Résumé
We investigate the asymptotic behavior of the dynamic response of a thin viscopiezoelectric plate as its thickness, taken as a parameter, approaches zero. We use Trotter theory of convergence of semi-groups of operators acting on variable spaces. Depending on the kind of electrical loading and on the orders of magnitude of the density and of the viscosity, we highlight four different sensor and actuator behaviors.
Key words and phrases. Approximation of semi-groups in the sense of Trotter, asymptotic analysis, dimension reduction, maximalmonotone operators, piezoelectricity, thin plates, viscoelasticity of non-linear Kelvin-Voigt type.