The bending problem of piezoelectric micro- beam based on micromorphic electroelastic theory

The linear theory of micromorphic electroelasticity is developed to investigate the bending problem of piezoelectric micro beam. The governing equations and boundary conditions are derived through variational principle. The solution of the cantilever beam loaded by a concentrated force at the free end is obtained. Numerical results reveal that the differences in the deflection predicted by the present model and the classical model are very large at the micro scale. The size effect is only significant when the beam thickness is comparable to the material length scale parameter.