Joël Pouget

Analytical and numerical approaches to piezoelectric bimorph

Abstract We propose an efficient and accurate approach to piezoelectric bimorph based on a refined expansion of the elastic displacement and electric potential. The field approximation of the through-the-thickness variation accounts for a shear correction and a layerwise modelling for the electric potential. A particular attention is devoted to the boundary conditions on the bottom and top faces of the plate as well as to the interface continuity conditions for the electromechanical variables. The continuity condition on the electric potential imposes some restrictions on the approximation of the electric potential. Moreover, the continuity condition on the normal component of the electric induction at the bimorph interface is ensured by a Lagrange multiplier. The equations of the piezoelectric bimorph are obtained by using variational formulation involving the appropriate boundary and continuity conditions. A selection of numerical illustrations is presented for the series and parallel piezoelectric bimorphs simply supported under cylindrical bending conditions. Two types of electromechanical load are considered (i) a surface density of force applied on the top face and (ii) an electric potential applied on the bottom and top faces of the bimorph. The results thus obtained are compared to those provided by finite element computations performed for the full 3D model and by a simplified model without shear effect. At last, the problem of piezoelectric bimorph vibration is also examined for both closed and open circuit conditions. Excellent predictions with low error estimates of the local (profile) and global responses as well as resonant frequencies are observed. The comparisons assess of the effectiveness of the present approach to piezoelectric bimorph.

Electroacoustic equations for one‐domain ferroelectric bodies

Based on a fully Galilean electrodynamics of dielectric deformable bodies, a completely deductive derivation of the coupled, dynamical, electromagnetic, electroacoustic, and energetic equations and constitutive equations for elastic, pyroelectric, ferroelectric dielectrics accommodating viscosity and dielectric‐relaxation phenomena is presented. Of necessity the theory is first constructed in a fully nonlinear framework even though applications to signal processing are envisaged. Then a linearization is performed by Lagrangian variation about an initial ferroelectric state in which there exist no strains, but there are present both stresses and local electric field as well as an initial electric polarization. The latter provokes a breaking of the ideal symmetry of the material, so that finally linearized coupled electroacoustic and heat‐propagation equations are deduced on which can be based the study of coupled acoustic‐soft optic modes in ferroelectrics of the BaTiO3‐type. No thermodynamical restriction...

An accurate modelling of piezoelectric multi-layer plates

The present work proposes a new approach to laminated plates with piezoelectric layers based on a refinement of the electric potential as function of the thickness coordinate and accounting for shearing correction of the elastic displacement. The approach deals with the combination of an equivalent single-layer approach for the mechanical displacement with a layerwise-type modelling of the electric potential considered as an additional degree of freedom. Such an approach offers flexibility in accommodating electric conditions at the layer interfaces. The equations governing the force, moment and electric charge resultants of the laminated piezoelectric plate are then deduced from a variational formulation involving mechanical surface loads or prescribed electric potential on the top and bottom faces of the plate as well as at layer interfaces. A particular attention is devoted to the interface conditions which are enforced by using Lagrange multipliers in the variational principle. Emphasis is placed on the performances, advantages and limitations of the present approach. The quality of the predictions of the global and local responses (the through-the-thickness variation of elastic displacements, stresses, electric potential and induction) is quantified for particular structures of practical interest such as piezoelectric bimorph, bilayer structure and piezoelectric sandwich undergoing applied density of force and electric potential. Moreover, comparisons of the results provided by the refined approach to those of finite element computations and simplified model are also presented. The comparisons assess of the effectiveness of the present laminated piezoelectric plate model that improves, in significant way, the predictions given by a simplified approach.

Identification of electromechanical modal parameters of linear piezoelectric structures

Reduced-order modal models of linear piezoelectric structures are useful in vibration control and health monitoring. We study experimental identification of the fundamental parameters of these modal models. We propose two identification techniques for estimating piezoelectric modal couplings and piezoelectric modal capacitances. Both methods are easily implementable and rely on elementary vibration tests. We show the application of these methods to a sample structure hosting multiple transducers.

Optimization of piezoelectric patch positioning for passive sound radiation control of plates

The purpose of this article is the optimization of piezoelectric patch positioning for reducing the radiated sound power of thin plates. To this end, an aluminium plate equipped with a set of piezoelectric patches connected to a passive circuit is considered. The difficulties in designing a smart structure are not only related to the conception of the electric circuit used as controller, but also to the choice of how the circuit itself is coupled with the structure. The selection of the number of transducers to be used, and their positioning, is a crucial step in the designing process. In this work the entire design process of a smart structure is proposed, with the goal of obtaining the best efficiency in terms of reduction of radiated sound power, while using a lightweight optimization procedure in terms of computational costs. To this end, classical instruments of vibrations mechanics are used together with acoustic concepts, such as the modal radiation efficiency. The introduction of this acoustic characterization of the structure in the optimization process is done by using a new utility function, the acoustic controllability, which will be used for the optimization of transducer positioning. The proposed optimization process is applied to the case study of an aluminium plate with nonstandard boundary conditions, and experimental results confirm the validity of this novel procedure.

