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Analysis of an optimization problem for a piezoelectric energy harvester.
- Source :
-
Archive of Applied Mechanics . Jun2019, Vol. 89 Issue 6, p1103-1122. 20p. - Publication Year :
- 2019
-
Abstract
- The problem of optimal energy harvesting for a piezoelectric element driven by mechanical vibrations is stated in terms of an ODE system with hysteresis under the time derivative coupling a mechanical oscillator with an electric circuit with or without inductance. In the piezoelectric constitutive law, both the self-similar piezoelectric butterfly character of the hysteresis curves and feedback effects are taken into account in a thermodynamically consistent way. The physical parameters of the harvester are chosen to be the control variable, and the goal is to maximize the harvested energy for a given mechanical load and a given time interval. If hysteresis is modeled by the Preisach operator, the system is shown to be well-posed with continuous data dependence. For the special case of the play operator, we derive first-order necessary optimality conditions and an explicit form of the gradient of the total harvested energy functional in terms of solutions to the adjoint system. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09391533
- Volume :
- 89
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Archive of Applied Mechanics
- Publication Type :
- Academic Journal
- Accession number :
- 136622036
- Full Text :
- https://doi.org/10.1007/s00419-018-1459-6