A Formal Method for Improving the Transient Behavior of a Nonlinear Flexible Link

This paper presents a procedure for improving the transient response of a boundary controlled nonlinear flexible elastic beam via a feed-forward action. It is shown that it is possible to obtain a formal analytic solution of an infinite-dimensional linear system, which approximates the nonlinear dynamics, under time-varying boundary conditions in terms of the free vibration modes of the structure, whose calculation is a relatively easy task. The feed-forward action is then obtained by inverting the relationship between input and output variables. A numerical example is presented and some simulation results are discussed.