Dynamic Bending of a Beam

Abstract

The article discusses problems of dynamic bending for beams of semi-infinite length. To solve such problems, the article uses a method based on the implementation of the conservation laws, namely, the law of energy conservation, the law of change in momentum and the law of change in angular momentum. The results obtained are compared with the analytical solution for the problem of a semi-infinite beam motion loaded at the free end with a transverse force. The peculiarity of this solution is that the change in the stress-strain state of the rod is characterized by a wave front. It is considered that all changes in the state of the beam occur at an infinite speed. All designed solutions are characterized by the presence of a wave front in the beam. It is shown that, in contrast to the transfer of longitudinal disturbances along the length of the beam, which occur at a constant speed, bending disturbances propagate at a variable speed, and, with increasing time, this speed decreases and tends to zero at an infinitely distant point of the beam. It was discovered that the propagation velocity of the wave front during the transfer of concentrated force and concentrated moment differs from each other. In this case, the speed of transverse force transfer is almost twice as high as the speed of the wave front from the bending moment.