Numerical simulation of the dynamical properties of the human tympanum

Abstract

A numerical simulation of the dynamical properties of the tympanic membrane is presented. A simple and different simulation of the vibratory patterns of the coupled system of the tympanum-malleus have been assessed by proposing the modeling of the tympanum through the vibrations of a forced elastic membrane, whereas the effect of the manubrium is introduced through a forced semi-membrane. We propose the superposition of these waveforms as a model for describing the vibrations of the coupled system of the tympanum-malleus. Both waveforms have analytical representations leading to simple computations. The results of the simulation for the vibrational mode (1,1) show an amplitude for the membrane larger than those for the handle of the malleus. The maximum amplitude obtained was around 1 $\mu $m, at a test frequency of 2 kHz. Also, level curves corresponding to the simulated vibrational modes were obtained. The numerical model presented can be easily handled to change input parameters, such as sound pressure and frequency. Also, other situations such as the conical shape of the tympanum or some asymmetries could be considered.