Abstract
•Modelling and solutions based on the Stroh-like formalism for 3-D static degenerate and electro-elastic multi-layered plates.•Coupled time trigonometric series and Stroh-like formalism for 3-D dynamic analysis of multi-layered electro-elastic plates.•Computation of generalized eigenvectors in the generate case and explicit formulation of the solution in complete bases.•Flexible matrix formulation to account for arbitrary mechanical and electrical surface loads and pulse excitations.•Investigation of electro-elastic, degeneracy and graded material’s factor effects on static and dynamic plate’s behaviours.
In this paper mathematical modelling and semi-analytical solutions are elaborated based on the extended Stroh-like formalism for 3-D static problems of electro-elastic mono and multilayered plates. For the dynamic analysis of such structures under various excitation types, a time trigonometric series was coupled with the Stroh-like formalism. The unknown coefficient vectors are solution of the resulted eigenvalue problems and the solution is obtained in the associated basis. Mechanical and electrical forces are applied on the top and/or bottom layer and may take arbitrary forms. A flexible matrix formulation is elaborated to easily account for arbitrary mechanical and electrical surface loads and excitations. The methodological approach focuses on various aspects including the electro-elastic effects, the degeneracy of elastic isotropic materials as well as the effect of the graded material’s factor. Analytical solutions are obtained for the static behavior of degenerate and non-degenerate Elastic FGM plates, where the eigenvalues and eigenvectors are explicitly given. Mainly, semi-analytical solutions are presented for the dynamic behavior of piezoelectric sandwich plates by coupling Stroh-like formalism and trigonometric series. The presented methodological approach is applied to the dynamical analysis of sandwich plates under various excitation forms, namely sinusoidal, rectangular and sawtooth excitation pulses. The obtained numerical results demonstrate the effect of the graded factor, degeneracy and the applied surface load as well as of the excitation on mechanical and electrical responses for various laminated plates.