Journal of Theoretical and Applied Vibration and Acoustics

Journal of Theoretical and Applied Vibration and Acoustics

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

Document Type : Research Article

Authors
Ghasem Zolfaghari 1
Mohammad Mahdi Jalili 2
1 M.Sc. Student, Department of Mechanical Engineering, Yazd University, Yazd, IRAN
2 Associate Professor, Department of Mechanical Engineering, Yazd University, Yazd, IRAN
10.22064/tava.2024.2013047.1230
Abstract
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.

Highlights

  • A beam on a nonlinear Kelvin–Voight foundation excited by moving mass is modelled.
  • Vibration analysis of the system due to rail irregularities is considered.
  • MMS perturbation method is applied to obtain system nonlinear response.
  • Steady-state responses of the main, as well as sub- and super-harmonics are obtained.
  • Jump phenomenon is found occurring only in the frequency response of super-harmonics.

Keywords
Travelling mass
Kelvin–Voight foundation
Nonlinear vibration
Multiple scales method
Jump phenomenon
Subjects
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Journal of Theoretical and Applied Vibration and Acoustics
Volume 9, Issue 1 - Serial Number 1
January 2023
Pages 29-59