Piezoelectric vibrations of composite beams with interlayer slip

Actuating piezoelectric effects in two-layer beams with interlayer slip are described in detail, and special attention is given to the identification of the piezoelectric actuation as eigenstrains. It is demonstrated that piezoelectrically induced strains conveniently can be interpreted as eigenstrains acting in a background composite beam without piezoelectric actuators. The analogy between the piezoelectric effect and that of thermal strains is utilized in the present paper, where a layer-wise first-order flexural theory is applied to two-layer beams with various boundary conditions. The layers are assumed to be made of piezoelectric materials. Bernoulli-Euler hypothesis is assumed to hold for each layer separately, and a linear constitutive relation between the horizontal slip and the interlaminar shear force is considered. The governing sixth-order initial-boundary value problem is solved by separating the dynamic response in a quasistatic and in a complementary dynamic portion. The quasistatic solution that may also contain singularities or discontinuities due to sudden load changes is determinded in a closed form. The remaining complementary dynamic part is nonsingular and can be approximated by a truncated modal series of accelerated convergence. The proposed procedure is illustrated for piezoelectrically induced flexural deformations, where the forcing function is the piezoelectric curvature.