Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Vibrations of long narrow plates. I

Author: R. S. Chadwick
Journal: Quart. Appl. Math. 36 (1978), 141-154
MSC: Primary 73.35
DOI: https://doi.org/10.1090/qam/502570
MathSciNet review: 502570
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Abstract: An asymptotic theory for the determination of the natural flexural modes and eigenvalues of a long narrow plate having a quite general planform shape is presented. A local transition layer exists in the vicinity of the widest portion of the plate, which reveals the essential structure of the flexural modes. Mode shapes are computed for trapezoidal and semi-elliptical planforms. The theory is relevant to an understanding of frequency discrimination in the cochlea (inner ear).

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

  • [1] Julian D. Cole and Richard S. Chadwick, An approach to mechanics of the cochlea, Z. Angew. Math. Phys. 28 (1977), no. 5, 785–804 (English, with German summary). MR 0475264, https://doi.org/10.1007/BF01603816
  • [2] A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
  • [3] N. F. Mott and I. N. Sneddon, Wave mechanics and its applications, Dover, New York, 1963, pp. 50-52
  • [4] F. W. J. Olver, Asymptotics and special functions, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Computer Science and Applied Mathematics. MR 0435697
  • [5] R. S. Chadwick, Vibration of long narrow plates--II, Quart. Appl. Math., this issue.

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DOI: https://doi.org/10.1090/qam/502570
Article copyright: © Copyright 1978 American Mathematical Society

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