Numerical Analysis Of Vehicle-bridge Coupled Vibration Based On MATLAB

As China's road and bridge construction industry becomes more prosperous,the vehicle's speed and load capacity increase significantly,and the quality of the bridge structure itself is gradually reduced,the stiffness is softer,and the span is greater.In this context,the problem of vehicle-bridge coupling vibration of highway bridges will be more severe.Accurately analyzing vehicle-bridge coupling vibrations has become an urgent and thorny issue.In this paper,based on the basic theory of vehicle-bridge coupled vibration,the differential equation of vehicle-bridge coupled system is obtained.Using the mode decomposition method to transform the system differential equation into a matrix form,The second-order development function based on the built-in function of matlab was written by the principle of Runge-Kutta method,and the second-order time-varying differential equation group was solved.Main contents and conclusions are as follows:(1)In this paper,the quadratic development function based on the built-in function is written using the solving principle of Runge-Kutta method.In this algorithm,the second derivative of the degree of freedom cannot appear in the load matrix.In this paper,the degree of freedom of the load matrix is divided by the block matrix.The derivative is expressed so that the second derivative of the degree of freedom in the load matrix is avoided.The secondary development function used in this paper has the advantages of fast solution speed and easy programming.(2)Aiming at the different driving speeds of the vehicle,the coupling model of the vehicle and bridge under the effect of a quarter vehicle model is analyzed,and the dynamic displacement,dynamic shearing force,dynamic bending moment,dynamic displacement and dynamic shear of the bridge are discussed.The law of force and dynamic bending moments.At the same time,three common uniaxial vehicle models and two common two-axle vehicle models were compared and analyzed respectively,and the dynamic response of the bridge under different vehicle models was studied.(3)Taking into account the geometric nonlinear effects of the bridge,on this basis,the dynamic effects of vehicle speed,axle quality,automobile spring stiffness,bridge damping,and bridge span on vehicles and bridges are discussed.At the same time,the effect of vehicle speed on the dynamic response of the bridge is considered when the wheel acceleration is not simplified.(4)The balance equation of the vehicle-bridge system is established when the moving mass and the quarter-vehicle model are used for uniform speed motion,and the influence of velocity and acceleration on the dynamic response of the bridge is analyzed.At the same time,the natural frequency of the axle system is obtained by the eigenvalue calculation method,and the influence of position ratio and mass ratio on the natural frequency of the axle system is discussed.The natural frequency of the bridge and the natural frequency of the axle system are compared.