Automatic locking of a parametrically resonating, base-excited, nonlinear beam

Abstract Described is a closed-loop control scheme capable of stabilizing parametrically excited nonlinear structure in several vibration modes. By setting the relative phase between spatially filtered response and excitation, open-loop unstable solution branches are stabilized under 2:1 parametric excitation chosen mode vibration. For given phase, automatically locks on limit cycle, through an Autoresonance scheme, at any desired point branches. Axially driven slender beams nanowires develop large transverse suitable amplitudes frequency base-excitation that sensitive to small potential coupled field. To utilize such as sensor, stable robust operation made possible by scheme. In addition, optimal operating with sensitivity sensed field can be set using tunable parameter. Detailed analysis dynamical behavior, experimental verifications, demonstrations sheds light some features system dynamics.