Dynamic Fiber Composite Continuum Model of the Tympanic Membrane. Part 1. Model Formulation

摘要

Fibrous layers of the lamina propria influence dynamic behavior of the tympanic membrane by producing strong anisotropic extensional stiffness, while the mucous and epidermal layers are primarily responsible for curvature dependent structural damping and relatively weak isotropic bending stiffness. These mechanical properties are combined with curvilinear shell equilibrium equations to formulate a comprehensive dynamic continuum model of the tympanic membrane. The resulting model contains several small parameters that are exploited to construct closed form asymptotic solutions for the general problem. Using the geometry and ultrastructure of the cat eardrum coupled with the outer ear, ossicular chain and tympanic cavities, the asymptotic solution reproduces the manifold of experimentally observed frequency and excitation dependent vibrational shapes. Demonstration of the model's ability to duplicate experimental results concludes part I. However, since the model is based on the actual geometry and ultrastructure, future investigations may use the model to address questions related to tympanoplasty, tympanosclerosis, tensor tympani cogency, as well as energy transmission and tympanic cavity coupling. (Author)