Computational fluid dynamics (CFD) and the finite element method (FEM) are used to investigate the wind-driven dynamic response of cantilever traffic signal support structures as a whole. By building a finite element model with the same scale as the actual structure and performing modal analysis, a preliminary understanding of the dynamic properties of the structure is obtained. Based on the two-way fluid-structure coupling calculation method, the wind vibration response of the structure under different incoming flow conditions is calculated, and the vibration characteristics of the structure are analyzed through the displacement time course data of the structure in the cross-wind direction and along-wind direction. The results show that the maximum response of the structure increases gradually with the increase of wind speed under 90° wind direction angle, showing a vibration dispersion state, and the vibration response characteristics are following the vibration phenomenon of galloping; under 270° wind direction angle, the maximum displacement response of the structure occurs at the lower wind speed of 5 and 6 m/s, and the vibration generated by the structure is vortex vibration at this time; the displacement response of the structure in along-wind direction increases with the increase of wind speed. The along-wind displacement response of the structure will increase with increasing wind speed, and the effective wind area and shape characteristics of the structure will also affect the vibration response of the structure.

With the rapid development of road construction, the development of various supporting facilities on the road has also entered a rapid development stage simultaneously. As the main support structure of the light pole, its reliability directly affects the traffic safety of the road. Cantilever traffic signals are a class of cantilevered flexible structures because their length and thickness are relatively large, so wind loads are particularly sensitive. Many scholars have started to study such structures because the dynamic effect of wind load has a continuous effect during the service life of the structure. Hong et al. [

Currently, the research methods for cantilever traffic signal structures are mainly based on field measurements and wind tunnel tests. Ding et al. [

Numerical simulation technology, as a means of experimental research in the computer age, is now receiving increasing attention and research. In many engineering fields, numerical simulation technology has been more widely used due to its advantages, such as high efficiency and accuracy. In high-rise buildings, Zhang et al. [

The purpose of this paper is to evaluate the wind vibration response of a cantilever traffic signal structure in a city using numerical simulation techniques. The validity of the structural modeling is demonstrated by establishing a numerical model of equal scale with the actual model and undergoing modal analysis and by comparing the modal analysis results with the actual structure. Then, a turbulence model close to the actual wind field is established, and finally, the structural response of the cantilevered traffic signal structure is analyzed in the cross-wind and along-wind directions based on the two-way fluid-solid coupling method.

The cantilever traffic signal structure is geometrically modeled according to a field structure, and the model dimensions are shown in ^{3}, elastic modulus ^{11} Pa, Poisson's ratio

Pole parts | Length | Top diameter | Bottom diameter | The thickness of pole |
---|---|---|---|---|

Vertical pole | 6000 | 300 | 370 | 9.5 |

Cantilever pole | 13400 | 130 | 290 | 6 |

Components | Three-headed signal light | Five-headed signal light |
---|---|---|

Mass | 18.98 | 30.23 |

The direction of the incoming wind load on the structure is shown in

In structural dynamics analysis, solving the dynamic response of a structure needs to be done based on the dynamic equilibrium equations of the mass system in the structure. When the engineering structure can be discretized as a constant, linear multi-degree-of-freedom system, the dynamic equilibrium equation of the structure can be expressed as

The modal analysis of this cantilever signal structure was carried out, and the first three orders of vibration patterns of the signal structure were obtained by using the Lanczos method with full restraint on the base of the signal riser without applying pre-stress, as shown in

Modal | Mode 1 | Mode 2 | Mode 3 | |||
---|---|---|---|---|---|---|

X | Y | Y | X | Y | X | |

Frequency/Hz | 1.094 | 1.137 | 4.382 | 4.595 | 6.614 | 7.728 |

Period/s | 0.91 | 0.879 | 0.228 | 0.217 | 0.151 | 0.129 |

The structure exhibits pendulum vibrations in the X and Y directions under the first-order vibration pattern, where the largest displacements all occur at the top of the cantilever end. When the wind speed direction approaches the structure from the leeward side of the signal light, the top of the cantilever pole of the structure will produce a larger displacement response. In the second-order vibration mode, the structure first vibrates in the Y-direction at a lower frequency,then X-direction vibration occurs, and the vibration shows that the middle of the cantilever and the top of the cantilever will produce a larger displacement response. In the third-order vibration mode, the Y-directional vibration mode shows that the top of the cantilever bends in the positive direction of Y, and the middle of the cantilever bends in the negative direction of Y. The X-directional vibration mode shows that the top of the cantilever and the top of the column bends in the positive direction of X, and the middle of the cantilever bends in the negative direction of X. The first three orders of the structure are shown in

First-order vibration type | Simulated fundamental frequency in the present study (Hz) ( |
Measured fundamental frequency in reference [ |
Relative error (%)|( |
---|---|---|---|

