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Sobieszczyk P.,The H Niewodniczanski Institute Of Nuclear Physicspan | Galazka M.,The H Niewodniczanski Institute Of Nuclear Physicspan | Trzupek D.,The H Niewodniczanski Institute Of Nuclear Physicspan | Zielinski P.,The H Niewodniczanski Institute Of Nuclear Physicspan
Physica Status Solidi (B) Basic Research | Year: 2015

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/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/-alna except for a certain range of parameters, where the high-frequency TSW does not exist. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source


Sobieszczyk P.,The H Niewodniczanski Institute Of Nuclear Physicspan | Galazka M.,The H Niewodniczanski Institute Of Nuclear Physicspan | Trzupek D.,The H Niewodniczanski Institute Of Nuclear Physicspan | Zielinski P.,The H Niewodniczanski Institute Of Nuclear Physicspan
Physica Status Solidi (B) Basic Research | Year: 2015

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. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source

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