Stochastic Response Determination of Hysteretic Vibratory Energy Harvesters with Fractional Derivatives via Stochastic Averaging
Publication: Journal of Engineering Mechanics
Volume 150, Issue 7
Abstract
The realistic modeling of vibratory energy harvesters is necessary to ensure their reliable performance when subjected to random excitation. However, the hysteretic behavior of piezoelectric materials and the nonlocality of fractional electrical components make the numerical estimation of their stochastic response computationally challenging. This paper proposes an iterative method based on equivalent linearization and stochastic averaging for estimating the stationary probability density function of the output voltage amplitude of vibratory energy harvesters modeled as a hysteretic oscillator with fractional electrical components subject to a broadband stochastic process. By estimating the average of hysteretic terms, one can find an amplitude-dependent linear governing equation for the output voltage, from which one can determine a stochastic differential equation governing the evolution of the output voltage amplitude. We obtain the stationary solution of the corresponding Fokker–Planck equation in a semianalytical form, and we include comparisons with pertinent Monte Carlo simulation data to show that the estimated probability density functions are accurate and obtained at a minimal computational cost.
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Data Availability Statement
All data, models, and code that support the findings of this study are available from the corresponding author upon reasonable request.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 7 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Nov 7, 2023
Accepted: Jan 17, 2024
Published online: Apr 22, 2024
Published in print: Jul 1, 2024
Discussion open until: Sep 22, 2024
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