Propagation of surface waves and surface resonances along cylindrical cavities in materials with any allowed Poisson's ratio - Part II: Thin-walled coating

摘要

Propagation of infinitely-lived true surface waves (TSW) and of the evanescent surface resonances (pseudo surface waves, PSW) on the inner surface of a cylindrical cavity in an elastic medium coated with a thin elastic membrane is studied. An analogous flat surface with the same coating is considered as a reference system. The dispersion relations of the true surface waves and of the surface resonances are shown to depend on the interplay between the sound speeds in the substrate and in the covering layer. The short-wavelength limit of the excitations in the cavity is checked to be consistent with the case of the flat surface. Analytical expressions are obtained for the cut-offs and for the asymptotic behaviors of the excitations in the long-wavelength and short wavelength limits. The local surface densities of states (LDOS) as well as the real parts of the Green's functions, i.e., analogues of the reactive power, are calculated. The most eminent anomalies of LDOS, which correspond to the longitudinal resonance, are shown to be located close to the apparently spurious roots of the secular determinant of the surface equations of motion. The roots correspond generally to the total conversion of the longitudinal to transverse bulk waves. These roots show cut-offs, where the life time of the longitudinal resonance increases to infinity. For still lower wave vectors the maxima of LDOS follow the lines of total conversion transverse-to-longitudinal with finite life-times. The radius dependence of the cut-off wave vector in the small-radius limit for a fully symmetric torsional mode is 1/root a and for a fully symmetric high-frequency axial-radial TSW follows a 1/a behavior, whereas the analogous dependence for a quasi-Rayleigh surface wave is proportional to 1/root alna except for a certain range of parameters, where the high-frequency TSW does not exist. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim