The Propagation of Elastic Waves in Elliptical Cylinders

The propagation of free harmonic waves in an infinite elliptical isotropic cylinder was examined in the following three cases: solid cylinder, hollow cylinder with a concentric elliptical bore, hollow cylinder with an excentric elliptical bore. The problem is solved through Mathieu's elliptical functions and it is reduced to the solution of an infinite linear system of algebraical equations concerning the amplitude coefficient of the propagated free waves. For each one of the three examined models the determinant of the respective system gives the proper wave spectra (wave numbers) of the treated model. The possibility of numerical calculation of the wave numbers from the system of linear equations is also shown in the present investigation.