Nonlinear vibrations of the Euler-Bernoulli beam subject to transversal load and impact actions

  • J. Awrejcewicz
  • O.A. Saltykova
  • Yu.B. Chebotyrevskiy
  • V.A. Krysko


In this work vibrations of a flexible nonlinear Euler-Bernoulli-type beam, driven by a dynamic load and with various boundary conditions at its edge, including an impact, are studied. The governing equations include damping terms, with damping coefficients $\epsilon_1,\epsilon_2$ associated with velocities of the vertical deflection $w$ and horizontal displacement $u$, respectively. Damping coefficients $\epsilon_1,\epsilon_2$ and transversal loads $q_0$ and $\omega_p$ serve as the control parameters in the problem. The continuous problem is reduced to a finite-dimensional one by applying finite differences with respect to the spatial coordinates, and is solved via the fourth-order Runge-Kutta method. This approach enables the identification of damping coefficients, as well as the investigations of elastic waves generated by the impact of rigid mass moving at constant velocity $V$.