Influence of an external electric field on the motion of a ferroelectric domain wall

Abstract The study of the influence of an external electric field on the motion from rest of a domain wall in ferroelectric crystals is presented. The solution of the problem representing the translational and rotational motions of the chain is sought in terms of solitary waves. Both electric and mechanical state of the structure in domains can be determined. The evolution of the velocity of the wall altered by the applied field is determined by means of energy arguments accounting for electromechanical couplings. A numerical simulation is given which illustrates the transient motion from rest of a wall separating two ferroelectric domains.

Coupled acoustic–optic modes in deformable ferroelectrics

Based on a fully Galilean electrodynamics of ferroelectric dielectric deformable bodies and the equations for weak fields linearized about an initial rigid‐body ferroelectric state with hexagonal symmetry deduced in a previous paper (in which a symmetry breaking was exhibited), a rather complete study of coupled, dispersive, and attenuated bulk wave‐propagation modes is presented. Apart from usual optic modes, resonance couplings and repulsion of branches for acoustic modes and polaritons are exhibited for various directions of propagation (longitudinal, orthogonal, and arbitrary settings of the bias polarization field). A birefringence effect for polaritons and an acoustical activity are placed in evidence. In addition to the analytical study which leans on the use of small coupling parameters in order to allow for a manageable discussion of the dispersion behavior for both nondissipative and dissipative processes, and to illustrate these theoretical results, numerical estimates and plots of the most int...

Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results

Abstract We propose a new approach to laminated piezoelectric plates based on a refinement of the electric potential as function of the thickness coordinate of the laminate and accounting for shear effects. Moreover, the variation of the electric potential as function of the thickness coordinate is modelled for each layer of the laminate. The equation for the laminated piezoelectric plate are then obtained by using a variational formulation involving mechanical surface loads or prescribed electric potential on the top and bottom faces of the plate. In addition to the equations for the generalized stress resultants (due to the shear effects), the equation of the electric charge conservation is also deduced for the 2D model. Particular attention is devoted to the single piezoelectric plate and bimorph structure and the through-thickness distribution of the displacements, electric potential as well as stresses are given for different kinds of electromechanical loads. The results thus obtained are compared to those provided by a finite element method performed for the full 3D model. A good agreement is observed for plates made of layers of PZT-4 piezoelectric material. The comparison ascertains the effectiveness of the present 2D approach to piezoelectric laminates.

Bleustein–Gulayev surface modes in elastic ferroelectrics

On the basis of a nonlinear theory of elastic ferroelectrics linearized about a fundamental ferroelectric state, it is shown that the symmetry breaking caused by the initial intense polarization orthogonal to the sagittal plane allows for the existence of Bleustein–Gulayev surface modes in ferroelectrics of the barium titanate type. The two cases of a free boundary and a grounded boundary are examined. In the first case it is shown that above a certain critical wavenumber (interaction of elastic and ferroelectric modes) the exponential decrease with depth of the amplitudes is sinusoidally modulated while there exists a minute dispersion of the mode. In the second case the Bleustein–Gulayev mode which is exhibited is strongly dispersive in the neighborhood of this critical wavenumber (which then corresponds to a unilateral repulsion of dispersion branches). All the features of this surface‐wave propagation problem are examined both analytically and numerically (for BaTiO3) with a particular emphasis on sec...

Analytical and Numerical Modelling of Laminated Composites with Piezoelectric Elements

We propose an accurate and efficient approach to laminated piezoelectric plates based on a refinement of elastic displacement and electric potential through the plate thickness. More precisely, the model accounts for a shearing function and a layerwise approximation for the electric potential. The layerwise approach becomes a necessity in order to accommodate electric potential at the electrode interfaces. The equations of motion for the piezoelectric composite are deduced from a variational formulation incorporating the continuity conditions at the layer interfaces by using Lagrange multipliers. Different situations are investigated among them (i) bimorph and (ii) sandwich structures for two kinds of electro-mechanical loads applied (density of force and electric potential) and are compared to the finite element computations performed on the 3D model. The vibration problem is also presented and the frequencies for the axial and flexural modes are obtained. At last performance and effectiveness of the model are also discussed and applications to control of the structure shape and vibration are proposed.