X-directional | 1.094 | 0.89/- | 18.6/- |

Y-directional | 1.137 | 0.98/1.181 | 13.7/3.9 |

The cantilever traffic signal support structure model is from an actual structural model in a certain place, and the model of this size specification is more representative in actual engineering, so the structure is selected as the wind vibration response analysis model for this type of structure. Since data transfer is required in the process of two-way fluid-solid coupling calculation, its calculation volume will change with the complexity of the model. In this paper, the main consideration is the wind vibration response of the main structure, so the structure shape is simplified as necessary, i.e., the bolts, flanges, and stiffening ribs are removed. Describing the coupling between fluid and solid is quite complicated, mainly because fluid-solid coupling is a nonlinear process. Therefore, in practical engineering applications, when the accuracy of the structure to be calculated is high and the calculation results need to be closer to the real situation, the calculation method of two-way fluid-structure coupling can be chosen. The calculation flow of bidirectional fluid-structure coupling is shown in

In the fluid-structure coupling analysis of the structure, due to the repeated actions between the structure and the air, the flow of air will lead to the deformation of the signal light support structure, and in turn, the deformation of the structure will affect the flow of air. Therefore, the three modules Fluent, Transient Structural, and System Coupling in the Workbench platform are used to interact in the fluid-structure coupling analysis to realize the fluid-structure coupling solution of the structure to obtain the wind vibration response of the structure under the action of wind loads.

When considering the coupling effect between the cantilever traffic signal structure and the wind, the control equation is generally used as the incompressible Navier–Stokes equation. Due to the small change in the density of air, the mass conservation equation of wind can be disregarded. The conservation of the momentum equation for the fluid is expressed as

For the above Navier–Stokes equation, to achieve the turbulence effect of wind, we need to choose a suitable turbulence model when we simulate it in Fluent [

The equation of motion of the structure can be obtained using the finite element method, expressed as

Since this paper mainly discusses the vibration response of the cantilever traffic signal structure caused by wind load, less attention is given to the flow details at the near-wall surface of the structure boundary, so the Realizable k-epsilon turbulence model based on two equations is selected in this paper. The fluid domain mesh is an unstructured tetrahedral mesh with local encryption. For the boundary layer mesh, the height of the first layer near the wall is 5 mm, the boundary layer is divided into 5 layers, and the expansion growth rate of each layer is 1.2. For the non-boundary layer mesh, free diffusion division is used, and the mesh size is 0.8 m. The final number of fluid domain meshes is 2125445, and the number of nodes is 390971. The delineated grid is shown in

In Fluent software, the standard wall function is used for this turbulence model near the wall. The boundary layer is divided into laminar boundary layer and turbulent boundary layer. The laminar boundary layer is the boundary layer when the flow is closest to the wall or laminar flow, and for general turbulent flow, then both boundary layers will exist. When divided by the parameter distribution law, the boundary layer is divided into inner and outer zones, where the inner zone is divided into the viscous bottom layer, transition layer, and logarithmic law layer; the outer zone is mainly dominated by inertial forces, and its upper limit depends on the Reynolds number.

To facilitate the description of the flow in the wall region, two dimensionless parameters

The wall function method is not solved for the region where the vicious influence is more obvious (^{+} smaller region), and for the turbulence model using the wall function, the thickness of the viscous sublayer ^{+} is generally required to be between 30 and 300. For this required ^{+} value, the grid size of the near-wall surface of the structure is between 2 and 20 mm. In this paper, the first layer of the near-wall surface of the structure is divided into a grid height of 5 mm, and its ^{+} value is 60, which satisfies the ^{+} value of this turbulence model.

The inlet boundary adopts the velocity-inlet boundary condition, the outlet boundary adopts the pressure-outlet boundary condition, the upper and lower surfaces of the fluid domain are the stationary boundary and the side surfaces are the symmetry boundary. The CFD model is shown in

Boundary location | Boundary conditions |
---|---|

Inlet | |

Outlet | |

Symmetry | |

Top | |

Bottom | |

Interface | / |

The base of the signal light support structure is fully constrained, acceleration is applied to the structure in the same direction as gravity, and the acceleration magnitude is also the same as the gravity magnitude. The surface of the structure is set as a coupling surface, which will be used for data transfer with the coupling surface of the fluid in the system coupling module. The solution type is chosen as a direct solution, and the large deformation switch is chosen to be turned on because the deformation of the structure is a nonlinear geometric deformation. The solution time of the structure is kept the same as the solution time of the fluid domain, with a solution time of 20 s and a time step of 0.02 s.

In the modal analysis, the structural dynamics of the cantilevered traffic signal support structure have been verified, and the structural model has been proven to be correct. In this part of the analysis, the main consideration is the correctness of the structural model when considering the coupling action.

