A new approach for modeling the vibrations of a finite solid transversely isotropic cylinder has been used in this paper. It is assumed that the periphery of the cylinder is traction-free and its ends are constrained by frictionless rigid walls. The interior displacement field of the cylinder is expressed in terms of three scalar potential functions representing the quasi-P, quasi-SV and SH wave modes, respectively. Unlike the previous models in which either approximate solutions are obtained or the final solution is somehow guessed, the new approach leads to exact frequency equations for the axisymmetric and asymmetric vibrations of the cylinder. Based on the calculated resonance frequencies, the frequency spectra as well as the vibration mode shapes are plotted for transversely isotropic cylinders. The results agree with those obtained from the previous models. The new approach has a number of advantages in comparison to the previous mathematical models. In the new approach the equations are solved systematically and there is no need to guess the solutions. Moreover, each of the three potential functions used for expressing the displacement field corresponds to a distinct wave mode; making it possible to carry out parametric studies. The new model can be used for studying other vibration modes of transversely isotropic cylinders as well as the problems of wave propagation and wave scattering from such cylinders.
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