The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.
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July 1996
Research Papers
The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response
S. F. Felszeghy
S. F. Felszeghy
Department of Mechanical Engineering, California State University, Los Angeles, Los Angeles, CA 90032-8153
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S. F. Felszeghy
Department of Mechanical Engineering, California State University, Los Angeles, Los Angeles, CA 90032-8153
J. Vib. Acoust. Jul 1996, 118(3): 277-284 (8 pages)
Published Online: July 1, 1996
Article history
Received:
June 1, 1993
Revised:
July 1, 1994
Online:
February 26, 2008
Citation
Felszeghy, S. F. (July 1, 1996). "The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response." ASME. J. Vib. Acoust. July 1996; 118(3): 277–284. https://doi.org/10.1115/1.2888178
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