Improved one-dimensional model of piezoelectric laminates for energy harvesters including three dimensional effects

Abstract

The application of piezoelectric composites in energy harvesters is continuously increasing even at the microscale, with the immediate corollary of a fundamental need for improved computational tools for optimization of performances at the design level. In this paper, a refined, yet simple model is proposed with the aim of providing fast and insightful solutions to the multi-physics problem of energy harvesting via piezoelectric layered structures. The main objective is to retain a simple structural model (Euler–Bernoulli beam), with the inclusion of effects connected to the actual three-dimensional shape of the device. A thorough presentation of the analytical model is presented, along with its validation by comparison with the results of fully 3D computations

Advanced Model for Fast Assessment of Piezoelectric Micro Energy Harvesters

“…The complete validation campaign is described in Gafforelli et al (2015). One of the analyses which have been considered for carrying out the comparison is related to free vibration: the beam's tip is quasi-statically moved until a certain position, and it is suddenly released.…”

“…After the integration, one finds the generalized version of the governing parameters: inertia, damping and stiffness for the mechanical terms, intrinsic capacitance for the electrical terms, and the coupling parameter, which summarizes the piezoelectric effects. All these parameters, whose complete expression can be found in (Gafforelli et al, 2015), account for the layered nature of the beam (along the thickness) and for the effect of f Λ (which depends on x 2 , along the width).…”

“…After some algebraic manipulations (see Gafforelli et al (2015) for details), one finds that the piezoelectric constitutive law can be written in the following form:…”

“…All the functionals in equations (12) and (13) are obtained by integration over the volume of the beam: it is thus necessary to take into account the layered nature of the piezoelectric beam, so a suitable modification of the CLT should be introduced (the relevant details have been explained in Gafforelli et al (2015)). For the computation of the internal energy, it is necessary to take into account the constitutive law described in Section 2.1.…”

“…In a previous paper (Gafforelli et al, 2015), we developed a simple 1D model in order to simulate piezoelectric thin beams. Starting from the fully coupled 3D constitutive equations of piezoelectricity, appropriate hypotheses should be introduced to model strains and stresses so that the 1D model takes into account the 3D effects (Maurini et al, 2004(Maurini et al, , 2006.…”