Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry

Georgiades, Fotios; Peeters, Maxime; Kerschen, Gaëtan; Golinval, Jean‐Claude; Ruzzene, Massimo

doi:10.2514/1.40461

Cited by 58 publications

(59 citation statements)

References 25 publications

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“…qualitative changes in system dynamics (see e.g. [19][20][21][22][23][24][25][26][27][28]). Nonlinear localization has been shown to appear not only in conservative systems [19] but also in friction-excited chains of weakly coupled oscillators [20,21], where the authors showed that the localization phenomenon is strongly related to the bistable behaviour of the single oscillator in the chain.…”

Section: Introductionmentioning

confidence: 99%

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Papangelo

Fontanela

Grolet

et al. 2019

Journal of Sound and Vibration

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Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.

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Section: Introductionmentioning

confidence: 99%

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Papangelo

Fontanela

Grolet

et al. 2019

Journal of Sound and Vibration

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“…We note that all these results hold for different sizes of the regularization intervals, as shown in Figure 16. Another interesting nonlinear phenomenon that the SmallSat satellite exhibits is the so-called localization phenomenon [18,33,34] during which new nonlinear modes with deformation localized to specific components of the structure appear. Figure 17 presents the FEP of NNM 7.…”

Section: Nonlinear Modal Analysis Of the Smallsat Spacecraftmentioning

confidence: 99%

Complex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes

2014

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This paper investigates the dynamics of a real-life aerospace structure possessing a strongly nonlinear component with multiple mechanical stops. A full-scale finite element model is built for gaining additional insight into the nonlinear dynamics that was observed experimentally, but also for uncovering additional nonlinear phenomena, such as quasiperiodic regimes of motion. Forced/unforced, damped/undamped numerical simulations are carried out using advanced techniques and theoretical concepts such as numerical continuation and nonlinear normal modes.

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“…Furthermore, the algorithm automatically controls the step size and exploits symmetry in the response to increase computational efficiency. So far, the authors of this method have computed the periodic solutions of a number of unforced, undamped nonlinear systems of high complexity and high order [24,[36][37][38][39][40][41][42] with exceptional detail. However, they have not extended their methods to the calculations of periodic solution branches of harmonically forced nonlinear systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Continuation of Periodic Orbits for Harmonically Forced Nonlinear Systems

Sracic

Allen

2011

Civil Engineering Topics, Volume 4

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A nonlinear structure will often respond periodically when it is excited with a sinusoidal force. Several methods are available that can compute the periodic response for various drive frequencies, which is analogous to the frequency response function for a linear system. The simplest approach would be to compute a sequence of simulations where the equations of motion are integrated until damping drives the system to steady state, but that approach suffers from a number of drawbacks. Recently, numerical methods have been proposed that use a solution branch continuation technique to find the free response of unforced, undamped nonlinear systems for different values of a control parameter. These are attractive because they are built around broadly applicable time-integration routines, so they are applicable to a wide range of systems. However, the continuation approach is not typically used to calculate the periodic response of a structural dynamic system to a harmonic force. This work adapts the numerical continuation approach to find the periodic, forced steady-state response of a nonlinear system. The method uses an adaptive procedure with a prediction step and a mode switching correction step based on Newton-Raphson methods. Once a branch of solutions has been computed, it explains how a full spectrum of harmonic forcing conditions affect the dynamic response of the nonlinear system. The approach is developed and applied to calculate nonlinear frequency response curves for a Duffing oscillator and a low order nonlinear cantilever beam.

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Modal Analysis of a Nonlinear Periodic Structure with Cyclic Symmetry

Cited by 58 publications

References 25 publications

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Complex dynamics of a nonlinear aerospace structure: numerical continuation and normal modes

Numerical Continuation of Periodic Orbits for Harmonically Forced Nonlinear Systems

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