Evaluation of exact electro-elastic static and free vibration solutions of multilayered plates for benchmarking: Piezoelectric composite laminates and soft core sandwich plates

Abstract

This work provides a study on three-dimensional exact electro-elastic static and free vibration solutions of multilayered plates, focused on a comprehensive evaluation of well-known benchmarks for piezoelectric and/or composite laminates as well as soft core sandwich plates, adding much to thus far available in the literature. The exact solution method for simply supported multilayered plates is fully described in line with earlier leading works, compiled in a single study in a consistent form throughout. The layers involved can be either piezoelectric layers poled through-thickness (i.e. extension mode) or purely elastic layers, including composite layers. For each layer, the form of the through-thickness exact solution depends strongly on its material properties, thus each case arising from an orthotropic, transversely isotropic or simply isotropic layer is considered specifically. Within the free vibration solution, in agreement with an in-plane mode (nx, ny), the so-called special modes for either nx=0 or ny=0, though often overlooked, are purposely addressed, along with thickness modes for each pair (nx, ny). The benchmarks cover purely elastic solutions, as in composite laminates and soft core sandwich plates, as well as electro-elastic solutions, namely piezoelectric composite laminates, involving not only but especially thick plates. For each multilayered plate, the static solution considers either an applied load or an applied electric potential, providing a detailed through-thickness evaluation of displacements and stresses, and when present, the electric potential and electric displacements. The respective free vibration solution reveals the first twenty natural frequencies and associated modes, including all together special modes and thickness modes.