Flexural vibrations of a moving rod

The problem of the transverse natural vibrations of part of a rod between two coaxially fixed guides, moving with an arbitrary constant velocity, is investigated. The conditions of rigid clamping are taken as the boundary conditions. Additional shear stresses, due to longitudinal tension or compression are taken into account. Relations defining the natural frequencies and forms are constructed in an exact formulation by Fourier method. The dependence of the natural frequencies and forms of the lowest vibration modes on the rate of displacement, unknown in the literature, are constructed, and their features are established. A modelling and animation of unusual wave motions of the rod are presented. The main characteristics for the higher vibration modes are constructed.