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 $V$.
|37N05||Dynamical systems in classical and celestial mechanics|
|37N15||Dynamical systems in solid mechanics|
|39A14||Partial difference equations|
|39A22||Growth, boundedness, comparison of solutions (difference equations)|