NATURAL FREQUENCIES OF VIBRATION OF A FIBER SUPPORTED HUMAN TYMPANIC MEMBRANE ANALYZED BY THE FINITE-ELEMENT METHOD

A finite element programme developed previously to calculate the natur al frequencies of vibration of the human tympanic membrane, has been m odified to take into account both natural and geometric rigidities. Th e natural rigidities take the form of internal membrane stress/strain parameters, while the geometric rigidities are the flexural and membra ne stress resultants. The first six natural frequencies calculated are similar to those measured by Laser holography on cadaver membranes an d analysed recently by interference techniques. Using a generalized st ress/strain constitutional relationship, the natural frequencies were found to be linearly related to the square root of the forces within t he membrane. It was proposed in our earlier work,1 that these internal stresses as well as maintaining the complex shape of the tympanic mem brane, 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 examin ed by super-imposing beam elements on the semi-loof membrane elements. It was found that the modes of vibration of the membrane are restrict ed to a fairly simple pattern up to beam moduli values of approximatel y 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-inforcement suggests a n on-Hookean behaviour of the drum displacements. In order to account fo r the earlier measured frequencies of Tonndorf & Khanna,2 the previous ly proposed internal stress/strain parameters1 are believed to be less important and have been calculated to be small compared with the memb rane modulus.