The Finite Beam With a Moving Load

[+] Author and Article Information
C. R. Steele

Lockheed Aerospace Sciences Laboratory, Palo Alto, Calif.

J. Appl. Mech 34(1), 111-118 (Mar 01, 1967) (8 pages) doi:10.1115/1.3607609 History: Received December 30, 1965; Revised June 27, 1966; Online September 14, 2011


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.

Copyright © 1967 by ASME
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