Twinkling Phenomena in Snap-Through Oscillators

Feeny, Brian F.; Diaz, Alfredo Peña

doi:10.1115/1.4000764

Cited by 14 publications

(9 citation statements)

References 24 publications

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“…2(a), which results in a chain of particles grounded nonlinearly and in a bistable onsite potential [247]. Again, small, moderate, and large excitations of the chain will result in, respectively, linear, weakly nonlinear, and strongly nonlinear wave motion [248].…”

Section: Multistability and Nonlinear Metamaterialsmentioning

confidence: 99%

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Kochmann

Bertoldi

2017

Applied Mechanics Reviews

189

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Instabilities in solids and structures are ubiquitous across all length and time scales, and engineering design principles have commonly aimed at preventing instability. However, over the past two decades, engineering mechanics has undergone a paradigm shift, away from avoiding instability and toward taking advantage thereof. At the core of all instabilities-both at the microstructural scale in materials and at the macroscopic, structural level-lies a nonconvex potential energy landscape which is responsible, e.g., for phase transitions and domain switching, localization, pattern formation, or structural buckling and snapping. Deliberately driving a system close to, into, and beyond the unstable regime has been exploited to create new materials systems with superior, interesting, or extreme physical properties. Here, we review the state-of-the-art in utilizing mechanical instabilities in solids and structures at the microstructural level in order to control macroscopic (meta)material performance. After a brief theoretical review, we discuss examples of utilizing material instabilities (from phase transitions and ferroelectric switching to extreme composites) as well as examples of exploiting structural instabilities in acoustic and mechanical metamaterials.

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Section: Multistability and Nonlinear Metamaterialsmentioning

confidence: 99%

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Kochmann

Bertoldi

2017

Applied Mechanics Reviews

189

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“…This model is an excellent model to mimic the experiment since both the lengths and the radii of the magnets are in the order of 0.01 meters and the minimum distance d m between the magnet centers is on the order of the length l m of the magnets. Using the magnetic force, from equation (11), between the fixed and oscillating magnets of the twinkler and the spring forces from equation (1), the governing equations of motion of the SDOF nonlinear energy generator are represented in equation (15).…”

Section: Numerical Simulation Of the Twinkling Energy Generatormentioning

confidence: 99%

“…To be able to harvest such energy, it is critical to understand the underlying dynamics of the coupled snap-through oscillators. Several authors have studied the dynamics of various snap-through negative-stiffness and bistable systems [1]- [8]. Vibration-based energy harvesting from linear systems [9], [10] has been optimized experimentally [11]- [13] by tuning the forcing frequency to the natural frequency of the oscillator.…”

Section: Introductionmentioning

confidence: 99%

Snap-through twinkling energy generation through frequency up-conversion

Panigrahi

Bernard

Feeny

et al. 2017

Journal of Sound and Vibration

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A novel experimental energy harvester is investigated for its energy harvesting capability by frequency up-conversion using snap-through structures. In particular, a single-degree-of-freedom (SDOF) experimental energy harvester model is built using a snap-through nonlinear element. The snap-through dynamics is facilitated by the experimental setup of a twinkling energy generator (TEG) consisting of linear springs and attracting cylindrical bar magnets. A cylindrical coil of enamel-coated magnet wire is used as the energy generator. The governing equations are formulated mathematically and solved numerically for a direct comparison with the experimental results. The experimental TEG and the numerical simulation results show 25-fold frequency up-conversion and the power harvesting capacity of the SDOF TEG.

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“…In addition, previous results have shown that chains of elements with nonmonotonic (piecewise-linear) forcedisplacement relations can dissipate energy at a fast rate by transforming kinetic energy into high-frequency oscillations (so-called twinkling modes). This was later extended to chains with smooth nonmonotonic force-displacement relations in a comprehensive stability analysis [75]. It was also experimentally demonstrated in chains of granular particles with a nonsmooth contact interaction [76].…”

Section: Introductionmentioning

confidence: 99%

“…[75] and references therein. Here we disregard just oscillations and focus on the propagating kink soliton whose energy can be determined by integrating the Hamiltonian spatial density over the complete lattice at any given time.…”

Section: Energy Of the Kink Solitonmentioning

confidence: 99%

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

2014

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We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

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Twinkling Phenomena in Snap-Through Oscillators

Cited by 14 publications

References 24 publications

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions

Snap-through twinkling energy generation through frequency up-conversion

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

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