Modal analysis of the human tympanic membrane of middle ear using the finite-element method

Abstract

This paper provides a theoretical vibrations model of tympanic membrane constructed and solved using the finite-element method. This method is an appropriate tool to analyze the middle-ear vibrations because it enables modeling in details the complicated shape of the middle-ear and, moreover, and allows to calculate the distribution of vibrations stimulated by sinusoidal signals. The number of the 3-dimensional tetrahedral elements was assumed to be 591 and material properties used were based on data available in the literature. This model has a uniform density of $1.2 \cdot 10^3$ kg/m$^3$, an area of $70\cdot 10^{−6}$ m$^2$, a depth of $1.54 \cdot 10^{−3}$ m at the umbo, a mean thickness of $1.32 \cdot 10^{−4}$ m, and a Poisson’s ratio 0.3. Constrains were accomplished by two different springs, linear and torsional. The results obtained are compared with their counterparts scattered in the literature.