Achieving maximum tip displacement during resonant excitation of piezoelectrically actuated beams

A linear, lumped-parameter, single-degree-of-freedom model is formulated to describe the dynamic response of the first mode of a piezoelectrically-actuated cantilevered beam. The modeled system consists of two identical, symmetrically disposed piezoelectric patch actuators bonded to a uniform beam with a tip mass. Specifically, the first mode of the system is described by an equivalent mass-spring-damper system where the equivalent mass, stiffness, damping, and force are functions of the parameters of the piezoelectrically-actuated system. Experimental data are used to verify model damping and displacement. The model is then used to show that the dynamic response of the system depends upon four independent non-dimensional geometric variables. Numerical simulations are performed to graphically demonstrate this dependence and to indicate an optimal configuration for achieving a maximum deflection at the beam's free end during resonant excitation.