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

Subramanian Ramakrishnan, Connor Edlund, Collin Lambrecht

Research output: Contribution to journalArticle


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.

Original languageEnglish (US)
Pages (from-to)945-967
Number of pages23
JournalEuropean Journal of Applied Mathematics
Issue number5
StatePublished - Oct 1 2019



  • applications of stochastic analysis
  • computational methods for stochastic equations
  • fractional processes
  • physical applications of random processes

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