Road Vehicle‐Bridge Interaction considering Varied Vehicle Speed Based on Convenient Combination of Simulink and ANSYS

Abstract

In order to cover the complexity of coding and extend the generality on the road vehicle-bridge iteration, a process to solve vehiclebridge interaction considering varied vehicle speed based on a convenient combination of Matlab Simulink and ANSYS is presented. In this way, the road vehicle is modeled in state space and the corresponding motion equations are solved using Simulink. The finite element model for the bridge is established and solved using ANSYS. The so-called inter-history iteration method is adopted to realize the interaction between the vehicle model and the bridge model. Different from typical method of road vehicle-bridge interaction in the vertical direction, a detailed longitudinal force model is set up to take into account the effects of varied vehicle speed. In the force model, acceleration and braking of the road vehicle are treated differently according to their mechanical nature. In the case studies based on a simply supported beam, the dynamic performance of the road vehicle and the bridge under varied vehicle speeds is calculated and discussed. The vertical acceleration characteristics of the midpoint of beam under varied vehicle speed can be grouped into two periods. The first one is affected by the load transform between the wheels, and the other one depends on the speed amplitude. Sudden change of the vertical acceleration of the beam and the longitudinal reaction force are observed as the wheels move on or off the bridge, and the bridge performs different dynamic responses during acceleration and braking.

Dynamic amplification factor of multi-span simply supported beam bridge under traffic flow

“…2-axle, 3-axle, 4-axle, 5-axle, and 6-axle vehicles are presented as the oscillatory dynamic systems with 7, 9, 11, 13, and 15 DoFs, respectively. The simplified models of the 2-axle vehicle are shown in Figure 6 Based on the D'Alembert principle, the differential equations of motion for the 2-axle vehicle model can be presented by the following equations (11–14) (Yu et al, 2018). The vertical motion of the vehicle body for the 2-axle vehicleThe pitching motion of the vehicle body for the 2-axle vehicleThe rolling motion of the vehicle body for the 2-axle vehicleThe vertical motion of the wheel for the 2-axle vehiclewhere m b is the mass of the vehicle body; m wi ( i = 1,2,3,4) is the mass of the i -th wheel; a x is the heading acceleration of the vehicle, which can consider the acceleration or deceleration of the vehicles under the control of the drivers; Ix, Iy are the mass moment of inertia of the vehicle body around the x,y axes, respectively; ks2i,kt2i(i=1,2,3,4) is the vertical stiffness of the i -th suspension spring and tire of the two-axle vehicle; Cs2i,Ct2i(i=1,2,3,4) is the vertical damping coefficient of the i -th suspension spring and tire of the two-axle vehicle; a,b is the distance between the vehicle’s mass center and the front and rear axles, respectively; t w is the transverse distance between the coaxial tire and the mass center; h is the vertical distance between the vehicle’s mass center and each wheel; I y , I x is the angular displacement of the vehicle body around the y and x axes, respectively; Z b is the vertical displacement of the vehicle body; zwi(i=1,2,3,4) is the vertical displacement of the i -th wheel; Z gi (i=1,2,3,4) is the road surface height of the i -th tire contact position (sum of surface roughness height and vertical response of bridge; …”

“…The transient displacement responses of the bridge nodes are extracted as the moving boundary of the vehicles. The whole process iterative method is used for the iterative solution as illustrated in Yu et al (2018). In order to verify the dynamic solution program, a verification model is considered for a 3-axle truck passing a single span simply supported beam as in Cai et al (2007).…”

“…2-axle, 3-axle, 4-axle, 5-axle, and 6-axle vehicles are presented as the oscillatory dynamic systems with 7, 9, 11, 13, and 15 DoFs, respectively. The simplified models of the 2axle vehicle are shown in Figure 6 Based on the D'Alembert principle, the differential equations of motion for the 2-axle vehicle model can be presented by the following equations (11-14) (Yu et al, 2018). The vertical motion of the vehicle body for the 2-axle vehicle…”

Dynamic analysis of high-speed maglev train–bridge system with fuzzy proportional–integral–derivative control

“…Meanwhile, the electromagnetic force of different magnetic suspension block at different time step is applied in the bridge model established by ANSYS in the form of concentrated force to calculate the dynamic response of the bridge. 24 Repeat the calculation until the difference in the electromagnetic force between two calculation results does not exceed the limit value, then it could be considered that the results converged.…”

Dynamic response of simple bridge due to moving vehicles in both along opposite directions

“…Especially, dynamic response of the structural bridge considered as beam subjected to moving vehicles has been attracted many researchers in during past decades. In this problem, the moving loads are considered as moving concentrate forces, moving masses or moving vehicles which move on the surface of the structure in the only direction from the left end to right end, presented in many previous types of research (Neves et al, 2012;Michaltsos, 2002;Wu and Chiang, 2004;Jun et al, 2010;Zhang et al, 2013;Reis and Pala, 2009;Yang and Yau, 1997;Yueqin and Wei, 2005;Yue et al, 2005;Ye et al, 2010;Yin et al, 2010;Yang et al, 2004;Yan et al, 2013;Sun and Zhang, 2014;Vaidya and Chatterjee, 2017;Yu et al, 2018;An et al, 2016;Pham et al, 2018;Hoang et al, 2019). But, in reality, the vehicles can completely move in the both along the opposite directions which were overlooked in most previous works rated to analyze the bridge-vehicle dynamic response.…”