passivity analysis of nonlinear euler-bernoulli beams

The Lagrangian equations for distributed-parameter systems based on Hamilton's principle are developed. These equations are subsequently used to derive nonlinear models for beams. The passivity properties of the flexible mechanical systems based on their distributed-parameter models are then investigated and direct output feedback control laws for control purposes are proposed. Finite gain L2 stability and passivity of closed-loop systems are proven. Illustrative cases with simulation of the nonlinear beams and stabilizing feedback control laws are included in the text.