Fast--slow analysis of a bistable nonlinear energy sink for simultaneous vibration mitigation and piezoelectric energy harvesting
Abstract
Nonlinear energy sinks (NES), and in particular bistable NES (BNES), provide a passive means of mitigating vibrations over a broad frequency range through targeted energy transfer. When coupled with a piezoelectric harvester (PEH), the absorbed vibrational energy can be converted into electricity, enabling self-powered structural monitoring, for instance in wind turbines. In this study, a harmonically forced damped oscillator is coupled to a BNES equipped with a PEH connected to a resistive circuit. Numerical simulations reveal a range of response regimes, including periodic, strongly modulated, and chaotic dynamics, together with their associated voltage outputs. The Multiple Scale/Harmonic Balance Method is adapted to account for the nonzero-mean oscillations of the BNES, yielding a reduced model, the amplitude-phase modulation dynamics (APMD). Its fast--slow analysis provides the critical manifold, its fold points, and their stability. The PEH parameters are shown to enter the fold conditions in closed form, demonstrating that the harvester can reshape the geometry of the critical manifold rather than merely rescale it. The harvested energy is finally related to the location of the fold points, revealing a trade-off between vibration mitigation and energy harvesting.
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BibTeX
@misc{couineaux2026fastslow,
title = {{Fast--slow analysis of a bistable nonlinear energy sink for simultaneous vibration mitigation and piezoelectric energy harvesting}},
author = {Audrey Couineaux and Baptiste Bergeot and Guylaine Poulin-Vittrant},
howpublished = {HAL},
year = {2026},
month = aug,
url = {https://hal.science/hal-05803651v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - Fast--slow analysis of a bistable nonlinear energy sink for simultaneous vibration mitigation and piezoelectric energy harvesting
AU - Audrey Couineaux
AU - Baptiste Bergeot
AU - Guylaine Poulin-Vittrant
PY - 2026
DA - 2026/08/18
PB - HAL
UR - https://hal.science/hal-05803651v1
AB - Nonlinear energy sinks (NES), and in particular bistable NES (BNES), provide a passive means of mitigating vibrations over a broad frequency range through targeted energy transfer. When coupled with a piezoelectric harvester (PEH), the absorbed vibrational energy can be converted into electricity, enabling self-powered structural monitoring, for instance in wind turbines. In this study, a harmonically forced damped oscillator is coupled to a BNES equipped with a PEH connected to a resistive circuit. Numerical simulations reveal a range of response regimes, including periodic, strongly modulated, and chaotic dynamics, together with their associated voltage outputs. The Multiple Scale/Harmonic Balance Method is adapted to account for the nonzero-mean oscillations of the BNES, yielding a reduced model, the amplitude-phase modulation dynamics (APMD). Its fast--slow analysis provides the critical manifold, its fold points, and their stability. The PEH parameters are shown to enter the fold conditions in closed form, demonstrating that the harvester can reshape the geometry of the critical manifold rather than merely rescale it. The harvested energy is finally related to the location of the fold points, revealing a trade-off between vibration mitigation and energy harvesting.
ER -