A size-dependent model to study nonlinear static behavior of piezoelectric cantilever microbeams with damage

Based on the modified couple stress theory and von Kármán nonlinear theory, a size-dependent nonlinear mathematical model for an electrostatically actuated microbeam with a piezoelectric layer bonded to the top surface is formulated by the Hamilton’s principle. In the developed model, the static behavior of the microbeam is discussed by using numerical methods. The results show that the size effect is significant when the microbeam thickness is comparable to the material length scale parameter. The effect of geometric nonlinearity on the pull-in voltage mainly depends on the initial gap. By applying a small negative voltage to the piezoelectric layer, the pull-in voltage may effectively reduce. To attain accurate analysis for the static behaviors of microscale beam devices, the damage has to be considered.