Analysis of an optimization problem for a piezoelectric energy harvester

0504848 - MÚ 2020 RIV US eng J - Journal Article
Kaltenbacher, B. - Krejčí, Pavel
Analysis of an optimization problem for a piezoelectric energy harvester.
Archive of Applied Mechanics. Roč. 89, č. 6 (2019), s. 1103-1122. ISSN 0939-1533. E-ISSN 1432-0681
R&D Projects: GA ČR(CZ) GA15-12227S
Institutional support: RVO:67985840
Keywords : hysteresis * piezoelectricity * control
OECD category: Pure mathematics
Impact factor: 1.374, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1007/s00419-018-1459-6

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.
Permanent Link: http://hdl.handle.net/11104/0296397