Asymptotic modeling of piezoelectric plates with electric field gradient

Abstract

To cite this version: AbstractWe extend our modeling of smart structures to second order piezoelectricity. We show that three different models have to be taken into account, which broadens the scope of the sensors and actuators field. Second order piezoelectricity being compatible with isotropy, we also propose a systematic study of the impact of crystalline symmetries on our models. To cite this article: T. Weller, C. Licht, C. R. Mecanique xxx (aaaa). RésuméModélisation asymptotique de plaques piézoélectriques avec gradient du champélectrique Nouś etendonsà la piézoélectricité avec gradient du champélectrique notreétude des couplagesélectromécaniques dans les structures minces. Nous montrons en particulier que trois modèles distincts apparaissentà la limite, ce qui enrichit substantiellement la description du comportement des capteurs et actionneurs en fonction du chargementélectrique qui leur est imposé. La piézoélectricité du second gradientétant compatible avec l'isotropie, nous proposonségalement uneétude systématique de l'influence des symétries cristallines sur les modèles obtenus. Pour citer cet article : T. Weller, C. Licht, C. R. Mecanique xxx (aaaa).

Asymptotic modeling of thin linearly quasicrystalline plates

“…iii) the boundedness of the "work of the exterior loading": (8) so that s p (ε) is the unique solution of the following mathematical problem:…”

“…We show that depending on the type of boundary conditions, 26 different models indexed by a triplet p = (p 1 , p 2 , p 3 ) ∈ {0, 1, 2} 3 appear at the limit. Comparing to our previous studies devoted to the mathematical modeling of thin plates in the framework of multi-physical couplings [6][7][8], we are here in front of a real 'explosion' of the number of limit models. This multiplication of models, however, has its roots in the very structure of QCs.…”

“…As explained in our previous papers [6][7][8][9], the signs of the various powers of ε in the components of k p (ε, ξ) induce an orthogonal decomposition of H in subspaces H p with ∈ {−, 0, +}, which allows a comprehensive description of our plate models in any theoretically admissible quasicrystallographic classes. We denote by h p the projection on H p of any element h of H. As an example, for p = (0, 1, 2), we have: H − p = (e, g) ∈ H; e αβ = 0, g 2α = 0, g 3i = 0 H 0 p = (e, g) ∈ H; e i3 = 0, g 1i = 0, g 23 = 0, g 3α = 0 H + p = (e, g) ∈ H; e ij = 0, g 1i = 0, g 2i = 0, g 33 = 0 Then, for a given triplet p, the operator Q can be decomposed in nine elements…”

New linear and quadratic prismatic piezoelectric solid–shell finite elements

“…Interesting contributions to the field were also made by Boudaoud et al [33], Belouettar et al [3] and Azrar et al [34], among others, with applications to vibration control of multilayer structures. From a fundamental perspective, it is important to mention the major theoretical contributions of Weller and Licht [35,36], who studied the asymptotic behavior of thin piezoelectric plates (with or without electric field gradient). All of the above formulations are able to efficiently model beam and plate structures with piezoelectric materials.…”

A piezoelectric screw dislocation near an elliptical inhomogeneity containing a confocal rigid line

“…Piezoelectric materials are widely used in modern technology such as sensors, micropositioner, electro-mechanical actuator and high power sonar transducers as a result of the intrinsic coupling behavior [1][2][3][4][5]. However, the presence of various defects, such as dislocations, cracks and inclusions, can greatly influence their characteristics and coupling behavior.…”