Axisymmetric plane vibration analysis of polar-anisotropic disks

Closed-form solutions for the uncoupled natural frequencies in radial and circumferential directions and dynamic response due to inside pressure of polar anisotropic disks are obtained. In studies available in literature, in general, the material is assumed to be polar-orthotropic allowing natural frequencies only in the radial direction. The novelty of the present paper is that it deals with the determination of natural frequencies in the radial and circumferential directions separately due to the fully anisotropic material behavior without performing mode shape study. The elasto-dynamic response of anisotropic disks for various pressure types is investigated. Laplace transform is used to obtain time-independent boundary value problems and modified Durbin's method is performed for inverse transformation into the real-time domain. The results are obtained in terms of non-dimensional parameters. The analytical results are compared with those calculated numerically by Complementary Functions Method.