Vibrations of long narrow plates. I

Chadwick, R. S.

doi:10.1090/qam/502570

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 | References | Similar Articles | Additional Information

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.