Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: (a) Asymmetrically constrained inverted pendulum under coexisting static axial load p and lateral dynamic excitation q1 (P = p; Q = q + q1 sin(ωt)) [40]. (b) Integrity surface for a fixed value of static imperfection q, with the robustness (for varying p) and erosion (for varying q1) profiles highlighting meaningful excitation coupling effects [30].

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: (a) Model of guyed mast with equal (k1 = k2 = k3) springs, under horizontal excitation F at the base in anyone of the three symmetry planes [35]. (b) Comparison of GIM erosion profiles for perfect and imperfect models, under either harmonic or control periodic (harmonic + one superharmonic) excitation [35], with also the homoclinic bifurcation thresholds (vertical lines) triggering the erosion.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: Parametrically excited pendulum (sole vertical support motion). (a) Response chart in the excitation parameters plane (ω, p): numerical boundaries of the region of existence of period 1 rotations (lines) and experimentally observed rotations (triangles). (b) Relevant IF and LIM profiles for h = 0.015 and ω = 1.3 (subfigures taken in part from Ref. [1]).

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: MEMS capacitive accelerometer with harmonic excitation close to primary resonance (Ωres = 192.5 Hz). (a) Response chart, with theoretical regions of existence of nonresonant/resonant attractors and of inevitable escape (delimited by solid lines), along with thresholds of experimental escape (dots) against level curves (dashed) of IF. (b) IF (solid) and LIM (dashed) profiles of nonresonant (left) and resonant (right) attractors at VAC = 15 V (lines with squares) and VAC = 30 V (lines with triangles) (subfigures taken in part from Ref. [1]).

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: Noncontact AFM. (a) Theoretical global (solid) and local (dashed) stability boundaries obtained separately with increasing parametric (the upper in the left part of the picture) and external (the lower in the left part of the picture) excitation in a frequency region encompassing fundamental (primary) and principal (subharmonic) resonances [32]. (b) Around fundamental resonance of parametric excitation, comparison between theoretical, global (bd) and local (ni), stability thresholds, and practical stability thresholds, the latter corresponding to level curves of possibly acceptable residual integrity depending on a priori defined design targets [32].

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: Noncontact AFM. Bounded resonant (PIH) and nonresonant (PIL) solutions, and global escape threshold for uncontrolled (a) and controlled (b) systems under scan excitation [71]. The latter also accounts for the occurrence of TR and T bifurcations, besides the SN and PD ones also occurring for the former.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: Noncontact AFM. Global escape thresholds for controlled (the thin deep tongues) and uncontrolled systems under scan excitation [71]. Dark gray area is the stability region of both controlled and uncontrolled system and light gray area is stable only for uncontrolled system.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: A Global Dynamics Perspective for System Safety From Macro- to Nanomechanics: Analysis, Control, and Design Engineering Appl. Mech. Rev. 2015;67(5):050802-050802-19. doi:10.1115/1.4031705 Figure Legend: Schematic safety chart for a system subjected to a harmonic excitation