Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise

Research output: Contribution to journalArticle

Abstract

In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and OrnsteinUhlenbeck-type excitations are considered. In the white noise limit, the stationary FokkerPlankKolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of OrnsteinUhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.

Original languageEnglish (US)
Pages (from-to)2554-2564
Number of pages11
JournalJournal of Sound and Vibration
Volume330
Issue number11
DOIs
StatePublished - May 23 2011

Fingerprint

White noise
random noise
Probability density function
generators
Statistics
Bandwidth
white noise
probability density functions
excitation
electric generators
output
noise intensity
statistics
bandwidth
augmentation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering

Cite this

Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise. / Daqaq, Mohammed.

In: Journal of Sound and Vibration, Vol. 330, No. 11, 23.05.2011, p. 2554-2564.

Research output: Contribution to journalArticle

@article{9184e005664e439b8161de62106bde4e,
title = "Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise",
abstract = "In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and OrnsteinUhlenbeck-type excitations are considered. In the white noise limit, the stationary FokkerPlankKolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of OrnsteinUhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.",
author = "Mohammed Daqaq",
year = "2011",
month = "5",
day = "23",
doi = "10.1016/j.jsv.2010.12.005",
language = "English (US)",
volume = "330",
pages = "2554--2564",
journal = "Journal of Sound and Vibration",
issn = "0022-460X",
publisher = "Academic Press Inc.",
number = "11",

}

TY - JOUR

T1 - Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise

AU - Daqaq, Mohammed

PY - 2011/5/23

Y1 - 2011/5/23

N2 - In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and OrnsteinUhlenbeck-type excitations are considered. In the white noise limit, the stationary FokkerPlankKolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of OrnsteinUhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.

AB - In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and OrnsteinUhlenbeck-type excitations are considered. In the white noise limit, the stationary FokkerPlankKolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of OrnsteinUhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.

UR - http://www.scopus.com/inward/record.url?scp=79952539208&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952539208&partnerID=8YFLogxK

U2 - 10.1016/j.jsv.2010.12.005

DO - 10.1016/j.jsv.2010.12.005

M3 - Article

AN - SCOPUS:79952539208

VL - 330

SP - 2554

EP - 2564

JO - Journal of Sound and Vibration

JF - Journal of Sound and Vibration

SN - 0022-460X

IS - 11

ER -