The Finite Beam With a Moving Load

Abstract

A “method of images” series solution is obtained which converges rapidly for a simply supported, long beam with a high-velocity, moving concentrated load. Each term of the series is a Fourier integral solution for an appropriate semi-infinite beam problem. The integrals are evaluated in closed form for the beam without a foundation and have a simple asymptotic evaluation for the beam with an elastic foundation. In particular, the asymptotic results provide a solution for the “critical” load velocity, for which a “steady-state” solution does not exist, and for the limiting case of infinite load velocity, for which the beam is given an initial uniform lateral velocity.