Fig. 2: Mechanism of an amplification in EsMV systems.
From: Elasto-magnetic instabilities for amplified actuation and mechanical memory
a, b Energy diagrams of NC-EsMV during the a repulsive phase (t0–t2) and b attractive phase (t2–t4). Kinetic energy (red) and potential energy (blue) are plotted over time. The yellow ball indicates the magnet’s actual position, considering its inertia. In NC-EsMV, the magnet oscillates around static equilibrium points (z = zoff) with low kinetic energy ( ~ 10−4 mJ). c, d Energy diagrams of C-EsMV during the c repulsive phase (t'0–t'3) and d attractive phase (t'4–t'6). When this barrier is overcome by the combined effects of elastic restoration force and electromagnetic repulsion, the magnet is launched with significantly higher kinetic energy ( ~ 10−1 mJ), resembling a slingshot motion (t'2–t'3). e–h Static and dynamic vibration analyses of NC-EsMV and C-EsMV systems. e Motion trajectories of each system derived from bifurcation diagram analysis. f Time-dependent vibration amplitudes showing dynamic responses of each system. g Phase portraits illustrating distinct dynamic states. h Dynamic vibration trajectories under sinusoidal input. All analysis was conducted representatively at fi = 5 Hz and Ipeak = 2.0 A.
