Piezoelectricd₁₅shear-response-based torsion actuation mechanism: An exact 3D Saint-Venant type solution

Abstract

This paper is concerned with the detailed analysis of the behavior of a piezoceramic bi-morph torsion actuator using the d 15 -effect. The bi-morph actuator is made of two oppositely polarized adjacent piezoceramic prismatic beams. The mathematical analysis is based on the Saint-Venant torsion theory; a formulation of the electromechanically coupled problem in terms of a stress function and of the electric potential is derived, which represents an exact solution of a specific three-dimensional problem; in particular, for the case when the axial stress and the axial component of the electric displacement vector are independent of the axial coordinate. The resulting boundaryvalue problem in the cross-section is solved using the method of finite differences. Solutions for the actuated rate of twist are presented and compared to three-dimensional electromechanically coupled finite element solutions using ABAQUS ® for the case of a cantilevered bi-morph actuator. A very good agreement is found. IntroductionStructures that integrate sensors and actuators into load-bearing structures by means of multi-functional materials like, e.g. piezoelectric materials, are usually denoted as smart or intelligent structures; see Crawley [1] or Chopra [2] for reviews. In combination with active and passive control strategies smart structures have applications in the fields of vibration damping, noise reduction, shape control, structural and health monitoring, and so on; see, e.g. Rao and Sunar [3].A piezoelectric material subjected to an electric field is mechanically deformed; conversely, a mechanical deformation results into an electric field. This behavior can be used to put piezoelectric actuators and sensors into practice. The actuator effect is denoted as the converse piezoelectric effect and the sensor effect as the direct piezoelectric effect; see Mason [4] or Yang [5]. In the following, the actuating piezoelectric strains are considered as mechanical eigenstrains, a generalized notion introduced by Mura [6] in order to describe incompatible parts of strain, such as thermal, plastic misfit as well as piezoelectric strains. In analogy, the sensing effect has been formally accounted for by means of a so-called

Enhanced torsional actuation and stress coupling in Mn-modified 0.93(Na0.5Bi0.5TiO3)-0.07BaTiO3 lead-free piezoceramic system

“…[14,15] The mathematical analysis is based on the Saint-Venant torsion theory which is a formulation of the electromechanically coupled problem in terms of a stress function and of the electric potential and represents an exact solution of the specific three-dimensional problem. In this study, these mathematical formulations are effectively used to model the rate of twist produced from the samples.…”

“…In that study, a bimorph d 15 torsion transducer was theoretically introduced [10] which was later experimentally demonstrated by Berik and Benjeddou [11] using a sandwich patch actuator made of axially oppositely poled (OP) two adjacent rows of triple PZT PIC 255 patches and glass fiber reinforced polymer (GFRP) face covering layers. The torsion actuation mechanism (TAM) [11,12] has been further analyzed [13] by conducting quasi-static and static experiments for a benchmark that was validated through Saint Venant-type solutions presented by Krommer et al [14,15]. Experimental visualization of the d 15 shear-induced torsion deformation through the quasi-static scanning laser deflection measurements has been investigated, setting the reference condition for further development.…”

“…Following on from the first author’s previous works on lead-based piezoceramic d 15 shear-induced torsion actuators [11,13] and the study on the effects of manganese additive on piezoelectric properties of BNT-BT ferroelectric ceramics,[16] the present study contributes:the first lead-free piezoceramic d 15 shear-induced torsion actuator; previously lead-based piezoceramic torsion actuators were analyzed;analysis of piezoelectric d 15 shear-mode properties of NBT-BT-Mn lead-free piezoceramics exhibiting improved piezoelectric shear response, transverse shear actuation force and fulfilling the needs of a high performance piezoceramic torsion actuator;piezoresponse force microscopy (PFM) investigation of the domain morphology and the discussion of the effect of domain size on the piezoelectric response of NBT-BT-Mn piezoceramics;systematic evaluation of a lead-free piezoceramic NBT-BT-Mn torsion actuator in terms of generated angle of twist using laser scanning vibrometery, finite element (FE) simulations and 3D Saint-Venant type exact mathematical solutions;experimental validation of Saint-Venant type torsion solutions;[14,15] previously their verifications were conducted only through FE analysis;discussion of piezoelectric nonlinearity of d 15 shear-mode NBT-BT-Mn piezoceramics; andan update to the process of FE simulations and mathematical solutions by taking into account the piezoelectric nonlinearity of d 15 shear-mode piezoceramics; in earlier works,[11,13] the verifications were conducted only through linear FE analysis. …”

“…experimental validation of Saint-Venant type torsion solutions;[14,15] previously their verifications were conducted only through FE analysis;…”

A European Association for the Control of Structures joint perspective. Recent studies in civil structural control across Europe

“… and Krommer et al . ), piezoelectric transducer design, and applications to structural control and health monitoring. In the present paper, we discuss two topics in some detail: (1) Passive and active structural shape control, and (2) structural health monitoring.…”