Stabilization of solitons in coupled nonlinear pendulums with simultaneous external and parametric excitations

Jallouli, Aymen; Kacem, Najib; Bouhaddi, Noureddine

doi:10.1016/j.cnsns.2016.05.012

Cited by 26 publications

(18 citation statements)

References 27 publications

(36 reference statements)

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“…The most dominant example being 1D arrays of pendulums periodically coupled with springs which have been utilized to study a variety of intriguing phenomena pertaining to coupled nonlinear oscillators. These include solitons [18], breathers [19], energy transmission in band gaps [20] and most recently helical edge states in topological insulators [21]. To this end, however, exploiting the periodicity of pendulum chains as an inherent and self-reliant mechanism for vibration absorption remains uncharted territory.…”

Section: Introductionmentioning

confidence: 99%

Emergence of Pseudo-Phononic Gaps in Periodically Architected Pendulums

2019

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Rejection of unmitigated vibrational disturbances represents an ongoing dilemma in complex linkage systems. In this work, we present an inherent and self-reliant vibration isolation mechanism in architected periodic chains of serially pivoted pendulums. Absorption of external excitations is achieved by virtue of Bragg-type band gaps which stem from the emergent chain dynamics. Owing to its coupled dynamics, the self-repeating cell of a Phononic Crystal (PC) is not trivial and cannot be readily identified from the periodic arrangement by inspection. As such, this work entails the extraction of a "pseudo" unit cell of an equivalent PC lattice from the derived motion equations of a finite chain, which departs from traditional wave dispersion methods. The model presented herein comprises a chain of linked pendulums with periodic variations of inertial/geometrical properties, carrying a payload at one end. We ultimately show evidence of forbidden wave propagation in prescribed frequency regimes, reminiscent of band gaps in PC lattices. The presented framework can be invaluable in applications that require vibration reduction in the delivery of payloads including gantry cranes, robotic arms and space tethers.

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Section: Introductionmentioning

confidence: 99%

Emergence of Pseudo-Phononic Gaps in Periodically Architected Pendulums

2019

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“…In addition, it was shown that the mass impurity in a parametrically driven, damped nonlinear coupled pendula has striking influence on the high-frequency modes [20]. Recently, The influence of adding external harmonic excitation on the intrinsic localized modes of coupled pendulums chains parametrically excited has been investigated [21]. Although the dynamics of coupled nonlinear pendulums was thoroughly investigated in the frequency and timespace domains, there is a real need to perform profound analysis of the collective dynamics of such systems in order to identify practical relations with the nonlinear energy localization phenomena in terms of modal interactions and bifurcation topologies [22].…”

Section: Introductionmentioning

confidence: 99%

Investigation of modal interactions and their effects on the nonlinear dynamics of a periodic coupled pendulums chain

Bitar

Kacem

Bouhaddi

2017

International Journal of Mechanical Sciences

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The nonlinear dynamics of a weakly coupled pendulums chain is investigated under primary resonance. The coupled equations governing the nonlinear vibrations are normalized and transformed into a set of coupled complex algebraic equations using the multiple scales method coupled with standing wave decomposition. A model reduction method is proposed to calculate the dominant dynamics without significant loss of accuracy compared to the full model. The validity of the proposed semi-analytical method is verified, and its role in identifying the type of the solution branches is highlighted. The modal interactions and their effects on the nonlinear dynamics are studied in the frequency domain in order to emphasize the large number of multimode solution branches and the bifurcation topology transfer between the modal intensities. Basins of attraction analysis have been performed, showing that the distribution of the multimodal solution branches generated by all modes collectively increases by increasing the number of coupled pendulums.

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“…Khomeriki and Leon [25] demonstrated numerically and experimentally the existence of three tristable stationary states. Jallouli et al [26] investigated the nonlinear dynamics of a two-dimensional array of coupled pendulums under parametric excitation and, recently [27], the energy localization phenomenon in an array of coupled pendulums under simultaneous external and parametric excitations by means of a nonlinear Schrodinger equation. The authors show that adding an external excitation increases the existence region of solitons.…”

Section: Introductionmentioning

confidence: 99%

Robustness Analysis of the Collective Nonlinear Dynamics of a Periodic Coupled Pendulums Chain

et al. 2017

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Perfect structural periodicity is disturbed in presence of imperfections. The present paper is based on a realistic modeling of imperfections, using uncertainties, to investigate the robustness of the collective nonlinear dynamics of a periodic coupled pendulums chain. A generic discrete analytical model combining multiple scales method and standing-wave decomposition is proposed. To propagate uncertainties through the established model, the generalized Polynomial Chaos Expansion is used and compared to the Latin Hypercube Sampling method. Effects of uncertainties are investigated on the stability and nonlinearity of two and three coupled pendulums chains. Results prove the satisfying approximation given by the generalized Polynomial Chaos Expansion for a significantly reduced computational time, with respect to the Latin Hypercube Sampling method. Dispersion analysis of the frequency responses show that the nonlinear aspect of the structure is strengthened, the multistability domain is wider, more stable branches are obtained and thus multimode solutions are enhanced. More fine analysis is allowed by the quantification of the variability of the attractors' contributions in the basins of attraction. Results demonstrate benefits of presence of imperfections in such periodic structure. In practice, imperfections can be functionalized to generate energy localization suitable for several engineering applications such as vibration energy harvesting.

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Stabilization of solitons in coupled nonlinear pendulums with simultaneous external and parametric excitations

Cited by 26 publications

References 27 publications

Emergence of Pseudo-Phononic Gaps in Periodically Architected Pendulums

Emergence of Pseudo-Phononic Gaps in Periodically Architected Pendulums

Investigation of modal interactions and their effects on the nonlinear dynamics of a periodic coupled pendulums chain

Robustness Analysis of the Collective Nonlinear Dynamics of a Periodic Coupled Pendulums Chain

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