Mathematical Modeling of a Piezo-Actuated Cantilever Beam With Interferometer Feedback

Abstract

Laser interferometry, commonly used in high-precision motion control systems, is rarely adopted in experimental vibration analysis because their installation and mounting are invasive to dynamical systems. However, new technology in high-precision manufacturing, such as vibration-assisted machining, has shown the meaningfulness of using laser interferometers implemented in motion control systems for vibration analysis, system identification, and feedback control. To this end, this study investigates the use of laser interferometry for vibration analysis through a piezoelectrically actuated cantilever beam. The complete dynamics of the cantilevered beam with a piezoelectric actuator and a laser interferometer is modeled through the Euler-Bernoulli beam theory. Through the method of separation of variables, the original continuous system is transformed into a discrete system represented in a state-space form. The response of the beam is analytically predicted, then compared with the numerical result from a multibody model constructed in Simscape. The frequency response at the retroreflector is obtained through the Laplace transformation of the state-space form. It is found that the first modal frequencies from analytical prediction precisely agree with their experimental counterpart.