A FEM model for active vibration control of flexible linkages

For the design of active vibration control laws for flexible linkages in high-speed mechanisms, dynamic models incorporating the coupling of rigid body motion and flexible motion and the electromechanical coupling of transduction devices and the host linkage are very important. In the first part of this paper, the Lagrange finite element (FE) formulation is used to derive such a dynamic model for a flexible planar linkage with one rotary and two translational degrees of freedom. Linear electromechanical coupling of surface-bonded lead zirconate titanate (PZT) patches with the host linkage is incorporated into the model. In the second part of this paper, this dynamic model is simplified and applied to simulate active vibration control of flexible linkages in a high-speed planar parallel platform based on kineto-elastodynamics assumptions: (1) the influence of flexible motion on rigid body motion is ignored; and (2) joint constraint forces in the flexible linkage case are close to those in the rigid linkage case. Based on these assumptions, the rigid body motion and joint constraint forces are regarded as inputs to flexible dynamics, which is obtained from rigid body simulation. Using the simplified dynamic model, simulation of strain rate feedback control using PZT sensors and actuators is performed. Experimental results are also presented. Both simulation and experimental results show that PZT actuators effectively damp the vibration of the flexible linkages.