In computational fluid dynamics, different mesh sizes can have an impact on the accuracy of the computational results. Too large a mesh size can lead to inaccurate capture of fluid details and bias the calculation results, while too small a mesh size can make the simulation more accurate, but the number of meshes will increase as a result, leading to higher computational effort and higher computational cost. Therefore, it is especially important to choose the appropriate mesh size when performing fluid-structure coupling analysis.

There are many methods for grid convergence verification, among which the Richardson extrapolation method [

For the mesh convergence analysis of fluid-structure coupling in this paper, three sets of different numbers of fluid domain meshes were selected. The numerical calculation of the fluid-structure coupling is carried out for three different sets of fluid domain meshes, and the three calculation results are also compared and analyzed. The scale factors can be obtained by

The grid density of the whole fluid domain is changed by changing the grid size at the boundary layer, and three sets of grid schemes with densities of 96, 203, and 380 W are selected. The selected working conditions were as follows: wind angle 90° and wind speed 5 m/s.

The most favorable grid density was selected by comparing the along-wind displacement of the cantilevered traffic signal support structure at the tip of the cantilever pole under the flow field with different grid densities and comparing the along-wind response of the structure under the flow-solid coupling with the theoretical method [

Number of grids | Boundary layer grid size (mm) | Theoretical calculation value (mm) ( |
The calculated value of fluid-solid coupling (mm) ( |
Relative error (%)|( |
---|---|---|---|---|

96 W | 10 | 80.2 | 70.3 | 12.3 |

203 W | 5 | 80.2 | 77.6 | 3.2 |

380 W | 2 | 80.2 | 78.1 | 2.6 |

Note: The calculated value of fluid-solid coupling is the average value of along-wind displacement at the top of the cantilever pole of the structure.

From the data in the table, it can be seen that with the increase in the number of grids, the error of the calculated values of fluid-solid coupling and the results obtained from the theoretical calculation do not produce large changes, and the error is within the acceptable range under the conditions of fewer grids and more grids. However, since the presented method is an approximation of the theoretical calculation, it can be considered that in this example, the fluid grid selection above 100 W has satisfied the calculation requirements, and in this paper, the fluid domain grid can be selected as the second set of grid schemes for subsequent calculations.

Through the dynamic response characteristics of the structure in the modal analysis, we can obtain the position of the maximum displacement of the dynamic response of the structure that is generated at the top of the cantilever pole. Therefore, the displacement measurement points are arranged at the top of the cantilever pole of the structure, as shown in

The mean value of the transverse wind displacement response of the structure is approximately zero under different working conditions.

In the initial stage of wind load action, the displacement response of the structure is small, but with increasing time, its displacement response also gradually increases and stabilizes.

Under a wind angle of 30°, the displacement response at low wind speeds is larger than that at high wind speeds, but this law is not constant. With the gradual increase in wind speed, the cross-wind displacement response will still gradually increase.

At a 270° wind angle, the displacement response of the structure is larger, and it can be seen that the maximum value of the displacement response at 5 m/s exceeds that at a wind speed of 10 m/s.

Since more working conditions are involved, this part only briefly presents two typical wind angles and two typical wind speeds in the displacement time domain. Through the above time domain analysis, we can understand the vibration of the cantilevered traffic model light support structure in the plane.

According to the displacement time equation above, the vibration response of the structure in the frequency domain can be obtained by Fourier transforming the above time domain results in MATLAB, as shown in

To compare with the time-frequency diagram obtained by the Fourier transform, the frequency domain analysis of the displacement time course of the structure was carried out based on the continuous wavelet transform [

Through the dynamic response of the cantilever traffic signal support structure under each wind angle and each wind speed condition, we can use the response time data of the structure to evaluate and judge the wind vibration response characteristics of the structure.

As indicated in

To more clearly understand the vibration response characteristics of the cantilever signal structure under transverse winds, the standard deviations of the transverse wind displacement on the front side and back side of the cantilever signal structure are also analyzed. The standard deviations trend contours of the displacement responses of the structure under different wind angles and different wind speeds are shown in

Speed (m/s) | Wind direction angle 90° | Wind direction angle 270° | ||
---|---|---|---|---|

Maximum value (m) | Standard deviation (m) | Maximum value (m) | Standard deviation (m) | |

3 | 0.01494 | 0.003736 | 0.06079 | 0.01732 |

4 | 0.01364 | 0.002708 | 0.0381 | 0.011174 |

5 | 0.03283 | 0.009641 | 0.09707 | 0.025946 |

6 | 0.06959 | 0.020616 | 0.08872 | 0.024421 |

7 | 0.08421 | 0.025215 | 0.06743 | 0.019398 |

8 | 0.09429 | 0.028521 | 0.05655 | 0.016487 |

9 | 0.10398 | 0.031653 | 0.05431 | 0.015682 |

10 | 0.11255 | 0.034268 | 0.0529 | 0.015526 |

11 | 0.12125 | 0.036845 | 0.0605 | 0.017303 |

12 | 0.12966 | 0.039333 | 0.05767 | 0.016766 |

The mean value of the along-wind displacement response of the structure is not zero under different working conditions. Moreover, the mean value increases with increasing wind speed.

