Described is a closed-loop control scheme capable of stabilizing a parametrically excited
nonlinear structure in several vibration modes. By setting the relative phase between the
spatially filtered response and the excitation, the open-loop unstable solution branches are
stabilized under a 2: 1 parametric excitation of a chosen mode of vibration. For a given
phase, the closed-loop automatically locks on a limit cycle, through an Autoresonance
scheme, at any desired point on the solution branches. Axially driven slender beams and …

Described is a closed-loop control scheme capable of stabilizing a parametrically excited
nonlinear structure. By setting the relative phase between the response and excitation, the
open-loop unstable solution branches are stabilized under a 2: 1 parametric excitation. For a
given phase, the closed-loop automatically locks on a limit-cycle, at any desired point on the
solution branches. Axially driven slender beams and nanofibers develop large transverse
vibration under suitable amplitudes and frequency base-excitation that are sensitive to small …