## Nonlinear vibrations of the Euler-Bernoulli beam subjected to transversal load and impact actions.(English)Zbl 1229.37103

Summary: 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 $$\varepsilon_1,\varepsilon_2$$ associated with velocities of the vertical deflection wand horizontal displacement $$u$$, respectively. Damping coefficients $$\varepsilon_1,\varepsilon_2$$ 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 $$V$$.

### MSC:

 37N05 Dynamical systems in classical and celestial mechanics 37N15 Dynamical systems in solid mechanics 39A14 Partial difference equations 39A22 Growth, boundedness, comparison of solutions to difference equations