Free-vibration analysis of laminated plates with embedded shear-mode piezoceramic layers

This paper presents a three-dimensional exact mixed state space solution and a parametric analysis for the free-vibration of simply-supported laminates with embedded transverse shear mode piezoceramic layers. The formulation retains, as state variables, the standard mechanical displacements and transverse stresses augmented with the electric transverse displacement and potential. It considers both non-electroded and electroded inner x-poled piezoceramic laminae. The solution validation is made through some demonstrated expected results. Then, a parametric study is conducted for various parameters variations. It was found that the thickness distributions of the electric state variables depend strongly on the electric boundary conditions and mode type. Moreover, in contrary to the common practice of the mechanical community, the small difference between short- and open-circuit natural frequencies should not be neglected but can be used to assess the piezoelectric effect through the so-called effective modal electromechanical coupling coefficient. Its level was found to depend on the poling direction, mode type, plate length-to-thickness ratio and piezoceramic lamina thickness and position in the laminate. This exact solution and its obtained results can be used for future reference and shear-mode piezoelectric vibration behavior comprehension purposes.