Free vibration model and theoretical solution of the tympanic membrane

Abstract

Myringoplasty is one of the routine surgeries in the treatment of tympanic membrane (TM) perforation. Since the gross anatomical structure of the middle ear cannot be simulated in clinical practice, the surgery is mainly performed by experience and expertise. Based on the mechanical properties of TM, four hypotheses are presented where TM is simplified as a sectorial annulus membrane. This paper proposes a free vibration model of TM whose natural frequency of free vibration and the analytical expressions of corresponding natural vibration mode are obtained by variables separation method and Bessel function. Compared with the ANSYS numerical results, it shows that natural frequency calculated by finite element (FE) method is slightly higher because of the increase of model stiffness by ignoring high-order quantity. Compared with the experimental data from volunteers, it shows that the first-order, second-order and third-order principal resonances in the test are the combined effects of multiple natural frequencies and natural vibration modes instead of the single one. The theoretical model deduced in this paper is in higher precision with comparatively fewer parameters. It provides more precise mechanical reference to myringoplasty by calculating the response of the normal human ear.