In the initial stage of wind loading, the displacement response of the structure is more violent, but with the time of loading, the displacement response gradually leveled off and stabilized and finally approached a stable value.

At a 30° wind direction angle, the maximum displacement response occurs at approximately 10 s under the low wind speed condition, but with the loading time, the displacement response gradually decreases and tends to be stable.

At a 270° wind angle, the displacement decays to a steady value state after 10 s in the full wind speed interval, but some fluctuations appear with time at lower wind speed conditions.

The vibration response of the structure in the frequency domain can be obtained by spectral analysis of the above along-wind displacement time domain results in MATLAB, as shown in

As can be seen from

The frequency-domain analysis of the displacement time range of the structure was carried out based on the continuous wavelet transform. The obtained wavelet transform time-frequency is shown in

Speed (m/s) | Wind direction angle 90° | Wind direction angle 270° | ||
---|---|---|---|---|

Maximum value (m) | Standard deviation (m) | Maximum value (m) | Standard deviation (m) | |

3 | 0.011122 | 0.002416 | 0.017547 | 0.002874 |

4 | 0.016416 | 0.003376 | 0.01211 | 0.001991 |

5 | 0.023014 | 0.004527 | 0.024164 | 0.003805 |

6 | 0.031425 | 0.005937 | 0.032509 | 0.00514 |

7 | 0.041178 | 0.007357 | 0.042282 | 0.006535 |

8 | 0.05197 | 0.008873 | 0.053123 | 0.00806 |

9 | 0.063864 | 0.010614 | 0.064813 | 0.009625 |

10 | 0.076597 | 0.012286 | 0.077295 | 0.011268 |

11 | 0.089977 | 0.01397 | 0.09066 | 0.012984 |

12 | 0.104067 | 0.015805 | 0.104565 | 0.014793 |

The overall displacement response of the cantilevered traffic signal support structure can be understood based on the cross-wind displacement and along-wind displacement time course results in

The relationship between the magnitude of along-wind displacement and crosswind displacement can be observed in

In this paper, by establishing a finite element model of equal scale with the actual structure of the cantilever traffic signal and conducting the dynamic analysis of the structure and then numerically simulating the wind vibration response of the structure based on the two-way fluid-solid coupling method, the following conclusions are mainly obtained by analyzing the vibration characteristics of the structure in the cross-wind direction and along-wind direction when subjected to wind loads.

Through the modal analysis of the cantilever traffic signal support structure, the self-vibration frequency and vibration type of the model established in this paper are obtained. The inherent frequency of the structure in the modal analysis is compared with the actual field measurement results of the structure in the literature, and the error is within the acceptable range, which shows the validity of the modeling. In the modal analysis, it can be observed that the maximum response position of the structure occurs at the top of the cantilever pole for each order of vibration mode. Therefore, in the wind vibration response analysis of the structure, the response at this location can be recorded to determine the vibration mode and the vibration degree of the structure under the wind load.

The analysis of the dynamic response time data of the cantilever traffic signal support structure under different wind angle and wind speed conditions shows that the structure produces a larger cross-wind vibration response under wind angles of 90° and 270°. This is because the structure plane is perpendicular to the direction of wind flow when the effective wind area of the structure is the largest. Under the 90° wind angle, the maximum response of the structure gradually increases with increasing wind speed, showing a vibration dispersion state. From 6 m/s, the increase in the displacement response of the structure is approximately linear. According to the vibrationeq response characteristics under the wind angle, the response follows the vibration phenomenon of galloping. Under a wind angle of 270°, the maximum displacement response of the structure occurs at wind speeds of 5 and 6 m/s over the whole wind speed range. Based on the nature of the vibration response, it can be judged that the vibration generated by the structure at a wind speed of 5 m/s at a wind angle of 270° is vortex-excited vibration.

In general, the along-wind displacement response of the cantilever traffic signal structure increases with increasing wind speed. Due to the different effective wind areas of the structure, the size of its displacement response also has some differences. When the effective wind area of the structure is the same, the shape characteristics of the structure will also have some influence on the vibration response of the structure.

The wind vibration displacement of the cantilever traffic signal structure studied in this paper is similar to the vibration of the structure seen in actual engineering. The vibration mechanism of the structure obtained in this paper can provide a reference solution for the design optimization of the actual structure to design a safer structure with a longer service life.