Abstract
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.
Highlights
Introduction and motivationThis paper is the preliminary result of an effort to produce an ultrasensitive sensor for measuring Nanoscale interaction forces in high-aspect ratio scenarios
We examined the closed-loop behavior when some changes are introduced to the system, imitating the change in Van der Waals (VdW) forces under gap change
It has been shown that the proposed closedloop control scheme can stabilize the open-loop unstable solution branches by three steps
Summary
This paper is the preliminary result of an effort to produce an ultrasensitive sensor for measuring Nanoscale interaction forces in high-aspect ratio scenarios. The motivation behind this paper is the idea of employing a transversely vibrating nanowire so that its interaction forces with side walls can be accurately measured. To achieve this goal, it is necessary to excite vibrations in a stable and predictable manner and choose an operating point for this slender structure so that it is sensitive to small, nano-scale interaction forces. By connecting a nanowire to a vibrating base, typically this is done with a piezoelectric element (e.g., a quartz tuning fork [4]), one can produce axial motion along the structure that would cause transverse motion orthogonal to the axial excitation [4]. Asymptotic Galerkin and multiple scales (MS) analysis are compared with largescale experiments
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