Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio – Part I: Clean inner surface

Abstract

The dynamics of the inner surface of an infinitely long circular‐cylindrical cavity in an isotropic elastic medium is studied in the whole range of the Poisson's ratio including negative values characteristic of auxetic materials. The existence of the unique long‐lived propagation mode (true surface wave, TSW) has been confirmed on the clean surface with the following properties: (i) existence of a low frequency cut‐off for all the azimuthal indices n except for n = 1 (flexural mode), (ii) polarization tending to that of the Rayleigh wave in the short wavelength limit, (iii) Airy phases (inflection points of dispersion curves) for n < 6 that shift towards short wave region when the Poisson's ratio becomes negative. A number of propagation modes with complex frequencies, i.e., with finite life times (surface leaky waves, pseudo surface waves) are found. The torsional leaky mode transforms into the skimming shear‐horizontal wave (Love wave) in the short wavelength limit. An axial–radial leaky mode, similar to the Rayleigh wave but with reverse elliptical polarization turns out a physical solution except for extremely short wavelengths. A strong radial component of the longitudinal resonance occurs at wavelengths comparable to the cavity's radius especially in the incompressible limit.