Nonlinear Analysis Of Vehicle-Bridge Coupling Vibration Of Continuous Beam Bridge With Variable Section

With the economic development and the advancement of the automobile industry,the impact of vehicles on the bridge structure has increased dramatically.With regard to the study of vehicle-bridge coupling vibration of continuous beam bridges,due to the limitations of methods and means,previous scholars have neglected the influence of variable cross-section on the coupling of axles and simplified the form into.However,the variable cross-section continuous beam bridge has been widely used in highway and railway bridges.It is obviously doubtful to use the equal cross-section beam bridge to conduct the research on the vehicle-bridge coupling vibration.In the study of vehicle-bridge coupling,the nonlinearity of the vehicle suspension is less considered,and less research is considered on the geometric nonlinearity of the variable cross-section bridge.Firstly,the variable cross-section continuous beam bridge is segmented,and the optimized semi-analytic method is proposed to solve the vibration mode function of the variable cross-section continuous beam bridge.Write the complex Simpson algorithm to solve the equivalent moment of inertia of each beam segment.The relationship between the displacement,the corner,the bending moment and the shear force between the beam sections at the mid-span,the support and the boundary is analyzed,and the relationship matrix of the to-be-determined coefficients of the adjacent beam sections is established.The iterative method is used to solve the total relationship matrix,and the mode shape function of the variable cross-section continuous beam bridge is obtained.Then based on the Euler–Bernoulli beam,the vibration equilibrium equation of the variable cross-section continuous beam bridge considering the geometric nonlinearity of the bridge is deduced,and the mode decomposition method are used to simplify the equilibrium equation.Taking the main and auxiliary suspensions of the vehicle into consideration in the 1/4 vehicle model,a 1/4 vehicle vibration equation considering the nonlinearity of the vehicle suspension is established;Combined with the bridge vibration balance equation and the vehicle vibration equation,the coupling equation of the variable cross-section continuous beam bridge considering the vehicle suspension nonlinearity and the bridge geometric nonlinearity is obtained.According to the Runge-Kutta method,the coupled vibration response of the axle at any position of the variable beam bridge can be solved.Based on the nonlinear vehicle-bridge coupling equation of variable-section continuous beam bridges,the three-span variable-section continuous beam bridge is taken as an example to analyze the vibration response of equivalent isometric beam bridges and variable-section beam bridges coupled with vehicles.And the effects of vehicle suspension nonlinearity and bridge geometric nonlinearity on coupled vibration of a variable cross section continuous girder bridge are studied.The results show: Vertical displacement of midpoints of each span curves of equivalent equal-section beam bridges and variable-section beam bridges are very similar,and the trend is similar.But the vertical displacement values are different,the vertical displacement of the variable section beam bridge is significantly larger than the equivalent beam bridge;The displacement curve considering the nonlinearity of the vehicle suspension is reduced in the mid-span of the variable-section bridge;Considering the geometric nonlinearity of the bridge will reduce the mid-span vertical displacement of the variable-section beam bridge to a certain extent,but the effect is very limited.