AXISYMMETRICAL AND ASYMMETRIC WAVE MOTION IN ORTHOTROPIC CYLINDERS

A method is presented for studying harmonic wave propagation in thick circular cylinders, which are orthotropic. The analysis is carried out within the framework of the complete three-dimensional theory of elas ticity. The displacements in the circumferential and longitudinal dire ctions are taken in the form of trigonometric functions, while the rad ial displacement field is modelled by Frobenius power series developed through the thickness of the shell. It is shown that the Frobenius me thod is a powerful tool in solving for wave motions in anisotropic ela stic continua. Dispersion curves are presented for axisymmetric and as ymmetric waves in the case of transverse isotropy. The methodology bre aks the problem dawn into four different tasks, which have then to be treated separately. They are as follows: the axisymmetric wave motion, n = 0; the flexural or beam-type wave motion, n = 1; the lobar wave m otion, n = 2; finally the wave motion with higher circumferential wave numbers, n > 2. Exact solutions have been found for waves travelling i n thick orthotropic shells. These solutions may serve as benchmark sol utions for comparison with approximate treatments of similar problems.