Size-dependent free vibration of nano/microbeams with piezo-layered actuators

The size-dependent free vibration of nano/microbeams with piezo-layered actuators is analytically investigated. The size-dependent dynamic modelling of the piezo-layered beam is presented on the basis of the non-local continuum theory. Equations of the motion and boundary conditions of the beam are obtained by implementation of Hamilton´s principle. Analytical solutions for natural frequencies and mode shapes are obtained as a function of the piezo-layered beam characteristic size and non-local size scale parameter. The size effects on the vibration behaviour of the beam are studied and it is found that the non-local parameter, length ratio and thickness ratio have significant effects on the free vibration of systems.