Modal effective electromechanical coupling approximate evaluations and simplified analyses: numerical and experimental assessments

This contribution presents numerical and experimental assessments of the modal effective electromechanical coupling coefficient (EMCC) using popular approximate evaluations and simplified analyses of piezoelectric structures. For this purpose, first, a common benchmark, consisting of a cantilever Aluminum (Al) beam with symmetrically surface-bonded two pairs of large piezoceramic (PZT) patches, is retained for the assessment of EMCC different evaluation formulas and plane strain (PStrain) and plane stress (PStress) two-dimensional (2D) analyses using ANSYS \({^\circledR}\) coupled piezoelectric three-dimensional (3D) and 2D finite elements (FE). Then, similarly, an experimental assessment is conducted on two benchmarks consisting of Al long and short cantilevers equipped symmetrically with pairs of small and large PZT patches. It is found that, in order to get EMCC accurate approximate numerical evaluation, it is crucial to consider the patches electrodes equipotential constraints and, in order to get EMCC accurate 2D results with regard to 3D calculations, it is necessary to use PStress kinematics for approximate 2D analysis. Besides, 3D FE and experimental frequencies are shown to be bounded from below by PStress and from above by PStrain 2D FE results. Moreover, EMCC 2D PStress results are found closer to 3D FE and experimental results than PStrain 2D FE ones.     

Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

A partial mixed finite element (FE)–state space method (SSM) semi-analytical approach is presented for the static analysis of piezoelectric smart laminate composite and functionally graded material (FGM) plates. Hence, using the Hamiltonian formalism, the three-dimensional piezoelectricity equations are first worked so that a partial mixed variational formulation, which retains the translational displacements, electric potential, transverse stresses, and transverse electric displacement as primary variables, is obtained; this allows, in particular, straightforward fulfillment of the electromechanical continuity constraints at the laminate interfaces. After an in-plane FE discretization only, the problem is first reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved using the symplectic approach; then, the multilayer solution is reached via the SSM propagator matrix. The proposed methodology is finally applied to the static analysis of piezoelectric-cross-ply hybrid laminated composite and FGM plates. In a comparison with open literature, available tabulated results show good agreements, thus validating the proposed approach.     

Enrichment of linear hexahedral finite elements using rotations of a virtual space fiber

The present paper deals with the enrichment of 3D low‐order finite elements. The used concept is based on the idea that a 3D virtual fiber, after a spatial rotation, introduces an enhancement of the strain field tensor approximation. A consistent stiffness matrix is obtained, allowing a better approximation of the actual solution compared with that resulting from low‐order finite elements. Implemented for two eight‐node hexahedral elements, the performance of the space fiber rotation concept is assessed by running some classical beam, plate, and shell benchmarks, and the obtained results are compared especially with those given by linear eight‐node and quadratic 20‐node hexahedral elements. In particular, it is shown that the developed elements accuracy is significantly superior to that of the classical eight‐node hexahedral element and close to that of the classical 20‐node hexahedral element. Copyright © 2013 John Wiley & Sons, Ltd.     

A New Discrete-Layer Finite Element for Electromechanically Coupled Analyses of Piezoelectric Adaptive Composite Structures

A new discrete layer finite element (DLFE) is presented for electro-mechanically coupled analyses of moderately thick piezoelectric adaptive composite plates. The retained kinematics is based on layer-wise first-order shear deformation theory, and considers the plies top and bottom surfaces in-plane displacements and the plate transverse deflection as mechanical unknowns. The former are assumed in-plane Lagrange linear, while the latter is assumed in-plane full (Lagrange) quadratic; this results in a nine nodes quadrangular (Q9) DLFE. The latter is validated in free-vibrations, first numerically against ANSYS three-dimensional piezoelectric finite elements for a cantilever moderately thick aluminum plate with two co-localized piezoceramic patches, and then experimentally against a free quasi-isotropic transverse composite thin plate with four piezoceramic patches. The obtained short-circuit and open-circuit (OC) frequencies were satisfactory for both benchmarks, while the post-treated modal effective electromechanical coupling coefficients agreed well with ANSYS results (first benchmark) but only fairly with the experimental ones (second benchmark). Once validated, the Q9-DLFE was used to assess numerically the equipotential (EP) physical condition influence on the OC sensed electric potential; for this purpose, the above first benchmark, but with the top piezoceramic patch only, was finally analyzed. It was found that the EP condition homogenizes and lowers the sensed potential on the OC electrode.     

