Torsional dispersion relations in a radially dual elastic medium

Abstract

Exact dispersion relations for torsional waves are derived for a system consisting of an elastic cylindrical core embedded in an elastic medium having different material properties. Dispersion curves are presented as a function of an aspect ratio and ratios of material properties. Cutoff wavelengths dependent on material properties are established. The results are compared with a previous solution obtained using a simplified approximate model. While the approximate model is seen to yield the correct range of phase velocities, the resulting dispersion relations are shown to be inaccurate for relatively short wavelengths in systems for which the surrounding material is markedly stiffer or denser than the core. The approximate model is also shown to be overly restrictive in predicting cutoff wavelengths.

Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium

“…Consequently, in the particular case where the initial stresses are absent in the constituents of the considered system, the results obtained in the present paper must coincide with the corresponding ones attained in the paper by Kleczewski and Parnes [28]. Note that we will turn again to the work of Kleczewski and Parnes [28] in the following sections.…”

“…Note that in the case where r ðmÞ;0 zz ¼ 0, the foregoing problem formulation proposed in case 1 coincides with that considered in the paper by Kleczewski and Parnes [28].…”

“…It should be noted that the geometrical model used in the present paper was also used in the papers of Parnes [26,27], Kleczewski and Parnes [28] and some others listed therein for determination of the dispersion relation of the ''cylinder (rod) + embedded elastic medium". The paper by Parnes [26] was related to axisymmetric waves, but the papers of Parnes [27] and Kleczewski and Parnes [28] were related to torsional wave dispersion in the ''rod + embedded" system.…”

“…The paper by Parnes [26] was related to axisymmetric waves, but the papers of Parnes [27] and Kleczewski and Parnes [28] were related to torsional wave dispersion in the ''rod + embedded" system. However, in the papers by Parnes [26,27] the cylinder (rod) was assumed to be radially rigid and the equation of motion of the cylinder is written within this assumption, but the equation of motion for the surrounding medium is written by exact equations of the linear theory of elastodynamics.…”

“…However, in the papers by Parnes [26,27] the cylinder (rod) was assumed to be radially rigid and the equation of motion of the cylinder is written within this assumption, but the equation of motion for the surrounding medium is written by exact equations of the linear theory of elastodynamics. The paper by Kleczewski and Parnes [28] employed the findings of the paper by Parnes [27] in developing a case where the equation of motion for the cylinder is also described by the exact equations of the linear theory of elastic waves.…”