Wave propagation in transversely isotropic cylinders

A new mathematical model for the propagation of longitudinal guided waves in free transversely isotropic cylinders is developed in this paper. The model uses three scalar potential functions to represent the three wave modes which can propagate inside the cylinder, i.e. compression (P), vertically polarized shear (SV) and horizontally polarized shear (SH) waves. This results in the decoupling of the equations of motion such that the SH wave is completely decoupled from P and SV waves. In this model the resulting partial differential equations are solved by the method of separation of variables and the frequency equation is derived in a systematic manner. The dispersion curves as well as displacement fields inside the cylinder at various frequencies are plotted for longitudinal waves propagating along a number of transversely isotropic cylinders. In this approach the equations are solved systematically and unlike other models, there is no need to guess the form of the final solution. This approach can also be used for solving similar problems which deal with cylindrical shells and multilayered cylinders having either finite or infinite lengths.