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On the stochastic dynamics of a nonlinear vibration energy harvester driven by Lévy flight excitations

Part of: Stochastic analysis Stochastic processes Special processes

Published online by Cambridge University Press:  08 October 2018

SUBRAMANIAN RAMAKRISHNAN Open the ORCID record for SUBRAMANIAN RAMAKRISHNAN [Opens in a new window] ,
CONNOR EDLUND  and
COLLIN LAMBRECHT
SUBRAMANIAN RAMAKRISHNAN
Affiliation:
Department of Mechanical and Industrial Engineering, University of Minnesota Duluth, Duluth, MN 55811, USA email: sramakri@d.umn.edu
CONNOR EDLUND
Affiliation:
Department of Electrical Engineering, University of Minnesota Duluth, Duluth, MN 55811, USA emails: edlun065@d.umn.edu; lambr035@umn.edu
COLLIN LAMBRECHT
Affiliation:
Department of Mechanical and Industrial Engineering, University of Minnesota Duluth, Duluth, MN 55811, USA email: sramakri@d.umn.edu
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Abstract

Vibration energy harvesting aims to harness the energy of ambient random vibrations for power generation, particularly in small-scale devices. Typically, stochastic excitation driving the harvester is modelled as a Brownian process and the dynamics are studied in the equilibrium state. However, non-Brownian excitations are of interest, particularly in the nonequilibrium regime of the dynamics. In this work we study the nonequilibrium dynamics of a generic piezoelectric harvester driven by Brownian as well as (non-Brownian) Lévy flight excitation, both in the linear and the Duffing regimes. Both the monostable and the bistable cases of the Duffing regime are studied. The first set of results demonstrate that Lévy flight excitation results in higher expectation values of harvested power. In particular, it is shown that increasing the noise intensity leads to a significant increase in power output. It is also shown that a linearly coupled array of nonlinear harvesters yields improved power output for tailored values of coupling coefficients. The second set of results show that Lévy flight excitation fundamentally alters the bifurcation characteristics of the dynamics. Together, the results underscore the importance of non-Brownian excitation characterised by Lévy flight in vibration energy harvesting, both from a theoretical viewpoint and from the perspective of practical applications.

Keywords

applications of stochastic analysisfractional processescomputational methods for stochastic equationsphysical applications of random processes

MSC classification

Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60H35: Computational methods for stochastic equations 60G22: Fractional processes, including fractional Brownian motion 60K40: Other physical applications of random processes
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 5: Stochastic Analysis in Applications , October 2019 , pp. 945 - 967
Copyright
© Cambridge University Press 2018 

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