Numerical and experimental characterizations of longitudinally polarized piezoelectric d 15 shear macro-fiber composites

This contribution presents original numerical and experimental characterizations for prototyped longitudinally polarized piezoelectric d ₁₅ shear macro-fiber composites (MFC). The numerical characterization consists of a finite element (FE) simulation based on a representative volume element. It implements an enthalpy-based homogenization method (EBHM), recently proposed by the authors, as an extension of the so-called strain energy method to orthotropic piezoelectric fiber-reinforced composites. The numerical validation is carried out on a previously assumed layout of shear MFC. Later on, the EBHM is used to get the effective electromechanical material parameters of the shear MFC actual layout. These parameters are further validated experimentally through their use in the FE simulation of an original actuation benchmark that is proposed for the manufactured shear MFC experimental characterization. The latter is based on low-frequency (quasi-static) displacement measurements where the shear MFC serves as a voltage-driven actuator. Due to the small overall dislocation, a laser vibrometer is used for the measurements. The comparison of experimental and numerical results shows a reasonably good agreement and a nonlinear actuation response is observed. This work’s major outcomes are the experimental validation of the EBHM and the actuation functional operability of the manufactured longitudinally polarized piezoelectric d ₁₅ shear MFC. This opens the possibility for their application as actuator and sensor of shear-induced bending and torsion for vibration, shape and health control, or as a transducer for energy harvesting.     

General numerical implementation of a new piezoelectric shunt tuning method based on the effective electromechanical coupling coefficient

Abstract

A recently proposed tuning method for resistive-inductive (RL) shunts is implemented in a commercial finite element (FE) code (ANSYS^®). A main result of the paper is therefore the consistent formulation of the tuning method in terms of variables directly available as solutions in any commercial FE code: The two natural frequencies associated with short- and open-circuit (SC and OC) electrodes and a modal charge obtained as the electrical SC reaction force. An alternative method is based on quasi-static solutions with SC and OC electrodes, convenient for both numerical analysis and experiments. The proposed shunt tuning method is suitable for implementation in any commercial FE software supporting electromechanical analysis and ANSYS^® has been used to assess its accuracy for a piezoelectric smart plate benchmark problem. The method is finally extended to multiple piezoceramic patches, placed symmetrically on the structure and shunted to a single RL network, whereby more vibration modes can be effectively controlled for the specific plate problem.     

Mathematical modelling and finite element simulation of smart tubular composites

This paper presents a mathematical modelling and numerical simulation method for three-dimensional smart tubular 1(0)-3 composites based on a representative composite volume (RCV) approach. For the problems we consider, numerical results show that the maximum mechanical displacement varies linearly with the applied electrical potential and grows nonlinearly with increasing the RCV height. Further, we observe that decreasing the distance between the inner and outer radii results in increasing the maximum displacement. This refers to composites with large Young’s modulus of the polymer phase, whereas for “soft” polymers (i.e. for Young’s modulus of the polymers of order less than GPa) no particular ‘rule’ is evident, in which case the Poisson’s ratio is the most important parameter.     

Finite element modelling of hybrid active–passive vibration damping of multilayer piezoelectric sandwich beams—part I: Formulation

This work, in two parts, proposes, in this first part, an electromechanically coupled finite element model to handle active–passive damped multilayer sandwich beams, consisting of a viscoelastic core sandwiched between layered piezoelectric faces. The latter are modelled using the classical laminate theory, whereas the face/core/face system is modelled using classical three‐layers sandwich theory, assuming Euler–Bernoulli thin faces and a Timoshenko relatively thick core. The frequency‐dependence of the viscoelastic material is handled through the anelastic displacement fields (ADF) model. To make the control system feasible, a modal reduction is applied to the resulting ADF augmented system. Validation of the approach developed in this part is presented in Part 2 of the paper together with the hybrid damping performance analysis of a cantilever beam. Copyright © 2001 John Wiley & Sons, Ltd.