In this study, active suspension control of the interaction between the bridge can be modeled according to the Euler-Bernoulli beam theory, and the quarter car model with three degrees of freedom is studied. The active suspension system consists of a spring, damper, and linear actuator. The active suspension control is designed using classical PID and self-tuning fuzzy PID (STFPID) to reduce the vehicle body's disruptive effects. To determine the performance of the designed controllers, two different road profiles with the bridge oscillations caused by the bridge flexibility were considered as the disruptive effect of the vehicle. When the simulation results were examined in terms of passenger seat displacement and acceleration, the proposed STFPID method significantly increased road holding and ride comfort.

This study analyzes excessive vibrations that occurred on the railway vehicle bogie with the computer simulation of a 4-DOF half car railway bogie dynamic physical model and Euler-Bernoulli flexible bridge beam with the simply supported boundary conditions has been introduced considering some limitations which affect problem formulation. To reduce these excessive vibrations other than conventional suspension systems such as passive one, an active suspension system has been designed and attached to the primary suspension system of the railway bogie car. Then, to control these active suspension systems, a control algorithm based on PID and SMC is considered. The coupled equation of motion of the railway bogie car and flexible Euler-Bernoulli bridge beam is obtained by Hamilton's principle in the time domain with the active suspension system. Finally, to demonstrate the effect of the active suspension system with the PID and SMC algorithm upon these excessive vibrations, a computer simulation has been implemented, and the results are presented comparatively. Consequently, the maximum railway vehicle bogie vertical displacement and vertical acceleration have been significantly reduced.

In this study, the parameters affecting the dynamic behavior of flexible structures under the influence of multiple vehicle passages are examined in detail. The flexible structure considered in the study is considered as a bridge girder with simple supported boundary conditions which modelled according to Euler-Bernoulli thin beam theory. The equations of motion of the bridge beam in contact with the vehicle passing over the bridge were obtained by using the Lagrange equation after the kinetic and potential energies of the system were obtained. The second-order differential equations representing the motion of the system are transformed from the first-order state space matrix representation to the first-order state using the state variables specified in the study. The system of differential equations is then solved with high accuracy using a special program prepared in the MATLAB commercial software using the Runge-Kutta algorithm from the fourth degree in the time domain.

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