# Probability and output analysis of asymmetric bistable energy harvesters subjected to Gaussian white noise

Wei Wang, Junyi Cao, Chris R. Bowen, Grzegorz Litak

Research output: Contribution to journalArticle

### Abstract

Due to their excellent broadband response and high sensitivity to low-amplitude excitations, there is significant interest in the theoretical analysis and experimental validation of bistable energy harvesters (BEHs). However, it is difficult in practice to obtain a perfectly symmetric bistable potential energy function, and our current understanding of the influence of asymmetric potentials on the response of BEHs is limited. As a result, this paper sheds light on the influence of asymmetric potentials on the response probability and electrical outputs of BEHs driven by Gaussian white noise. Firstly, the influence of potential well depth on the power outputs and response probability of symmetric BEHs is illustrated. When a quadratic nonlinearity is introduced to characterize the asymmetry, numerical simulations demonstrate that it has a negative effect on the output of BEHs when the noise intensity is relatively low, and the negative influence becomes great with an increase in the degree of asymmetry. From the probability analysis, it is concluded that the probability density function of displacement strongly depends on the degree of asymmetry of the potential function and it is also affected by the excitation intensity. Finally, experiments are carried out which demonstrate that the average output power is indeed influenced by the asymmetric potential of the BEHs under different excitation levels.

Original language English 558 European Physical Journal Plus 134 11 8 Nov 2019 https://doi.org/10.1140/epjp/i2019-13080-6 Published - 30 Nov 2019

### ASJC Scopus subject areas

• Physics and Astronomy(all)

### Cite this

Probability and output analysis of asymmetric bistable energy harvesters subjected to Gaussian white noise. / Wang, Wei; Cao, Junyi; Bowen, Chris R.; Litak, Grzegorz.

In: European Physical Journal Plus, Vol. 134, No. 11, 558, 30.11.2019.

Research output: Contribution to journalArticle

title = "Probability and output analysis of asymmetric bistable energy harvesters subjected to Gaussian white noise",
abstract = "Due to their excellent broadband response and high sensitivity to low-amplitude excitations, there is significant interest in the theoretical analysis and experimental validation of bistable energy harvesters (BEHs). However, it is difficult in practice to obtain a perfectly symmetric bistable potential energy function, and our current understanding of the influence of asymmetric potentials on the response of BEHs is limited. As a result, this paper sheds light on the influence of asymmetric potentials on the response probability and electrical outputs of BEHs driven by Gaussian white noise. Firstly, the influence of potential well depth on the power outputs and response probability of symmetric BEHs is illustrated. When a quadratic nonlinearity is introduced to characterize the asymmetry, numerical simulations demonstrate that it has a negative effect on the output of BEHs when the noise intensity is relatively low, and the negative influence becomes great with an increase in the degree of asymmetry. From the probability analysis, it is concluded that the probability density function of displacement strongly depends on the degree of asymmetry of the potential function and it is also affected by the excitation intensity. Finally, experiments are carried out which demonstrate that the average output power is indeed influenced by the asymmetric potential of the BEHs under different excitation levels.",
author = "Wei Wang and Junyi Cao and Bowen, {Chris R.} and Grzegorz Litak",
year = "2019",
month = "11",
day = "30",
doi = "10.1140/epjp/i2019-13080-6",
language = "English",
volume = "134",
journal = "European Physical Journal Plus",
issn = "2190-5444",
publisher = "Springer Science + Business Media",
number = "11",

}

TY - JOUR

T1 - Probability and output analysis of asymmetric bistable energy harvesters subjected to Gaussian white noise

AU - Wang, Wei

AU - Cao, Junyi

AU - Bowen, Chris R.

AU - Litak, Grzegorz

PY - 2019/11/30

Y1 - 2019/11/30

N2 - Due to their excellent broadband response and high sensitivity to low-amplitude excitations, there is significant interest in the theoretical analysis and experimental validation of bistable energy harvesters (BEHs). However, it is difficult in practice to obtain a perfectly symmetric bistable potential energy function, and our current understanding of the influence of asymmetric potentials on the response of BEHs is limited. As a result, this paper sheds light on the influence of asymmetric potentials on the response probability and electrical outputs of BEHs driven by Gaussian white noise. Firstly, the influence of potential well depth on the power outputs and response probability of symmetric BEHs is illustrated. When a quadratic nonlinearity is introduced to characterize the asymmetry, numerical simulations demonstrate that it has a negative effect on the output of BEHs when the noise intensity is relatively low, and the negative influence becomes great with an increase in the degree of asymmetry. From the probability analysis, it is concluded that the probability density function of displacement strongly depends on the degree of asymmetry of the potential function and it is also affected by the excitation intensity. Finally, experiments are carried out which demonstrate that the average output power is indeed influenced by the asymmetric potential of the BEHs under different excitation levels.

AB - Due to their excellent broadband response and high sensitivity to low-amplitude excitations, there is significant interest in the theoretical analysis and experimental validation of bistable energy harvesters (BEHs). However, it is difficult in practice to obtain a perfectly symmetric bistable potential energy function, and our current understanding of the influence of asymmetric potentials on the response of BEHs is limited. As a result, this paper sheds light on the influence of asymmetric potentials on the response probability and electrical outputs of BEHs driven by Gaussian white noise. Firstly, the influence of potential well depth on the power outputs and response probability of symmetric BEHs is illustrated. When a quadratic nonlinearity is introduced to characterize the asymmetry, numerical simulations demonstrate that it has a negative effect on the output of BEHs when the noise intensity is relatively low, and the negative influence becomes great with an increase in the degree of asymmetry. From the probability analysis, it is concluded that the probability density function of displacement strongly depends on the degree of asymmetry of the potential function and it is also affected by the excitation intensity. Finally, experiments are carried out which demonstrate that the average output power is indeed influenced by the asymmetric potential of the BEHs under different excitation levels.

UR - http://www.scopus.com/inward/record.url?scp=85074849185&partnerID=8YFLogxK

U2 - 10.1140/epjp/i2019-13080-6

DO - 10.1140/epjp/i2019-13080-6

M3 - Article

VL - 134

JO - European Physical Journal Plus

JF - European Physical Journal Plus

SN - 2190-5444

IS - 11

M1 - 558

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