Dynamical Integrity: A Novel Paradigm for Evaluating Load Carrying Capacity

Rega, Giuseppe; Lenci, Stefano; Ruzziconi, Laura

doi:10.1007/978-3-319-99710-0_2

Cited by 4 publications

(1 citation statement)

References 98 publications

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“…This analysis is conducted by following the seminal works of Thompson [51], and Rega and Lenci [52,53]. For a deep overview, we refer to Thompson [54] and Rega et al [55]; for applications on AFM we refer to Settimi and Rega [56], and for applications on MEMS to Ruzziconi et al [26].…”

Section: The Principal Resonance: Pres and Pnonresmentioning

confidence: 99%

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

et al. 2021

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This work investigates the dynamics of a microbeam-based MEMS device in the neighborhood of a 2:1 internal resonance between the third and fifth vibration modes. The saturation of the third mode and the concurrent activation of the fifth are observed. The main features are analyzed extensively, both experimentally and theoretically. We experimentally observe that the complexity induced by the 2:1 internal resonance covers a wide driving frequency range. Constantly comparing with the experimental data, the response is examined from a global perspective, by analyzing the attractor-basins scenario. This analysis is conducted both in the thirdmode and fifth-mode planes. We show several metamorphoses occurring as proceeding from the principal resonance to the 2:1 internal resonance, up to the final disappearance of the resonant and non-resonant attractors. The shape and wideness of all the basins are examined. Despite they are progressively eroded, an appreciable region is detected where the compact cores of the attractors involved in the 2:1 internal resonance remain substantial, which allows effectively operating them under realistic conditions. The dynamical integrity of each resonant branch is discussed, especially as approaching the bifurcation points where the system becomes more vulnerable to the dynamic pull-in instability.

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Section: The Principal Resonance: Pres and Pnonresmentioning

confidence: 99%

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

et al. 2021

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Intra-well and cross-well chaos in membranes and shells liable to buckling

et al. 2020

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Parameter uncertainty and noise effects on the global dynamics of an electrically actuated microarch

Benedetti

Gonçalves

Lenci

et al. 2023

J. Micromech. Microeng.

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This work aims to study the effect of uncertainties and noise on the nonlinear global dynamics of a micro-electro-mechanical arch obtained from an imperfect microbeam under an axial load and electric excitation. An adaptative phase-space discretization strategy based on an operator approach is proposed. The Ulam method, a classical discretization of flows in phase-space, is extended here to nondeterministic cases. A unified description is formulated based on the Perron-Frobenius, Koopman, and Foias linear operators. Also, a procedure to obtain global structures in the mean sense of systems with parametric uncertainties is presented. The stochastic basins of attraction and attractors’ distributions replace the usual basin and attractor concepts. For parameter uncertainty cases, the phase-space is augmented with the corresponding probability space. The microarch is assumed to be shallow and modelled using a nonlinear Bernoulli-Euler beam theory and is discretized by the Galerkin method using as interpolating function the linear vibration modes. Then, from the discretized multi degree of freedom model (mdof) model, an accurate single degree of freedom (sdof) reduced order model, based on theory of nonlinear normal modes, is derived. Several competing attractors are observed, leading to different (acceptable or unacceptable) behaviours. Extensive numerical simulations are performed to investigate the effect of noise and uncertainties on the coexisting basins of attraction, attractors` distributions, and basins boundaries. The appearance and disappearance of attractors and stochastic bifurcation are observed, and the time-dependency of stochastic responses is demonstrated, with long-transients influencing global behaviour. To consider uncertainties and noise in design, a dynamic integrity measure is proposed via curves of constant probability, which give quantitative information about the changes in structural safety. For each attractor, the basin robustness as a function of a stochastic parameter is investigated. The weighted basin area can quantify the integrity of nondeterministic cases, being also the most natural generalization of the global integrity measure. While referring to particular MEMS, the relevance of the dynamical integrity analysis for stochastic systems to quantify tolerances and safety margins is underlined here.

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Dynamical Integrity: A Novel Paradigm for Evaluating Load Carrying Capacity

Cited by 4 publications

References 98 publications

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

Internal resonance in the higher-order modes of a MEMS beam: experiments and global analysis

Intra-well and cross-well chaos in membranes and shells liable to buckling

Parameter uncertainty and noise effects on the global dynamics of an electrically actuated microarch

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