Nonlinear investigation of the possibility to exceed the critical speed by a load on a string

摘要

The paper is devoted to the investigation of a possibility of overcoming the critical speed by a moving concentrated load on a string. It is known that exceeding the critical speed is impossible in the framework of the linear statement for this problem. The general geometrically nonlinear statement for the problem is suggested. It allows one to take into account the coupling between transversal and longitudinal waves and the contact friction between the string and the load. It is shown that solutions corresponding to the case in which the load tries to overcome the critical speed are essentially nonlinear. The conception of critical speed for the case of nonlinear waveguide is discussed. It is shown that overcoming the critical speed is impossible in the system without friction. The speed of the load can reach and exceed the value of the critical speed for an unstrained string, but the solution remains subcritical. The case of decelerating load is also considered. Taking into account the contact friction between the string and the load explains that exceeding the critical speed can be possible. The nature of the wave resistance force exerting on the load from the string is discussed.