The Application of Continued Fractions to Wave Propagation in a Semi-Infinite Elastic Cylindrical Membrane

[+] Author and Article Information
J. E. Akin

Engineering Mechanics Department, The University of Tennessee, Knoxville, Tenn.

J. Counts

Engineering Mechanics Department, Virginia Polytechnic Institute, Blacksburg, Va.

J. Appl. Mech 36(3), 420-424 (Sep 01, 1969) (5 pages) doi:10.1115/1.3564696 History: Received May 28, 1968; Revised November 21, 1968; Online September 14, 2011


The Laplace transform of the axial stress resultant in an impacting semi-infinite elastic cylindrical membrane is generated in the form of an exponential function involving the wave speed, and a series in powers of the reciprocal of the transform parameter. Continued fractions are used to obtain rational approximations for the transform represented by the series. The rational approximations, which are in the form of the ratio of two polynomials, are inverted by standard techniques. Results are presented for the axial stress resultant for small and large values of time and are compared with previously published results.

Copyright © 1969 by ASME
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