Vibrations of finite beams on nonlinear Kelvin–Voight foundations subjected to a traveling mass

With the development of high-speed trains, the interest in studying the possibility of resonance in rail and railroad vehicles has increased. In this paper, an Euler–Bernoulli beam model rested on a nonlinear Kelvin–Voight viscoelastic foundation is used to investigate the vibration of the system due to a moving mass. The Galerkin method is used to discretize the solutions of the non-linear partial differential equations of motion to the time and position functions. The method of multiple scales is then used to obtain the frequency of the system's responses. The steady-state responses of the primary, sub, and superharmonic resonances are then obtained. The effects of different parameters, such as moving mass suspension characteristics, the foundation's nonlinearity and damping coefficients, and rail roughness on the system response, are examined. As a case study, a conventional railroad track is used for dynamic simulation, and the jump phenomenon in the response is detected for all superharmonic resonances. The results show that the backbone curve is not observed for the superharmonic resonance cases. Additionally, for the subharmonic resonance cases, the steady-state amplitude of the frequency response decreases by increasing the nonlinear stiffness coefficient.

کلیدواژه ها:

Travelling mass ، Kelvin–Voight foundation ، Nonlinear vibration ، Multiple Scales Method ، Jump Phenomenon