Active Control of a Cantilevered Beam Subjected to the Transverse Follower Force of a Fluid Jet

Abstract

Theoretical studies on the dynamic stability and active control of a cantilevered beam subjected to the transverse follower force of a fluid jet are presented in this paper. In order to control the response of the beam, the active control force is derived from the bending moment produced by a pair of piezoelectric actuators partially attached to both sides of the beam. The equations of motion and the boundary conditions are first derived from the extended Hamilton's principle and then reduced to a finite degree of freedom system using Galerkin's method. A control law is determined using the optimal regulator theory. Numerical calculations are given displayed for various conditions. It is cantilevered beam subjected to a transverse follower force.