Dynamic Response of an Infinite Beam

[+] Author and Article Information
H. Durlofsky

Nuclear Services Corp., Campbell, Calif.

J. Pressure Vessel Technol 97(2), 107-109 (May 01, 1975) (3 pages) doi:10.1115/1.3454259 History: Received March 26, 1975; Online October 25, 2010


Both the exact and an approximate solution for the dynamic response of an infinite Bernoulli-Euler beam under an instantaneously applied, concentrated load are presented in this paper. The exact solution is obtained by means of complex Fourier transforms. The approximate solution is obtained by assuming the dynamic response has the form of a deflected infinite beam on an elastic foundation, with wavelength a function of time. This assumption is motivated by the similarity between the dynamic response problem and the problem of an infinite beam on an elastic foundation. A governing equation for the wavelength in the assumed response is derived by application of the principle of conservation of energy, and solved by straightforward methods. A comparison of the two solutions shows good agreement near the point of loading. Results applicable to pipe whip problems are presented.

Copyright © 1975 by ASME
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