Investigation on parametric excitation vibration and piezoelectric active control of axially moving viscoelastic beams

Abstract

The nonlinear dynamics equation governing the behavior of axially moving viscoelastic beams is established in this paper, based on Hamilton’s principles. The Galerkin method is employed to discretize the equation for numerical analysis. Nonlinear parametric vibration control for axially moving viscoelastic beams is explored using piezoelectric laminated actuators based on LQR optimal linear control and SMC sliding mode control strategies. The stability of the moving beam is examined in respect of moving speed and active control. The influence of actuator position and control schemes on vibration control performance for the moving beam is also examined. In respect to linear and nonlinear equations, two control strategies of LQR are given to illustrate the control performances. The sliding mode control (SMC) is also given to reduce the vibration of the moving viscoelastic beam and exhibit the control performance and its robustness.