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).
- 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 475264, DOI https://doi.org/10.1007/BF01603816
- A. E. H. Love, A treatise on the Mathematical Theory of Elasticity, Dover Publications, New York, 1944. Fourth Ed. MR 0010851
N. F. Mott and I. N. Sneddon, Wave mechanics and its applications, Dover, New York, 1963, pp. 50–52
- 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
R. S. Chadwick, Vibration of long narrow plates—II, Quart. Appl. Math., this issue.
J. D. Cole and R. S. Chadwick, An approach to mechanics of the cochlea, Zeit, Ang. Math. Physik 28, 785–804 (1977)
A. E. H. Love, The mathematical theory of elasticity, Dover, New York, 1944, p. 465
N. F. Mott and I. N. Sneddon, Wave mechanics and its applications, Dover, New York, 1963, pp. 50–52
F. W. J. Olver, Asymptotics and special functions, Academic Press, New York, 1974, p. 408
R. S. Chadwick, Vibration of long narrow plates—II, Quart. Appl. Math., this issue.
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Article copyright:
© Copyright 1978
American Mathematical Society