Vibration analysis and control of cantilever micro-beam integrated piezoelectric actuator and sensor layers considering surface effects

Nowadays, accurate prediction of micro structure vibration and dynamic behavior have been considered by many researchers. In this work, vibration analysis and control of cantilever micro-beam integrated with piezoelectric actuator and sensor layers considering surface effects have been investigated. Hamilton’s principle and Energy method are used to derive governing partial differential equation of the motion. GDQM is applied to discretize the PDE into the ordinary differential equation. The effects of system geometry, Young’s modules of surface stress, surface residual stress and surface mass density on natural frequency are analyzed. Also, the effect of linear optimal controller design on dynamic the response time and piezoelectric control voltage has been evaluated. Results indicate that respond on model increases and vibration amplitude decreases faster.