A new discovery of bending behaviors of low-dimensional piezoelectric materials

The measurement of mechanical and electrical properties has become an important topic in studying low-dimensional piezoelectric materials. In this paper, the analytical solution of a piezoelectric beam is derived based on the Bernoulli hypothesis and the three-dimensional constitutive equations. The bending behaviors of the piezoelectric cantilever beam with and without electrodes are studied. It is found that the form of the governing equations and final solutions for the piezoelectric beam is similar to the one for an elastic beam by defining the equivalent bending stiffness.