Freely propagating waves in a supported nonlinear elastic beam (Q2724679)

The title problem is investigated for an elastic beam of finite length supported on a flat inelastic surface and subjected to gravitational force and to compressive longitudinal loads. Using the general form of Lagrangian depending on horizontal and vertical displacements, the author derives nonlinear equations of motion. If one retains only the quadratic part of potential energy, one obtains a system of linear equations. In this case the author proves the existence of freely propagating inertial waves in the beam. Moreover, one can get in this case a closed solution. Next, the potential energy is completed by a quartic term which leads to a system of nonlinear equations. Some numerical experiments allow to gain insight into the solution behavior in this nonlinear case; in particular, the author obtains the time evolution of the beam profile.NEWLINENEWLINEFor the entire collection see [Zbl 0959.00041].