Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling

0504463 - MÚ 2020 RIV US eng J - Journal Article
Krejčí, Pavel - Monteiro, Giselle Antunes
Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling.
Discrete and Continuous Dynamical Systems-Series B. Roč. 24, č. 7 (2019), s. 3051-3066. ISSN 1531-3492. E-ISSN 1553-524X
Institutional support: RVO:67985840
Keywords : hysteresis * Preisach operator * inversion formula * piezoelectricity
OECD category: Pure mathematics
Impact factor: 1.270, year: 2019
Method of publishing: Open access
http://dx.doi.org/10.3934/dcdsb.2018299

Hysteresis is an important issue in modeling piezoelectric materials, for example, in applications to energy harvesting, where hysteresis losses may influence the efficiency of the process.The main problem in numerical simulations is the inversion of the underlying hysteresis operator.Moreover, hysteresis dissipation is accompanied with heat production, which in turn increases thetemperature of the device and may change its physical characteristics. More accurate models thereforehave to take the temperature dependence into account for a correct energy balance.We prove here that the classical Preisach operator with a fairly general parameter-dependenceadmits a Lipschitz continuous inverse in the space of right-continuous regulated functions, propose a time-discrete and memory-discrete inversion algorithm, and show that higher regularity of the inputs leads to a higher regularity of the output of the inverse.
Permanent Link: http://hdl.handle.net/11104/0296089