Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Discontinuities in integral-transform solutions

Author: Bruno A. Boley
Journal: Quart. Appl. Math. 19 (1962), 273-284
MSC: Primary 44.28
DOI: https://doi.org/10.1090/qam/131729
MathSciNet review: 131729
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Abstract: Criteria are derived for the determination of the magnitude and the location of discontinuities of solutions in the form of definite integrals obtained by means of integral-transform techniques. The types of integrals arising with the Fourier sine or cosine transforms and those arising with the Laplace transforms are considered in detail. Applications of the theory arise particularly with problems of wave propagation, where interest is centered on the location of wave fronts and the magnitude of jumps there; two illustrative examples of such problems relating to Timoshenko beams are included.

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  • [1] E. W. Hobson, The theory of functions of a real variable, Dover Publications, Inc., New York, 1957
  • [2] B. A. Boley and C. C. Chao, Some solutions of the Timoshenko beam equations, J. Appl. Mechanics, Trans. of A.S.M.E. 77, 579-586 (Dec. 1955)
  • [3] Ruel V. Churchill, Operational mathematics, 2nd ed, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR 0108696
  • [4] B. A. Boley, On the use of sine transforms in Timoshenko beams impact problems, J. Appl. Mechanics, 152-153 (March 1957)
  • [5] Robert W. Leonard and Bernard Budiansky, On traveling waves in beams, NACA Rep. 1954 (1954), no. 1173, iii+27 pp. (1955). MR 0088900
  • [6] B. A. Boley and C. C. Chao, An approximate analysis of Timoshenko beams under dynamic loads, J. Appl. Mechanics 25, No. 1 31-36, in particular the Appendix (March 1958)

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DOI: https://doi.org/10.1090/qam/131729
Article copyright: © Copyright 1962 American Mathematical Society

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