Green׳s function method for piezoelectric energy harvesting beams

Danesh-Yazdi, Amir H.; Elvin, Niell; Andreopoulos, Yiannis

doi:10.1016/j.jsv.2014.02.023

Cited by 20 publications

(5 citation statements)

References 18 publications

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“…This kind of load, which is created to simulate the approximate actual working conditions of the harvester, is used frequently in the literature. According to Danesh-Yazdi et al (2014), if the base displacement is not equal to zero, the absolute transverse displacement of the beam can be expressed as…”

Section: Specific Case Study: Harmonic Base Excitationmentioning

confidence: 99%

“…If we consider a piezoelectric cantilever beam with a tip mass M t and mass moment of inertia J t subjected to a base acceleration, the external harmonic force f(x, t) = F(x)e iOt can be written as (Danesh-Yazdi et al, 2014)…”

Section: Specific Case Study: Harmonic Base Excitationmentioning

confidence: 99%

“…Mode expansion method was used by Erturk and Inman (2008a) to ascertain the series solutions. Using the coupled model proposed by Erturk and Inman (2008a), Danesh-Yazdi et al (2014) developed the closed-form solutions for the piezoelectric energy harvester by employing Green's function method and Fourier transform technology.…”

Section: Introductionmentioning

confidence: 99%

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Closed-form solutions for forced vibrations of piezoelectric energy harvesters by means of Green’s functions

Zhao

Yang

et al. 2017

Journal of Intelligent Material Systems and Structures

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In this article, the closed-form solutions are obtained for the forced vibrations of cantilevered unimorph piezoelectric energy harvesters. A tip mass is attached at the free end, and the moment of its inertia to the fixed end is considered. Timoshenko beam assumptions are used to establish a coupled electromechanical model for the harvester. Two damping effects, transverse and rotational damping effects, are taken into account. Green’s function method and Laplace transform technique are used to solve the coupled electromechanical vibration system. The conventional case of a harmonic base excitation is considered, and numerical calculations are performed. The present model is validated by comparing its predictions with the existing data, the experimental results, and the finite element method solutions. The influences of shear deformation and rotational inertia on the predictions are discussed. The effect of load resistance on the electrical power is studied, and the optimal load resistances are obtained. Ultimately, the optimal schemes are proposed to improve electricity generation performance for the soft piezoelectric materials: PZT-5A/5H.

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Section: Specific Case Study: Harmonic Base Excitationmentioning

confidence: 99%

Section: Specific Case Study: Harmonic Base Excitationmentioning

confidence: 99%

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Closed-form solutions for forced vibrations of piezoelectric energy harvesters by means of Green’s functions

Zhao

Yang

et al. 2017

Journal of Intelligent Material Systems and Structures

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“…However, this method becomes difficult to apply for beams with non-ideal boundary conditions because of the required eigenfunctions in the modal expansion series. Danesh-Yazdi et al (2014) and Zhao et al (2017) applied a Fourier Transform Green’s function approach (FTGF) to develop closed-form solutions. However, the success of the FTGF method hinges on the ability to derive the Green’s function of the mechanical beam.…”

Section: Introductionmentioning

confidence: 99%

Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

Amoozegar

Tan

2022

Journal of Intelligent Material Systems and Structures

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The purpose of this paper is to investigate the effect of boundary flexibility on the performance of piezoelectric vibration energy harvester (PVEH) beam systems, which has not been studied comprehensively in the literature despite its importance. The coupled electromechanical equations of motion of a piezoelectric cantilever beam with a tip mass are established, with the base boundary constrained by translational and rotational springs. An exact closed-form solution of the frequency response function (FRF) of the PVEH is obtained by the distributed transfer function method (DTFM). The DTFM is a systematic powerful tool for the dynamic analysis of distributed parameter continua with non-classical boundary conditions, intermediate constraints, coupled fields, and non-proportional damping without adding much complexity to the solution formulation. Moreover, the DTFM computes the derivatives of the response, that is, the strains, which are required in the electromechanical coupling formulation, simultaneously without any differentiation. Numerical results showing the effects of boundary flexibility on energy harvesting efficiency are presented. A first-order rational function relating the boundary stiffness parameters and the harvesting efficiency is determined by nonlinear curve fitting of the calculated data. Physical insights and applicability of this analytical function for end-of-line quality check of the boundary of PVEH are discussed.

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“…The majority of the work done on piezoelectric beams in the literature involves harvesting energy from harmonic (sinusoidal) base excitation (Danesh-Yazdi et al, 2014; Erturk and Inman, 2008; Shu and Lien, 2006), where the frequency of vibration is known and generally desired to match the natural frequency of the beam. There have also been a few studies on random vibration energy harvesting.…”

Section: Introductionmentioning

confidence: 99%

Parametric analysis of fluidic energy harvesters in grid turbulence

Danesh-Yazdi¹,

Elvin

Andreopoulos

2016

Journal of Intelligent Material Systems and Structures

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Even though it is omnipresent in nature, there has not been much research in the literature involving turbulence as an energy source for piezoelectric fluidic harvesters. In the present work, a grid-generated turbulence forcing function model which we derived previously is employed in the single degree-of-freedom electromechanical equations to find the power output and tip displacement of piezoelectric cantilever beams. Additionally, we utilize simplified, deterministic models of the turbulence forcing function to obtain closed-form expressions for the power output. These theoretical models are studied using experiments that involve separately placing a hot-wire anemometer probe and a short PVDF beam in flows where turbulence is generated by means of passive and semi-passive grids. From a parametric study of the deterministic models, we show that a white noise forcing function best mimics the experimental data. Furthermore, our parametric study of the response spectrum of a generic fluidic harvester in grid-generated turbulent flow shows that optimum power output is attained for beams placed closer to the grid with a low natural frequency and damping ratio and a large electromechanical coupling coefficient.

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Green׳s function method for piezoelectric energy harvesting beams

Cited by 20 publications

References 18 publications

Closed-form solutions for forced vibrations of piezoelectric energy harvesters by means of Green’s functions

Closed-form solutions for forced vibrations of piezoelectric energy harvesters by means of Green’s functions

Investigation of boundary flexibility on the performance of piezoelectric vibration energy harvesting beam systems by DTFM

Parametric analysis of fluidic energy harvesters in grid turbulence

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