Citation: Daraki, M.-S.; Marakakis,
K.; Stavroulakis, G.E. Modeling of
Shunted Piezoelectrics and
Enhancement of Vibration
Suppression through an Auxetic
Interface. Micromachines 2023, 14, 289.
https://doi.org/10.3390/
mi14020289
Academic Editor: Liang Wang
Received: 22 December 2022
Revised: 17 January 2023
Accepted: 19 January 2023
Published: 22 January 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
micromachines
Article
Modeling of Shunted Piezoelectrics and Enhancement of
Vibration Suppression through an Auxetic Interface
Maria-Styliani Daraki , Konstantinos Marakakis and Georgios E. Stavroulakis *
Institute of Computational Mechanics and Optimization (Co.Mec.O),
School of Production Engineering and Management, Technical University of Crete, GR-73100 Chania, Greece
* Correspondence: gestavroulakis@tuc.gr
Abstract: In this study, a new technique is presented for enhancing the vibration suppression of
shunted piezoelectrics by using an auxetic composite layer. Finite element models have been created
to simulate the dynamic behavior of the piezoelectric composite beam. In particular, 2D FE and
3D FE models have been created by simulating the shunt as a passive controller and their results
are compared. Furthermore, a parametric analysis is presented of the circuit elements, i.e., the
resistors, inductors, and capacitors and of the auxetic material, i.e., the thickness. It was found
that the proposed modification by adding an auxetic layer of a considerable thickness enhances the
electromechanical coupling and indirectly influences the vibration control of the whole structure.
However, the use of 3D modeling is necessary to study this auxetic enhancement.
Keywords: auxetic material; piezoelectrics; shunt circuits; parametric analysis; vibration control
1. Introduction
The vibration damping of the structures due to an external excitation is one of the most
common problems in engineering. A reduction in the vibration is needed for functional rea-
sons, for example, for tracking the accuracy in flexible robotics, which leads, amongst other
things, to reduced fatigue which, in this way, extends the life of the vibrating components.
Several techniques have been proposed on this subject in the literature [1,2]. Composite
layered structures and microstructures with bonded piezoelectric materials can be used for
this purpose [3,4].
Piezoelectric materials are distinguished by their special characteristics. Specifically,
during the application of a mechanical strain, opposite electrical charges are generated on
opposite crystal surfaces, which are analogous to the magnitude of the mechanical strain.
This phenomenon is called the direct piezoelectric effect. However, when an electric field
is applied to the material, then mechanical deformation is generated. This phenomenon
is called the inverse piezoelectric effect. The piezoelectric effect was discovered by the
brothers Jacques and Pierre Curie in the late nineteenth century [5]. Additionally, piezo-
electric materials are widely used for vibration damping, energy harvesting, and many
other applications due to their excellent electromechanical coupling properties and their
frequency response. Piezoelectric transducers can be found in several different shapes, the
most common of which are thin sheets known as piezoelectric patches [6]. In addition,
shunt circuits, which are paired with piezoelectric elements, form a structural, usually
passive, damping method. This method is called shunt damping and it has attracted a lot
of scientific interest during the past two decades in vibration control engineering due to
its simplicity and applicability in real life applications. Among others, this method can be
used in civil structures [7], in smart panels for noise reduction [8], in the design of hard
disk drives [9], in the damping of turbine blades [10], etc.
Shunt circuits have also been used for the development of smart metamaterials in
order to enhance their properties. For example, in [11], synthetic impedance shunt circuits
Micromachines 2023, 14, 289. https://doi.org/10.3390/mi14020289 https://www.mdpi.com/journal/micromachines