Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators

Gendelman, Oleg; Sapsis, Themistoklis P.; Vakakis, Alexander F.; Bergman, Lawrence A.

doi:10.1016/j.jsv.2010.08.014

Cited by 86 publications

(30 citation statements)

References 15 publications

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“…This is related to how a spring with a lower n-value has lower stiffness for small displacements. We limit the smallest allowable n-value to 3 to ensure that the spring is essentially nonlinear and has a cubic spring-like stiffness (as described in Section 2), which is required for a robust energy harvester [4,13,14,350 15]. Fig.s 13a and 13 b, therefore, show the power harvested when we vary the 1DOF nonlinear system cantilever rigidity and electromagnetic damping.…”

Section: Energy Harvesting Performance and Robustness From Walking VImentioning

confidence: 99%

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Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

Kluger

Sapsis

Slocum

2015

Journal of Sound and Vibration

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In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is comprised of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly with the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces.To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized by the cantilever-surface mechanism. The optimization results show that the 2DOF nonlinear system presents the best average performance when the excitation signals have three possible forms. Moreover, we observe that while for the linear systems the optimal performance is obtained for small values of the electromagnetic damping, for the 2DOF nonlinear system optimal performance is achieved for large values of damping. This feature is of particular importance for the the system's robustness to parasitic damping.

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Section: Energy Harvesting Performance and Robustness From Walking VImentioning

confidence: 99%

“…For example, Mitcheson et al [10] robust to variations in the external excitation and preserve their good performance level for a wide range of conditions, as described in Vakakis et al [4], Gendelman et al [13], Sapsis et al [14], and Quinn et al [15]. The simplest form of an essentially nonlinear spring is a cubic one.…”

Section: Introductionmentioning

confidence: 99%

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

Kluger

Sapsis

Slocum

2015

Journal of Sound and Vibration

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“…Nonlinear vibration absorbers (NESs) are light weight devices, possessing essentially nonlinear stiffness and low damping [18][19][20][21]. When connected to a linear (primary) system, the NES nonlinearity couples with the vibration modes of the primary system, allowing irreversible energy transfer between them [22].…”

Section: Introductionmentioning

confidence: 99%

Targeted energy transfer and modal energy redistribution in automotive drivetrains

et al. 2016

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The new generations of compact high output power-to-weight ratio internal combustion engines generate broadband torsional oscillations, transmitted to lightly damped drivetrain systems. A novel approach to mitigate these untoward vibrations can be the use of nonlinear absorbers. These act as Nonlinear Energy Sinks (NESs). The NES is coupled to the primary (drivetrain) structure, inducing passive irreversible targeted energy transfer (TET) from the drivetrain system to the NES. During this process, the vibration energy is directed from the lower-frequency modes of the structure to the higher ones. Thereafter, vibrations can be either dissipated through structural damping or consumed by the NES. This paper uses a lumped parameter model of an automotive driveline to simulate the effect of TET and the assumed modal energy redistri- bution. Significant redistribution of vibratory energy is observed through TET. Furthermore, the integrated optimization process highlights the most effective configuration and parametric evaluation for use of NES.

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“…Nonlinear oscillator models represent a wide class of dynamic systems in many areas of physics and engineering [1][2][3]. For example, the classic Duffing model for mechanical systems [4,5], the delayed-reaction model for sensors and actuators [6], the time-varying mass model for crane and bridge cables [7], the M-shaped bent-beam model [8], and the coupled linear-nonlinear oscillator model [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions

Chen

Dunne

2016

Journal of Sound and Vibration

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A new algorithm is proposed to combine the split-frequency harmonic balance method (SF-HBM) with arc-length continuation (ALC) for accurate tracing of the frequency response of oscillators with non-expansible nonlinearities. ALC is incorporated into the SF-HBM in a two-stage procedure: Stage I involves finding a reasonably accurate response frequency and solution using a relatively large number of low-frequency harmonics. This step is achieved using the SF-HBM in conjunction with ALC. Stage II uses the SF-HBM to obtain a very accurate solution at the frequency obtained in Stage I. To guarantee rapid path tracing, the frequency axis is appropriately subdivided. This gives high chance of success in finding a globally optimum set of harmonic coefficients. When approaching a turning point however, arc-lengths are adaptively reduced to obtain a very accurate solution. The combined procedure is tested on three hardening stiffness examples: a Duffing model; an oscillator with non-expansible stiffness and single harmonic forcing; and an oscillator with nonexpansible stiffness and multiple-harmonic forcing. The results show that for non-expansible nonlinearities and multiple-harmonic forcing, the proposed algorithm is capable of tracingout frequency response functions with high accuracy and efficiency.

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Enhanced passive targeted energy transfer in strongly nonlinear mechanical oscillators

Cited by 86 publications

References 15 publications

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

Targeted energy transfer and modal energy redistribution in automotive drivetrains

A fast continuation scheme for accurate tracing of nonlinear oscillator frequency response functions

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