Experimental nonlinear localization in a periodically forced repetitive system of coupled magnetoelastic beams

Emad, J.M.; Vakakis, Alexander F.; Miller, N.R.

doi:10.1016/s0167-2789(99)00176-1

Cited by 5 publications

(2 citation statements)

References 11 publications

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“…Response localizations have been demonstrated in experiments of macro-cantilever beam arrays, wherein the beams represent the blades or components of turbomachinery and VEHs [8,9,10,11,12]. The localized high amplitude oscillations can, on one hand, be destructive in turbomachinery [2,13,14,15,16] and, on the other hand, be beneficial for energy harvesting systems [17,18].…”

Section: XI F(t)mentioning

confidence: 99%

Most probable escape paths in periodically driven nonlinear oscillators

Cilenti,

Cameron,

Balachandran

2022

Preprint

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The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and transitions between them may occur under the influence of random factors. A methodology for finding most probable escape paths and estimating the transition rates in the small noise limit is developed and applied to a collection of arrays of coupled monostable oscillators with cubic nonlinearity, weak damping, and harmonic external forcing. The methodology is built upon the action plot method (Beri et al., 2005) and relies on the large deviation theory, optimal control theory, and Floquet theory. The action plot method is promoted to non-autonomous high-dimensional systems, and a method is proposed for solving the arising optimization problem with discontinuous objective function restricted to a certain manifold. The most probable escape paths between stable vibrational modes in arrays of up to five oscillators and the corresponding quasipotential barriers are computed and visualized. The dependence of the quasipotential barrier of the parameters on the system is discussed.Response transitions from one dynamic state to another can occur due to random perturbations in a variety of systems, including mechanical and structural systems. Some examples are sensor arrays, energy harvesters, and rotating machinery. The aim of the present work is to elucidate these transitions, in particular, when the random perturbations are weak. To that end, a methodology based on the Action Plot Method from Large Deviation Theory and Optimal Control Theory is developed and illustrated for a range of periodically forced systems.

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Section: XI F(t)mentioning

confidence: 99%

Most probable escape paths in periodically driven nonlinear oscillators

Cilenti,

Cameron,

Balachandran

2022

Preprint

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“…Passive nonlinear localization was extensively studied in previous works for discrete 3,4] and continuous systems 3,5,6]. In these works it was shown that weakly coupled nonlinear oscillators can possess strong and weak localized modes corresponding to energy con nement in one or more substructures of the system.…”

Section: Introductionmentioning

confidence: 99%

Mode Localization Induced by a Nonlinear Control Loop

M’Closkey

Vakakis

Gutierrez

2001

Normal Modes and Localization in Nonlinear Systems

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We present the analysis of a nonlinear control system that is used to excite and maintain a speci ed amplitude of oscillation in the Jet Propulsion Laboratory vibratory gyroscope. This experimental application shows that nonlinear localization through active means can be implemented in a practical system when it is desirable to con ne the response to a favorable mode. The closed-loop system response predicted by the model shows very close agreement w i t h t h e experimental results for a signi cant range of controller parameters. We also experimentally demonstrate that the actively localized motion is eliminated through bifurcation, similar to what was observed in previous passive localization studies applied to extended exible oscillators.

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