Unified theory of dislocation damping with a special reference to point-defect dragging

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Abstract
The complete and compact mathematical solution of dislocation damping for the equally spaced multidragging-point-defect case is investigated by the Laplace-transformation method combined with a proper variational procedure. It is shown that the dragging leads to an expression which is identical to the exact solution of the Koehler-Granato-Lücke (KGL) model with a modified viscous damping constant. The apparent dissimilarity between the point-defect dragging model of Simpson and Sosin (SS) and the KGL theory is due to the retention of only the first term in the Fourier expansion by KGL and concomitantly the omission of the inertial term by SS. A new frequency-normalization procedure is introduced which facilitates the examination of the dependence of the decrement and modulus defect on the dragging-point-defect density at any given driving-frequency range.