title: Natural frequencies of vibration of a fibre supported human tympanic membrane analysed by the finite element method.
abstract: A finite element programme developed previously to calculate the natural frequencies of vibration of the human tympanic membrane, has been modified to take into account both natural and geometric rigidities. The natural rigidities take the form of internal membrane stress/strain parameters, while the geometric rigidities are the flexural and membrane stress resultants. The first six natural frequencies calculated are similar to those measured by Laser holography on cadaver membranes and analysed recently by interference techniques. Using a generalized stress/strain constitutional relationship, the natural frequencies were found to be linearly related to the square root of the forces within the membrane. It was proposed in our earlier work, that these internal stresses as well as maintaining the complex shape of the tympanic membrane, serve to enhance its frequency range and response. The role of the radial and circular fibres embedded within the ground substance of the membrane on the frequencies and mode shapes have also been examined by super-imposing beam elements on the semi-loof membrane elements. It was found that the modes of vibration of the membrane are restricted to a fairly simple pattern up to beam moduli values of approximately 50 MPa. Above this beam modulus, the normal mode shape was observed with a gradually increasing complex vibration pattern as the frequency increases. This new treatment of membrane re-enforcement suggests a non-Hookean behaviour of the drum displacements. In order to account for the earlier measured frequencies of Tonndorf & Khanna, the previously proposed internal stress/strain parameters are believed to be less important and have been calculated to be small compared with the membrane modulus.
authors.affiliation: Department of Basic Dental Science, University of Wales, College of Medicine, Cardiff, UK.
authors.forename: K R
authors.initials: KR
authors.lastname: Williams
authors.forename: T H
authors.initials: TH
authors.lastname: Lesser
mesh_terms: D006801:Humans; D008953:Models, Anatomic; D014432:Tympanic Membrane / Q000502:physiology*; D014732:Vibration