural Science Foundation of Jiangsu (No. BK20201274) and Zhishan Youth Scholar Program of SEU.

ORCID iD

Xiaodong Song

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Sound contribution of the low frequency underwater noise radiated from a suspension bridge

Abstract

Keywords

Introduction

Vehicle-induced structural vibration

Natural vibration characteristics of the bridge-sediment structure

Vehicle-induced structural vibration response

Characteristics and mechanism of underwater noise radiation

Analysis of underwater noise contribution

Spatial distribution of underwater noise

Directivity analysis of underwater noise

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References