Abstract
These notes represent some of the efforts by the author to understand mechanisms which have relevance to the mechanics of the cochlea. The use of asymptotic methods is stressed. In particular, the “WKB” method or its generalization, the two-variable expansion procedure (Cole, 1968, Chapter 3) is used throughout. The notes are arranged in the format of three specific problems, in the order of increasing relevance and difficulty. Section II deals with the sinusoidal forced vibrations of an isotropic membrane with a tapered planform in the absence of a fluid. Section III considers the response of a partition having mass, internal damping and variable stiffness and which is immersed in an inviscid fluid undergoing two dimensional motions. Section IV illustrates some aspects of the response to sinusoidal forcing of a highly anisotropic tapered plate immersed in a viscous fluid undergoing three dimensional motions. Special consideration is given to the low and high frequency limits of this problem.
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Chadwick, R.S. (1981). Studies in Cochlear Mechanics. In: Holmes, M.H., Rubenfeld, L.A. (eds) Mathematical Modeling of the Hearing Process. Lecture Notes in Biomathematics, vol 43. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46445-4_2
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DOI: https://doi.org/10.1007/978-3-642-46445-4_2
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