By A. S. Nowick
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Extra resources for Anelastic Relaxation in Crystalline Solids
3 THE STANDARD ANELASTIC SOLID 51 1 y l o g ( t / T C) F I G . 3-6. Stress relaxation and χ(ω) M|M-MR or log (Ι/ωτ €) functions for the standard anelastic solid. strain equation for this model. 3-11) T h i s equation is the same as E q . 3-8), which has been regarded as t h e defining equation of the standard anelastic solid. T h e parameter τ ε , which was initially introduced into t h e model of Fig. 3-7 as an arbitrary as given b y E q . 3-9). parameter, is n o w seen to be identical with (a) F I G .
I n fact, t h e result of Fourier analysis of a periodic pulse of finite duration is that it may be represented as a frequency distribution which becomes m o r e sharply peaked as t h e pulse is expanded to contain more a n d m o r e waves. T h u s , from t h e viewpoint of defining t h e frequency, t h e longer t h e pulse, t h e better. However, as already mentioned, for experimental reasons the pulse m u s t be short compared to t h e specimen length. A suitable compromise may usually be obtained by taking pulses about ten waves long.
T h e propagation direction is taken along the coordinate axis, while the particle displacement u may be in the direction (longitudinal or dilatational wave) or normal to it (transverse, or shear wave). S u c h a NU, AT TIME t F I G . 1-10. medium. 6-1) is the appropriate m o d u l u s . 6 25 WAVE PROPAGATION METHODS F o r anelastic material, if t h e motion is strictly h a r m o n i c (circular frequency ω), may be replaced by t h e complex m o d u l u s M*. 6-2) Before proceeding further it is desirable to consider w h y E q .