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Parameter studies of modal vibrations associated with impurity pinned dislocations in a metal single crystal
Author(s) -
Cooke Charlie H.,
Kroll John
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1020
Subject(s) - vibration , impurity , steady state (chemistry) , oscillation (cell signaling) , crystal (programming language) , transient (computer programming) , condensed matter physics , mathematical analysis , mathematics , chemistry , physics , quantum mechanics , computer science , programming language , operating system , biochemistry
Koehler's model [1–2] of motion for edge‐type dislocations in a metal single crystal that are pinned down by impurity atoms is studied. An exact solution can be found, which is composed of a rapidly decaying transient and a steady time‐oscillating, steady state vibration. This solution is used to improve Koehler's [1] approximation to the steady time‐oscillating steady state vibration. General parameter studies of the modes of oscillation are then performed. The present result is of some significance, because it allows insight into the behavior of crystalline solids over a wide parameter range, whereas Koehler's asymptotic approach is valid only for materials that exhibit order‐of‐magnitude variation in system parameters. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 427–439, 2001.