On the bending of plates in the electromagnetic theory of microstretch elasticity

Abstract

This paper deals with the electromagnetic theory of microstretch elasticity. The full dynamic theory, which describes the interaction of electromagnetic fields with piezoelectric bodies, called piezoelectromagnetism, is considered. First, we derive the equations governing the bending theory of thin piezoelectromagnetic microstretch plates. Then, the boundary‐initial value problem is formulated and a uniqueness result is presented. Finally, the effects of a concentrated charge density in an infinite plate are studied.

Asymptotic piezoelectric plate models in microstretch elasticity

“…As already mentioned in the Introduction, few authors have developed mechanical models for piezoelectric microstretch elastic plates. Several improvements have been carried out with respect to papers , dealing with the bending problem of a piezoelectric/piezoelectromagnetic microstretch elastic plate. First of all, even though our asymptotic model represents a first order approximation model, we deduce the complete equilibrium problem for a piezoelectric microstretch elastic plate, taking into account both membrane and bending behaviors.…”

“…The fundamental paper by Ericksen and Truesdell extended the Cosserat theory to the construction of nonlinear rods and shells models by means of the direct approach. From that moment on, generalized Cosserat‐type theories of plates and shells have been widely discussed in the literature, see, for instance, the papers and their extensive bibliography, for a complete overview on this topic, as well as the papers , for their contributions on modeling the bending of microstretch piezoelectric and piezoelectromagnetic plates.…”

“…The present paper aims at putting together the ideas on modeling piezoelectric sensor and actuator plates, by means of the asymptotic analysis, and applying them to the case of a thin isotropic piezoelectric plate within the framework of microstretch elasticity. To the author's knowledge, few works (see, e.g., ) have been dedicated to the deduction of thin structure models, taking into account the coupling between piezoelectricity and microstructure: that is why it is necessary to provide an accurate and formal mathematical modeling on this topic. The two two‐dimensional plate problems are obtained, as in , with different scaling assumptions on the electric potentials, according to the different applied electric boundary conditions.…”

Impact of the Psychiatric Comorbidities in Chronic Obstructive Pulmonary Disease

“…Depression causes decreased daily physical activity, quality of life and treatment adherence, and correlates with more frequent exacerbations of COPD and increased mortality from COPD (Gales et al, 2014;Hillas et al, 2015).…”

The Static Behavior of a Ship Deck Panel Made of Composite Materials

“…In order to obtain answers such as stresses and strains for various cases of loading, of the natural vibration modes or of behavior of the structural elements to the buckling in the structural analyses that are applied in the ship structures, analytical calculations or the finite elements method are often used [15][16][17][18]. In general, in order to correctly define a structural analysis, various stages are taken, starting from the setting of objectives, type and size of the analysis, modeling of the structure and boundary conditions, modeling itself and evaluation of the results.…”