Piezoelectric vibrations of composite beams with interlayer slip
The authors describe actuating piezoelectric effects in two-layer beams with interlayer slip. Special attention is given to identification of piezoelectric actuations as eigenstrains. An analogy between the piezoelectric effect and that of thermal strains is utilized, 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, the Bernoulli-Euler hypothesis is assumed to hold separately for each layer, and a linear constitutive relation between horizontal slip and interlaminar shear force is considered. The authors solve the governing sixth-order initial-boundary value problem by separating the dynamic response into a quasistatic and into a complementary dynamic portion. The quasistatic solution that may also contain singularities or discontinuities due to sudden load changes is determined in a closed form. The remaining complementary dynamic part is nonsingular and can be approximated by a truncated modal series of accelerated convergence.
sixth-order initial-boundary value problem
scientific article; zbMATH DE number 1487298