Energy harvesting using rattleback: Theoretical analysis and simulations of spin resonance

Nanda, Aditya; Singla, Puneet; Karami, M. Amin

doi:10.1016/j.jsv.2015.12.032

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…Similar simulations were performed by Lindberg and Longman independently [16]. Nanda et al simulated the spin resonance of the rattleback on a vibrating base [17].…”

Section: Introductionmentioning

confidence: 78%

Rattleback dynamics and its reversal time of rotation

Kondo

Nakanishi

2017

Phys. Rev. E

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A rattleback is a rigid, semi-elliptic toy which exhibits unintuitive behavior; when it is spun in one direction, it soon begins pitching and stops spinning, then it starts to spin in the opposite direction, but in the other direction, it seems to spin just steadily. This puzzling behavior results from the slight misalignment between the principal axes for the inertia and those for the curvature; the misalignment couples the spinning with the pitching and the rolling oscillations. It has been shown that under the no-slip condition and without dissipation the spin can reverse in both directions, and Garcia and Hubbard obtained the formula for the time required for the spin reversal tr [Proc. R. Soc. Lond. A 418, 165 (1988)]. In this work, we reformulate the rattleback dynamics in a physically transparent way and reduce it to a three-variable dynamics for spinning, pitching, and rolling. We obtain an expression of the Garcia-Hubbard formula for tr by a simple product of four factors: (1) the misalignment angle, (2) the difference in the inverses of inertia moment for the two oscillations, (3) that in the radii for the two principal curvatures, and (4) the squared frequency of the oscillation. We perform extensive numerical simulations to examine validity and limitation of the formula, and find that (1) the Garcia-Hubbard formula is good for both spinning directions in the small spin and small oscillation regime, but (2) in the fast spin regime especially for the steady direction, the rattleback may not reverse and shows a rich variety of dynamics including steady spinning, spin wobbling, and chaotic behavior reminiscent of chaos in a dissipative system.

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“…Similar simulations were performed by Lindberg and Longman independently [16]. Nanda et al simulated the spin resonance of the rattleback on a vibrating base [17].…”

Section: Introductionmentioning

confidence: 78%

Rattleback dynamics and its reversal time of rotation

Kondo

Nakanishi

2017

Phys. Rev. E

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“…The repulsive force between the magnets reduces the natural frequency of the beam and makes the vibration system nonlinear and, therefore, less sensitive to the frequency of excitation. Using magnetic forces for tuning and manipulation of mechanical dynamical systems (Nanda and Karami, 2018;Nanda, 2018, Nanda et al, 2016 has a long and storied history. A schematic diagram of a nonlinear harvester is shown in Figure 1(b).…”

Section: Nonlinear Energy Harvestersmentioning

confidence: 99%

“…This article focuses on energy harvesting from vibrations. Such ambient energy may come from vibrations of a bridge (Erturk, 2011), the spinning of a top (Nanda et al, 2016), the human heart beating (Amin Karami and Inman, 2012), or mechanical motion of blood vessels (Nanda and Karami, 2017). Minute amounts of ambient energy can power up sensor nodes and therefore go a long way in reducing wiring complications and/or the need of changing batteries frequently.…”

Section: Introductionmentioning

confidence: 99%

Conjugate unscented transformation–based uncertainty analysis of energy harvesters

Nanda

Singla

Karami

2018

Journal of Intelligent Material Systems and Structures

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This article presents a probabilistic approach to investigate the effect of parametric uncertainties on the mean power, tip deflection, and tip velocity of linear and nonlinear energy harvesting systems. Recently developed conjugate unscented transformation algorithm is used to compute the statistical moments of the output variables with multidimensional Gaussian uncertainty in parameters. The principle of maximum entropy is used to construct the probability density function of output variables from the knowledge of obtained statistical moments. The probability density functions for mean power were significantly complicated in shape with two and three distinct peaks for the nonlinear monostable and nonlinear bistable harvesters, respectively. Monte-Carlo simulations with N = 8 × 104 samples for monostable harvester and N = 6.5 × 104 samples for bistable harvester were used for validating the probability density functions. It is concluded that conjugate unscented transformation methodology affords a significant computational advantage without compromising accuracy. In addition, using conjugate unscented transformation method, we show that the dependence of mean power on parameters (excitation frequency, excitation amplitude, etc.), when multidimensional uncertainties are present, is decidedly different relative to a purely deterministic trend. The discrepancy in predicted power between the deterministic and uncertain trends for the monostable harvester, for instance, reach a maximum of 100%, 234%, and 110% for base frequency, base acceleration, and magnet gap, respectively. The deterministic trend consistently overestimates the harvested power relative to the uncertain trends. This work, therefore, may have applications in evaluating “worst case scenario” for harvested power. The major advantage of the presented methodology relative to extant techniques in energy harvesting literature is the accurate and computationally effective applicability to multidimensional uncertainty in parameters.

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“…Влиянию трения на динамику вращения/качения твердого тела посвящено много работ (начиная с классических монографий [1][2][3] и до современных исследований [4,5]), в то время как влиянию сухого трения в подшипниках и подпятниках на вращательную динамику ротора с чисто динамическим дисбалансом -мало (для опор качения см., например, [6,7]). Основной объем работ (см., например, [8][9][10]) посвящается так называемому кельтскому камню (Rattleback -"задрожал и назад! "), являющему собой интересный с точки зрения теории динамических систем объект [10].…”

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“…Основной объем работ (см., например, [8][9][10]) посвящается так называемому кельтскому камню (Rattleback -"задрожал и назад! "), являющему собой интересный с точки зрения теории динамических систем объект [10].…”

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Kinetics of dynamically unbalanced rotator with dry sliding friction in the axle supports

Chistyakov¹

2018

Izv. vysš. učebn. zaved., Priborostr.

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Математически моделируется динамика свободного и вынужденного вращения твердого тела вокруг центральной, но не главной оси инерции Oz, опирающейся на подшипник и подпятник скольжения, а также в условиях действия гидродинамического и сухого трения. Показано, что возникающие в плоскостях оси инерционные пары M x , y (J xz , J yz , ω, ε) и пары сухого трения зависят не только от центробежных моментов инерции J xz , J yz и угловой скорости ω, но и от ускорения ε. Такая зависимость приводит в общем случае к динамическим уравнениям с иррациональной правой частью, а в частном-с разрывной. Проинтегрированы аналитически и численно уравнения простейших видов движений.

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Energy harvesting using rattleback: Theoretical analysis and simulations of spin resonance

Cited by 10 publications

References 17 publications

Rattleback dynamics and its reversal time of rotation

Rattleback dynamics and its reversal time of rotation

Conjugate unscented transformation–based uncertainty analysis of energy harvesters

Kinetics of dynamically unbalanced rotator with dry sliding friction in the axle supports

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