Masters Theses


"An analysis based on linear theory is presented for determining the dynamic response of a simply supported beam on an elastic foundation acted upon by a moving time dependent point force with axial forces included. This thesis extends the present theory to include an analysis of a point force accelerating uniformly across the beam. In particular, it is shown that the customary resonance conditions which are prevalent for a point force moving with uniform velocity no longer exist for the case of a point force accelerating uniformly across the beam.

The basic problem and its solution are presented for a simply supported beam on an elastic foundation subjected to a time dependent point force moving across the beam with either (A) uniform acceleration or (B) uniform velocity. The solutions for both cases are effected [sic] by employing standard Fourier techniques to the governing linear fourth order beam equation. Furthermore, the solution for Case (A) is completed by employing known properties of the Fresnel Integrals. The general solution for both cases is determined for two sets of initial displacement conditions corresponding to (I) a point force dropped from zero height at an arbitrary position on an initially undeformed beam and (II) a point force initially at rest at an arbitrary position on the beam. The beam velocity is initially taken to be zero everywhere in both cases.

In conclusion the graphical results exhibit salient characteristics for problems of this type and in addition give a qualitative idea of how a beam may be expected to respond to a uniformly accelerating point force"--Abstract, pages ii-iii.


Hansen, Peter G., 1927-2010

Committee Member(s)

Raske,Theodore J.
Scott, James J.
Cheng, Franklin Y.


Mechanical and Aerospace Engineering

Degree Name

M.S. in Engineering Mechanics


University of Missouri at Rolla

Publication Date



xi, 46 pages

Note about bibliography

Includes bibliographical references (pages 44-45).


© 1967 Joseph Victor Cusumano, All rights reserved.

Document Type

Thesis - Open Access

File Type




Subject Headings

Beams -- Elastic properties
Foundations -- Elastic properties
Vibration -- Mathematical models

Thesis Number

T 1964

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