Flexural Vibrations of Piezolaminated Slender Beams: A Balanced Model

Abstract

A balanced model describing the behavior of piezolaminated composite beams was developed based on a first order shear deformation theory. The model takes into account the additional induced stiffness due to the direct piezoelectric effect for the case of “closed electrodes”, for symmetric and non-symmetric lay-ups. To comply with the condition of “closed electrodes” two cases were considered, E x = 0 or D x = 0. The three-coupled equations of motion were solved to yield eigenfrequencies and eigenmodes for various boundary conditions, materials and lay-up configurations. For the cases studied, the influence of the induced stiffness due to the direct piezoelectric effect on the natural frequencies was found to increase the natural frequencies by a few percent.