Size-dependent static bending of a micro-beam with a surface-mounted 0–1 polarized PbLaZrTi actuator under various boundary conditions

This article presents modified couple stress theory–based size-dependent deflection curve equations for a micro-beam with a surface-mounted 0–1 polarized PbLaZrTi patch under various boundary conditions. In these models, only an internal material length scale parameter is used to capture the size-dependent mechanical behaviors. When this parameter is set to zero, these models are simplified to the available solution based on the classical Euler–Bernoulli theory. The effect of the actuator stiffness on the deflection of the beam is thoroughly discussed. It is observed that whether the deformation of the beam is sensitive to the added actuator or not depending on the stiffness of the host beam. The larger the stiffness of the host beam, the less the effect of the added actuator. It is also observed that the less the ratio of the beam thickness to the actuator stiffness, the larger the ratio of the size-dependent solution to the local one.