The Timoshenko Beam with a Moving Load

摘要

The problem of a semi-infinite Timoshenko beam of an elastic foundation with a step load moving from the supported end at a constant velocity is discussed. Asymptotic solutions are obtained for all ranges of load speed. The solution is shown to approach the 'steady-state' solution, except for three speeds at which the steady state does not exist. Previous investigators have considered only the steady-state solution for the moving concentrated load and have indicated that the three speeds are 'critical.' It is shown, however, that only the lowest speed is truly critical in that the response increases with time. For the load speed equal to either the shear or bar velocity, the transients due to the end condition never attained. However, the response is shown to be bounded in time for a distributed load. Thus the nonexistence of a steady state does not necessarily indicate a critical condition. Asymptotic results have also been obtained for the beam without a foundation. (Author)