Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals

Figure 3

Comparison between experimental and theoretical results for a driving frequency  kHz, which lies in the second spectral gap. (a) Profile of solution for a driving amplitude of  nm. Experimental values (green shaded areas) are shown as a superposition of the velocities measured over the 50 ms time window of recorded data. The numerically predicted extrema (over one period) of the exact solution obtained via Newton’s method are shown with blue (open) circles. (b) The quantity as a function of the amplitude of the drive. For the numerically exact solutions, is the maximum velocity of the 4th bead over one period of motion. Note that the blue segments correspond to stable parametric regions while the red and green ones correspond to real and oscillatory unstable parametric regions, respectively. Black squares with error bars represent the experimentally measured mean values of the quantity over three experimental runs, where was calculated as the maximum measured over the 50 ms time window of recorded data. Finally, the dashed gray line is the maximum velocity (over one period) of bead 4 as predicted by the linear solution of (17). (c) Zoomed out version of panel (b). The gray circles correspond to numerical results that were obtained by dynamically running the equations of motion and monitoring the maximum velocity over the experimental time window. The experimental data in this panel are shown again by black squares.

(a)

(b)

(c)