Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On nonlinear steady-state solutions to moving load problems

Author: G. A. Hegemier
Journal: Quart. Appl. Math. 26 (1968), 239-248
MSC: Primary 73.35
DOI: https://doi.org/10.1090/qam/231572
MathSciNet review: 231572
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Abstract: In certain moving load problems involving elastic solids or structures with an idealized infinite or semi-infinite spatial domain, steady-state solutions of the governing equations of motion are frequently sought as an alternative to a more complex transient analysis. In seeking a solution of this type the implication is, of course, that it represents the limit of a transient problem. While this appears to be generally true of well-posed linear elastic problems, the same cannot be said of nonlinear elastic formulations. To substantiate this point the case of an infinite-length string supported by a nonlinear elastic foundation and subjected to a concentrated load moving with constant velocity is studied in this paper. It is shown that although the steady-state solution of the problem is unique for load velocities both above and below the signal velocity of the string, that above is locally unstable and therefore cannot represent the limit of transient motions.

References [Enhancements On Off] (What's this?)

  • [1] L. M. Milne-Thomson, Jacobian elliptic function tables, Dover, New York, 1950 MR 0088071
  • [2] J. J. Stoker, Nonlinear vibrations in mechanical and electrical systems, Interscience Publishers, New York, 1950 MR 0034932
  • [3] W. Magnus and S. Winkler, Hill's equation, Intersicence, New York, 1966 MR 0197830
  • [4] H. Hochstadt, On the determination of a Hill's equation from its spectrum, Arch Rat. Mech. and Anal. 19, 353-362 (1965) MR 0181792
  • [5] P. Ungar, Instability of wave trains, Comm. Pure Appl. Math. XIV, 637-643 (1961) MR 0137914
  • [6] B. A. Fleischman, Progressing waves in an infinite nonlinear string, Proc. Amer. Math. Soc. 10, 329-334 (1959) MR 0105903

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DOI: https://doi.org/10.1090/qam/231572
Article copyright: © Copyright 1968 American Mathematical Society

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