Figure 6
From: Non-cuttable material created through local resonance and strain rate effects
(a) Vibration modes consist of angular waves denoted with n = 1 for one wave, n = 2 for two waves, n = 3 for three waves, as well as radial waves propagating from the center of the disc toward the circumference, which are denoted with s = 0 (resembling deflected shape under uniform pressure, s = 1 for one axisymmetric wave). Combination of both radial and angular components appears at higher frequencies (e.g. n = 1 and s = 2). (b) Vibrational signal transferred to the sphere by the first set of the forward and backward travelling waves in the rotating disc is bi-modal. (c) Cumulative effect of the first three modes (f1,0 + f0,0 + f2,0) compared with the superposition of the first two modes and the first mode signal only. When multiple travelling waves are excited, the excitation becomes multi-modal and the signal increasingly irregular. (d) Computational vibrational mode of the actual cutting disc with a central hole (n = 4, s = 0 with \({f}_{B}=713\,Hz\) and \({f}_{F}=2175\,Hz\)), (e) Vibrational mode of a ceramic sphere in a flexible continuum (9340 Hz), (f) metallic foam vibrational mode accounting for the interactions between multiple embedded spheres.
