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ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

The Delayed Oscillator and Energy Harvesting

Journal of Vibration Testing and System Dynamics 10(4) (2026) 379--405 | DOI:10.5890/JVTSD.2026.12.006

Zakaria Ghouli$^{1,2}$

$^1$ Royal Naval School, Casablanca, Morocco

$^{2}$ Polydisciplinary Faculty of Taroudant, University Ibn Zohr, Morocco

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Abstract

This paper presents a comprehensive review of recent developments in energy harvesting (EH) from quasi-periodic (QP) vibrations in nonlinear oscillatory systems, particularly those incorporating time-delay effects. Unlike traditional resonance-based harvesting strategies that often suffer from narrow bandwidth and stability issues, QP-based approaches offer enhanced robustness and a broader operational frequency range. The study focuses on various delayed nonlinear oscillators-including Van der Pol, Duffing, Van der Pol-Duffing, Duffing-Mathieu-Van der Pol, and galloping-type systems-each c oupled to piezoelectric transducers. These configurations explore both constant and modulated feedback delays in either the mechanical or electrical domains. The analysis synthesizes insights from analytical approximations, bifurcation analysis, and numerical simulations, highlighting how delay-induced dynamics and QP responses can be harnessed to improve harvesting efficiency. By strategically tuning the delay parameters, large-amplitude QP oscillations can be stabilized even away from resonance, circumventing common issues such as bistability and amplitude jumps. The findings underscore the potential of delay engineering as a viable route toward broadband and efficient energy harvesting in both macro and microscale systems.

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