Research on the Tympanic Membrane Free Vibration Model Based on Thin Plate Theory

Abstract

Myringoplasty is one of the routine surgeries in the treatment of tympanic membrane (TM) perforation. Since the anatomic structure of the middle ear cannot be simulated in clinical treatment, the surgery is mainly directed by experiences. Based on the mechanical properties of TM in the anatomy, four hypotheses are presented and TM is simplified as a sectorial annulus plate with fixed boundary condition. This paper proposes a free vibration model of TM. Its natural frequencies of free vibration are obtained by variables separation method and Bessel function. The system of fundamental solutions of fourth-order homogeneous equations can be solved for the analytical expressions of corresponding natural vibration mode. The theoretical model is proved to be valid since the natural frequency of the model is consistent with the experimental data. The effect of geometric parameters and material parameters on TM natural frequency is subsequently discussed in the numerical examples. Especially, the diameter and thickness of TM will cause different natural frequency errors above 40%, while the Young’s modulus and density of TM cause errors below 15% as well.