Vibration reduction of a harmonically excited beam with one-sided spring using sliding computed torque control

Abstract

Vibration reduction of a harmonically excited multi Degree of Freedom (DOF) beam system with a local nonlinearity represented by a one-sided spring is considered. The linear beam system is modeled with a 3-DOF model which is obtained by applying a component mode synthesis method on the linear finite element model of the beam system. The low frequency response of the linear system can be described very accurately while the number of DOFs for the nonlinear analysis is kept small. Vibration reduction is realized in both simulations and experiments by forcing the system at a prescribed excitation frequency from the stable 1/2 subharmonic response of high amplitude towards the coexisting unstable harmonic response of low amplitude using a Sliding Computed Torque Controller (SCTC). The advantage besides the reduction of vibration amplitude is the small control effort needed once the unstable harmonic solution is stabilized. This is due to the fact that the unstable harmonic solution is a natural solution of the uncontrolled system.