The well known transfer matrix scheme of Ehrich for calculating the vibration characteristics of uniform and varying thickness discs is extended to include polar orthotropic material behaviour. The exact deflection equations for an annular element of material are used in the solution. Comparisons with alternative solutions in the literature show excellent agreement for both annular and complete discs of uniform and varying thickness profile.

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Journal Topics in Catalysis
Bell, R., & Kirkhope, J. (1980). Vibration analysis of polar orthotropic discs using the transfer matrix method. Topics in Catalysis, 71(3), 421–428. doi:10.1016/0022-460X(80)90423-X