Abstract
As the suspension bridge structures become more flexible and the forms of the vehicle load become more diverse, the dynamic coupling problem of the vehicle-bridge system has become gradually prominent in long-span suspension bridges, resulting in an increase in accuracy and efficiency requirements for dynamic coupling analysis of the vehicle-bridge system. Conventional method such as finite element method (FEM) for dynamic coupling analysis of vehicle-bridge system often requires separate iteration of vehicle system and bridge system, and the contact and coupling interactions between them are used as the link for convergence inspection, which is too computationally intensive and time-consuming. In addition, the dynamic response of the vehicle-bridge coupling system obtained by FEM cannot be expressed explicitly, which is not convenient for engineering application. To overcome these drawbacks mentioned above, the backpropagation (BP) neural network technology is proposed to the dynamic coupling analysis of the vehicle-bridge system of long-span suspension bridges. Firstly, the BP neural network was used to approximate the dynamic response of the suspension bridge in the vehicle-bridge coupling system, and the complex finite element analysis results were thus explicitly displayed in the form of a mathematical analytical expression. And then the dynamic response of the suspension bridge under vehicle load was obtained by using a dynamic explicit analysis method. It is shown through a numerical example that, compared with FEM, the proposed method is much more economical to achieve reasonable accuracy when dealing with the dynamic coupling problem of the vehicle-bridge system. Finally, an engineering case involving a detailed finite element model of a long-span suspension bridge with a main span of 1688 m is presented to demonstrate the applicability and efficiency under the premise of ensuring the approximation accuracy, which indicates that the proposed method provides a new approach for dynamic coupling analysis of the vehicle-bridge system of long-span suspension bridges.
Highlights
With the development of bridge engineering in the direction of long span, lightweight, and more flexibility, as well as improvement of vehicle load forms, wheel weight, and driving speed, the dynamic interaction between vehicle and bridge has been increasingly emphasized
The BP neural network approach defined in previous sections and the finite element method for dynamic coupling analysis of vehicle-bridge system are applied to an actual suspension bridge, whose span arrangement is (658 + 1688 + 658) m, and the overall elevation is shown in Figure 5; more detailed information can be found in the literature [24]
According to the comparison results between the BP neural network approach and finite element method in Figure 10, it is shown that the results of dynamic coupling analysis of the vehicle-bridge system of long-span suspension bridge calculated based on BP neural network are in good agreement with finite element method, which indicates that the BP neural network approach exhibits a better performance in terms of accuracy and feasibility, as measured by the closeness of the exact values calculated by ANSYS software and by CPU running time comparison of the two approaches for dynamic coupling analysis of vehicle
Summary
With the development of bridge engineering in the direction of long span, lightweight, and more flexibility, as well as improvement of vehicle load forms, wheel weight, and driving speed, the dynamic interaction between vehicle and bridge has been increasingly emphasized. Li et al [5] derived both vibration equations of vehicle and bridge by using the virtual work principle and finite element method and studied the dynamic response of a single-tower self-anchored suspension bridge under different road roughness, vehicle speed, and bridge damping. Summing up the above studies, we can find that some progress pointing at the basic theory and method as well as the model sensitivity analysis of the dynamic coupling response of vehicle-bridge system has been made in decades; there are mainly two issues remaining to study. The computational workload will have a significant decrease in the precondition of meeting the accuracy requirements for actual engineering analysis when the BP neural network technology is used to approximate the bridge response under the dynamic coupling effect of the vehicle-bridge system effect, so as to obtain the explicit expression of the dynamic response and to predict the bridge dynamic response of other vehicle-bridge coupling types
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