Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: A typical curved panel, and two schematic scenarios in which such a system might exhibit a snap-through event in its force-displacement relationship. (a) Presnap, (b) post-snap, (c) limit point buckling, and (d) pitchfork bifurcation.

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: A single degree of freedom (SDOF) link model

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: (a) Photograph of experimental setup, (b) the low-friction pin joint, (c) the Scotch-yoke forcing mechanism

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Identification of damping parameter β (Kg/s). (a) A typical nonlinear free decay. The points are experimental data, and the continuous line represents the numerical integration of Eq. (4) with β = 1.2. (b) Normalized average error versus β for the large amplitude time series (in part (a)). (c) Normalized average error versus β for a small amplitude time series.

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Free response characteristics. (a) Force versus natural frequency (squared), (b) force versus deflection, and (c) natural frequency (squared) versus deflection. The points are experimental data, and the continuous lines are the theoretical results.

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Experimental and simulated time series superimposed on the restoring force. Numerical, (a) Ω = 4.40 rad/s, and (b) Ω = 3.36 rad/s. Experimental, (c) Ω = 4.40 rad/s, and (d) Ω = 3.36 rad/s.

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Numerical ((a)-(d)) and experimental ((e)-(h)) time series. (a) Ω = 4.9 rad/s, (b) Ω = 4.9 rad/s, (c) Ω = 7.6 rad/s, (d) Ω = 7.8 rad/s, (e) Ω = 4.9 rad/s, (f) Ω = 4.9 rad/s, (g) Ω = 7.9 rad/s, (h) Ω = 8.1 rad/s.

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Experimental and simulated DFT’s for Figs. 7(c), 7(d), 7(g), and 7(h), respectively

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Occurrence of snap-through. (a) Simulation, (b) experiment, and (c) relative dominance of co-existing attractors (simulation only). Green - nonsnap, red - P1 snap-through, and blue - higher periodic or chaotic (less frequent) snap-through. The vertical dashed red lines in (a) and (b) indicate the specific frequencies relating to Fig. 7.

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Average kinetic energy as a function of forcing frequency: (a) simulation and (b) experiment

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Distinction between chaotic and nonchaotic behavior based on (a) the largest Lyapunov exponent, (b) the peak- count criterion, (c) and (d) typical chaotic time series, and (e) relative dominance of chaotic behavior

Date of download: 11/5/2017 Copyright © ASME. All rights reserved. From: Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System J. Comput. Nonlinear Dynam. 2012;8(1):011010-011010-11. doi:10.1115/1.4006201 Figure Legend: Experimental LE and peak count: (a) and (b) typical linear fits for the local rate of divergence, (c) largest LE as a function of the forcing frequency, and (d) corresponding peak count result