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 to difference equations