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 nanowires develop large transverse vibration under suitable amplitudes and frequency base-excitation that are sensitive to small potential coupled field. To utilize such a structure as a sensor, stable and robust operation are made possible by the control scheme. In addition, an optimal operating point with large sensitivity to the sensed potential field can be set using phase as a tunable parameter. Detailed analysis of the dynamical behavior, experimental verifications, and demonstrations sheds light on some features of the system dynamics.

Presented is a closed-loop, phase control scheme of a parametrically excited nonlinear structure, capable of stabilizing open-loop unstable solutions while automatically locking onto a desired point on any solution branch. Axially driven slender beams develop large transverse vibration under suitable amplitude and precise frequency base-excitation. The latter can induce parametric excitation along with a nonlinear response. The phase-lag of the 2:1 response over the excitation serves as a tunable parameter affecting the operating point of steady vibrations of a limit cycle. The operating point is tuned to exhibit great sensitivity to small interaction forces thus paving the way towards an ultrasensitive sensor. The paper analyzes the behavior of the mentioned configuration using asymptotic analysis, numerical simulations and an experimental system. Detailed analysis of the dynamical behavior, experimental verifications and demonstrations shed light on some features of the system dynamics.