Manifold based feedback linearization of a 1-DOF beam with one-sided spring (Q1126998)

This paper describes an approach to vibration reduction in a harmonically excited one-degree-of-freedom beam with one-sided spring. The authors propose to cause the system state to move from a stable large amplitude one-half subharmonic response towards a coexisting unstable small amplitude harmonic response using feedback linearization. To reduce the control effort when stabilizing the unstable harmonic response, the stable manifold can be used within the control design because -- at the stable manifold -- the system state approaches the unstable harmonic response without control effort. The stable manifold, difficult and awkward to compute exactly, can be approximated by the stable eigenvectors of the monodromy matrix.