The European Physical Journal Special Topics

, Volume 222, Issue 7, pp 1665–1673 | Cite as

Stationary response of nonlinear magneto-piezoelectric energy harvester systems under stochastic excitation

  • W. MartensEmail author
  • U. von Wagner
  • G. Litak
Regular Article


Recent years have shown increasing interest of researchers in energy harvesting systems designed to generate electrical energy from ambient energy sources, such as mechanical excitations. In a lot of cases excitation patterns of such systems exhibit random rather than deterministic behaviour with broad-band frequency spectra. In this paper, we study the efficiency of vibration energy harvesting systems with stochastic ambient excitations by solving corresponding Fokker-Planck equations. In the system under consideration, mechanical energy is transformed by a piezoelectric transducer in the presence of mechanical potential functions which are governed by magnetic fields applied to the device. Depending on the magnet positions and orientations the vibrating piezo beam system is subject to characteristic potential functions, including single and double well shapes. Considering random excitation, the probability density function (pdf) of the state variables can be calculated by solving the corresponding Fokker-Planck equation. For this purpose, the pdf is expanded into orthogonal polynomials specially adapted to the problem and the residual is minimized by a Galerkin procedure. The power output has been estimated as a function of basic potential function parameters determining the characteristic pdf shape.


European Physical Journal Special Topic Energy Harvester Piezoelectric Energy Harvest White Noise Excitation Stochastic Excitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Chair of Mechatronics and Machine Dynamics, TU BerlinBerlinGermany
  2. 2.Faculty of Mechanical Engineering, Lublin University of TechnologyLublinPoland

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