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Nonlinear multi-scale dynamics modeling of piezoceramic energy harvesters with ferroelectric and ferroelastic hysteresis

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Abstract

Hysteretic nonlinearities significantly affect the behavior of devices based on piezoelectric materials. The topic has been widely addressed in the actuation framework, as modeling nonlinear effects is crucial for the dynamic control of piezoelectric actuators. Far less studies, however, discuss the role of hysteresis in the dynamic response of piezoelectric energy harvesters, usually adopting phenomenological modeling approaches. In this work, a physics-based model is employed to reproduce—through a probabilistic thermodynamic approach—the process behind hysteresis in piezoceramic transducers, i.e., the switching of dipoles in crystal domains. A multi-scale approach is then adopted in order to comprise hysteretic effects in the dynamic response of a piezoelectric energy harvester, modeled as a SDOF system. Effects of hysteretic nonlinearities on the device behavior are investigated by means of simulations, and a detailed discussion on the role of material parameters is reported. Moreover, a comparison between predictions of two models—with and without hysteresis—is presented.

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Notes

  1. Note that this representation of the coupling between the two ports coincides with an ideal transformer having a voltage ratio equal to \(\alpha ^{\mathrm{LTIM}}\).

  2. Note that in this representation of the system the voltage on \(C^{\mathrm{MsM}}_{\mathrm{PZT}}\) differs from the device output voltage (see Fig. 5-c).

  3. In Figs. 9-g–i, 10-g–i and 11-g–i, TIM curves relative to the different values assumed by \(\sigma _{e_{\pm ,0}}\), \(\epsilon _{\pm ,0}\), and \(\Delta g_0\), respectively, are overlapped.

  4. Blue, red, and yellow curves in Fig. 10-a–e are overlapped.

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Authors and Affiliations

  1. Department of Electrical and Information Engineering, Polytechnic University of Bari, Bari, Italy

    Pasquale Montegiglio & Giuseppe Acciani

  2. Faculty of Naval Architecture and Ocean Engineering, Istanbul Technical University, Istanbul, Turkey

    Claudio Maruccio

  3. Department of Systems Engineering, Saarland University, Saarbrücken, Germany

    Gianluca Rizzello & Stefan Seelecke

  4. Department of Material Science and Engineering, Saarland University, Saarbrücken, Germany

    Gianluca Rizzello & Stefan Seelecke

Authors
  1. Pasquale Montegiglio
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  2. Claudio Maruccio
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  3. Giuseppe Acciani
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  4. Gianluca Rizzello
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  5. Stefan Seelecke
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Correspondence to Pasquale Montegiglio.

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Appendix: Equivalence of proposed MsMs

Appendix: Equivalence of proposed MsMs

Figure 11 reports simulation results obtained assuming a \(1 g_{\mathrm{acc}}\) sinusoidal base acceleration, in near-resonance condition, as input for the device.

Fig. 15
figure 15

Comparison between MsMs (23) and (28) responses: \(1 g_{\mathrm{acc}}\) input acceleration in near-resonance condition. Blue solid lines refer to numerical simulation of MsM (28). a Input force; b rate of change of the system displacement; c comparison between the output voltages provided by the two MsMs. Reported curves perfectly overlap. (Color figure online)

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Blue solid lines refer to the numerical integration of MsM (28). Red dashed line in Fig.  15-c refers to the device output voltage determined by indirect calculation based on the application of the Kirchhoff’s voltage law (KVL) to the equivalent lumped circuit in Fig.  5-a (which is relative to the MsM (23)). With reference to Fig. 5-a, by writing the KVL for the circuit loop connected to the mechanical port, the following expression of the device output voltage can be obtained:

$$\begin{aligned} v(t) = \frac{1}{\alpha ^{\mathrm{MsM}}}\left( -F_b + c_D{\dot{\eta }} + m\ddot{\eta } + \frac{A}{l_0d}\eta - \frac{Af}{d} \right) \ ,\nonumber \\ \end{aligned}$$
(36)

where the evolution in time of quantities \(\alpha ^{\mathrm{MsM}}\), d, and f can be assumed the same as that provided by the numerical integration of MsM (28). The same input quantities (\(F_b\), \({\dot{\eta }}\)) are considered applied to the mechanical port of both the models. The perfect coincidence of curves reported in Fig. 15-c confirms MsM (23) and (28) equivalence in terms of external behavior.

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Montegiglio, P., Maruccio, C., Acciani, G. et al. Nonlinear multi-scale dynamics modeling of piezoceramic energy harvesters with ferroelectric and ferroelastic hysteresis. Nonlinear Dyn 100, 1985–2003 (2020). https://doi.org/10.1007/s11071-020-05660-0

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