Fig. 4: Analytical and numerical results in the absence of dissipation.
From: Universally bistable shells with nonzero Gaussian curvature for two-way transition waves
a Schematic of our system, showcasing the i − 1, i and i + 1 shells during the propagation of a transition waves that sequentially switches the shells from one stable state to another. b Discrete mass-spring model used to represent the response of our system. c,d Effect of the input energy provided to initiate the pulse on (c) the pulse velocity, c, and (d) the pulse width, w, for three shell geometries with (H, Ttotal) = (12.5, 3) mm (yellow), (H, Ttotal) = (15, 4) mm (blue) and (H, Ttotal) = (17.5, 5) mm (red) and R = 25.4 mm, as predicted by the discrete (markers) and continuum models (lines). e Wave velocity, c, and (f) width, w, vs. input energy, Ein, for an array of universally bistable shells with (H, Ttotal) = (15, 4) mm and R = 25.4 mm, for three values of shell-to-shell spacing, Lt = 32 mm (yellow), 28 mm (blue) and 22 mm (red), as predicted by the discrete (markers) and continuum model (lines). Note that in c–f we report two analytical solutions: one in which c is obtained by solving Eq. (13) (solid lines) and one in which c is given by Eq. (14) (dashed lines).
