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Imagine a system that converts vibrations into useful energy, much like a power generator. This is the goal of a new study combining a Duffing oscillator, a pendulum, and a piezoelectric device. The system, called PHPD, uses the device's electrical output to control vibrations and harness them. Through mathematical analysis and simulations, researchers reduced oscillations and improved efficiency. This could revolutionize energy in mobile devices and automated systems.

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The study explores the nonlinear dynamics of a hybrid system consisting of a Duffing oscillator, a pendulum, and a piezoelectric generator. The governing equation, derived theoretically, is analyzed using the Multiple-Scale Perturbation Technique (MSPT) to obtain reduced dynamics. Bifurcation analysis identifies stability conditions and critical parameters. Simulations based on the Runge-Kutta method confirm analytical predictions. Frequency response curves (FRCs) show how PHPD control reduces vibration amplitude and accelerates convergence. The computation of the Largest Lyapunov Exponent (LLE) helps classify bifurcations. These results offer a new approach for nonlinear electromechanical systems, improving energy efficiency and performance.

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Authors:
Fatma Taha El-BahrawyRageh K. HusseinAshraf Taha EL-SayedMoamen Wafaie
Date Published:
Original Article www.mdpi.com
Fact-check verified on 03/10/2026
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Creative Commons License CC BY-NC-SA 4.0

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