A novel hyperbolic composite coupling has been recently introduced by the authors. Amathematical model based on Timoshenko beam was developed and used to solve for thedynamic characteristics of the coupling. The results indicated that small values of the coupling'slength and minimum diameters, relative to the maximum outer diameter, are needed in order toachieve the dynamic requirements of a successful coupling. That is, a 'deep' hyperboliccoupling is needed.In this paper a more accurate mathematical model of the 'deep' coupling is developed basedon 'shell/beam' assumptions and using the energy approach and the extended Lagrange'sequations. Together with the appropriate boundary conditions, the mathematical model is solved,using the finite element method, to study the effect of the minimum diameter of the coupling onthe dynamic characteristics of a specific 'deep' coupling. The results are compared with thecorresponding 3D ANSYS ones. The merits of the proposed approach and coupling arediscussed.
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