Energy Transfer from High-Frequency to Low-Frequency Modes in Structures

Nayfeh, A. H.; Mook, Dean T.

doi:10.1115/1.2838662

Cited by 20 publications

(6 citation statements)

References 13 publications

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“…We use the term non-resonant to distinguish from commonly studied one-to-one, one-to-two, and oneto-three resonances. This type of nonlinear modal coupling was first studied by Nayfeh & Nayfeh (1992) in structural systems. For structural systems, which typically have cubic nonlinearity, the mechanism for the coupling is found to be caused by the cross-softening effect of the fast mode on the slow mode (Feng 1995).…”

Section: Discussionmentioning

confidence: 99%

“…In the present paper we will show the presence of modal coupling when no apparent frequency relationships exist between the interacting modes. This work is motivated by the paper of Nayfeh & Nayfeh (1992) on nonlinear structural vibrations. Nayfeh & Nayfeh show that nonlinear modal coupling occurs in linearly independent modes whose frequencies are widely spaced.…”

Section: Introductionmentioning

confidence: 99%

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Instability caused by the coupling between non-resonant shape oscillation modes of a charged conducting drop

Feng

1997

J. Fluid Mech.

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By examining the modal interaction between two non-resonant shape oscillation modes of a charged liquid drop, we have identified a new route to instability via nonlinear coupling. We present numerical simulation results to show that when shape perturbation of a high-mode number Legendre mode is applied to the drop, the prolate–oblate mode of the drop may grow unbounded. Using multiple-scale analysis, we derive amplitude equations for the high-mode-number shape mode and the prolate–oblate mode to show the nonlinear coupling between the two modes.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Instability caused by the coupling between non-resonant shape oscillation modes of a charged conducting drop

Feng

1997

J. Fluid Mech.

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“…Instead, we prefer to model the pendulum as a cantilevered vibration "amplifier". Previous research [28] indicated that we might design a system with the opposite parametric condition in order to produce a large-amplitude vibration on the PVDF stalk with lowamplitude high-frequency excitation.…”

Section: Simplified Dynamic System Modelmentioning

confidence: 99%

Vertical-Stalk Flapping-Leaf Generator for Wind Energy Harvesting

Lipson

2009

Volume 2: Multifunctional Materials; Enabling Technologies and Integrated System Design; Structural Health Monitoring/Nde; Bio-

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We study a parallelized flapping piezo-leaf generator for harvesting ambient wind energy and demonstrate an initial design. We fabricated prototypes in various configurations and performed a series of experiments to study performance trends. We propose a novel vertical-stalk L-shape design that exhibits improved output power density over horizontal piezoelectric configurations. While a significant power density performance gap still exists between the current state of piezoelectric devices and commercial wind turbines, their advantage remains in their robust solid-state, low-cost, low-maintenance and scalable construction.

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“…Internal resonances (IRs) under certain conditions also promote energy transfer between non-linear modes [14,[42][43][44][45]. It was explained, both theoretically and experimentally, how a low-amplitude highfrequency excitation can produce a large-amplitude low-frequency response (called energy cascading [46]).…”

Section: Introductionmentioning

confidence: 99%

Passive non-linear targeted energy transfer and its applications to vibration absorption: A review

Lee

Vakakis

Bergman

et al. 2008

Proceedings of the Institution of Mechanical Engineers, Part K:

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This review paper discusses recent efforts to passively move unwanted energy from a primary structure to a local essentially non-linear attachment (termed a non-linear energy sink) by utilizing targeted energy transfer (TET) (or non-linear energy pumping). First, fundamental theoretical aspects of TET will be discussed, including the essentially non-linear governing dynamical mechanisms for TET. Then, results of experimental studies that validate the TET phenomenon will be presented. Finally, some current engineering applications of TET will be discussed. The concept of TET may be regarded as contrary to current common engineering practise, which generally views non-linearities in engineering systems as either unwanted or, at most, as small perturbations of linear behaviour. Essentially non-linear stiffness elements are intentionally introduced in the design that give rise to new dynamical phenomena that are very beneficial to the design objectives and have no counterparts in linear theory. Care, of course, is taken to avoid some of the unwanted dynamic effects that such elements may introduce, such as chaotic responses or other responses that are contrary to the design objectives.

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Energy Transfer from High-Frequency to Low-Frequency Modes in Structures

Cited by 20 publications

References 13 publications

Instability caused by the coupling between non-resonant shape oscillation modes of a charged conducting drop

Instability caused by the coupling between non-resonant shape oscillation modes of a charged conducting drop

Vertical-Stalk Flapping-Leaf Generator for Wind Energy Harvesting

Passive non-linear targeted energy transfer and its applications to vibration absorption: A review

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