Modeling of electromechanical response and fracture resistance of multilayer piezoelectric energy harvester with residual stresses

Abstract

The article focuses on a modeling and subsequent optimization of a novel layered architecture of the vibration piezoceramic energy harvester composed of ZrO2/Al2O3/BaTiO3 layers and containing thermal residual stresses. The developed analytical/numerical model allows to determine the complete electromechanical response and the apparent fracture toughness of the multilayer vibration energy harvester, upon consideration of thermal residual stresses and time-harmonic kinematic excitation. The derived model uses the Euler–Bernoulli beam theory, Hamilton’s variational principle, and a classical laminate theory to determine the first natural frequency, steady-state electromechanical response of the beam upon harmonic vibrations, and also the mechanical stresses within particular layers of the harvester. The laminate apparent fracture toughness is computed by means of the weight function approach. A crucial point is the further optimization of the layered architecture from both the electromechanical response and the fracture resistance point of view. Maximal allowable excitation acceleration of the harvester upon which the piezoelectric layer will not fail is determined. It makes possible to better use the harvester’s capabilities in a given application and simultaneously guarantee its safe operation. Outputs of the derived analytical model were validated with finite element method simulations and available experimental results, and a good agreement between all approaches was obtained.

Experimentally Verified Analytical Models of Piezoelectric Cantilevers in Different Design Configurations

“…This beam model is subsequently reduced to a single degree-of-freedom (DOF) system using the first mode shape function. Although, the derivation of a coupled electromechanical model was published several times, e.g., [19][20][21][22][23], here, we also show the effect of chosen mode shape function which is used in reducing the beam model into single DOF model. Then, the model is verified with 3 different experimental results.…”

“…The piezoelectric constitutive relations, which are required further in the derivation of the analytical model, take the following form for the uniaxial stress state [23]:…”

Design, modeling, and experiment of a multi-bifurcated cantilever piezoelectric energy harvester

“…Among them, optimizing the external circuit (Huang et al, 2019), using of the structural stability (Łygas et al, 2019) and nonlinearity (Litak et al, 2010; Wang and Inman, 2013; Yang et al, 2013; Zhao et al, 2013), and other methods were explored to improve energy harvesting performance. Particularly, different types of energy harvesters with broadband dynamic characteristics were designed and tested (Azadeh-Ranjbar et al, 2020; Kim, 2020; Machů et al, 2020; Wang et al, 2020).…”