BASILAR MEMBRANE MODELLED AS A LINEARLY ELASTIC PLATE.
Viergever, Max A.
Delft Prog Rep 2 (3), p. 257-272
Abstract
A three-dimensional model of the cochlea is analyzed. The basilar membrane is presented by a linearly elastic plate of variable width and thickness, enclosed by a rigid structure. The description of the model leads to a boundary value problem; the pressure difference in the cochlea must satisfy Laplace's equation in three variables and boundary conditions at the six walls. The condition at the cochlear partition is too complex to allow a straightforward treatment. By means of Fourier series expansions in the direction along the width of the membrane and with the help of an asymptotic method utilizing the slender geometry of the plate, the problem can be reduced to a number of coupled Helmholtz-equations in two variables with appropriate boundary conditions.