6 Solitary Waves to Infer Axial Stress in Slender Structures: A Numerical Model 55 Fig. 6.9 One chain configuration. Ratio associated with the amplitude of the vibration-induced and incident waves as a function of the axial stress and the particles’ diameter Fig. 6.10 One chain configuration. Time of flight of the reflected wave as a function of the axial stress and the particles’ diameter and mechanical properties of the particles; in addition, the beam’s motion is the combination of many modes of vibration. We conclude that for this complex dynamical system, the feature associated with the amplitude of the vibration-induced solitary wave is not monotonic. At a given diameter the variation of the ratio is similar to what found and discussed in Sect. 6.2.3. Similar to Figs. 6.8 and 6.9, Figs. 6.10 and 6.11 show the feature associated with the time of flight of the reflected and the vibration-induced solitary wave, respectively. The TOF of the reflected wave (Fig. 6.10) does not change significantly with stress irrespective of the particles diameter or the particles materials. Thus, the same conclusion drawn in Fig. 6.4 can
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