Modeling the eardrum as a string with distributed force

Abstract

In this paper, an analytical model of the tympanic membrane is introduced where the two-dimensional tympanic membrane is reduced to a one-dimensional string. It is intended to bridge the gap between lumped-element models and finite-element models. In contrast to known lumped-element models, the model takes the distributed effect of the sound field on the tympanic membrane into account. Compared to finite-element models, it retains the advantage of a low number of parameters. The model is adjusted to forward and reverse transfer functions of the guinea-pig middle ear. Although the fitting to experimental data is not perfect, important conclusions can be drawn. For instance, the model shows that the delay of surface waves on the tympanic membrane can be different from the signal transmission delay of the tympanic membrane. In a similar vein, the standing wave ratio on the tympanic membrane and within the ear canal can considerably differ. Further, the model shows that even in a low-loss tympanic membrane the effective area, which commonly is associated with the transformer ratio in a lumped-element and some hybrid circuit models, not only is frequency-dependent, but also different for forward and reverse transduction.