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Title: Frequency division using a micromechanical resonance cascade

A coupled micromechanical resonator array demonstrates a mechanical realization of multi-stage frequency division. The mechanical structure consists of a set of N sequentially perpendicular microbeams that are connected by relatively weak elastic elements such that the system vibration modes are localized to individual microbeams and have natural frequencies with ratios close to 1:2:⋯:2{sup N}. Conservative (passive) nonlinear inter-modal coupling provides the required energy transfer between modes and is achieved by finite deformation kinematics. When the highest frequency beam is excited, this arrangement promotes a cascade of subharmonic resonances that achieve frequency division of 2{sup j} at microbeam j for j = 1, …, N. Results are shown for a capacitively driven three-stage divider in which an input signal of 824 kHz is passively divided through three modal stages, producing signals at 412 kHz, 206 kHz, and 103 kHz. The system modes are characterized and used to delineate the range of AC input voltages and frequencies over which the cascade occurs. This narrow band frequency divider has simple design rules that are scalable to higher frequencies and can be extended to a larger number of modal stages.
Authors:
; ; ; ;  [1] ;  [2] ;  [3] ;  [2] ;  [3]
  1. Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, California 93106 (United States)
  2. Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48823 (United States)
  3. (United States)
Publication Date:
OSTI Identifier:
22395570
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Physics Letters; Journal Volume: 105; Journal Issue: 24; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COUPLING; DEFORMATION; DESIGN; ELECTRIC POTENTIAL; ENERGY TRANSFER; MECHANICAL STRUCTURES; NONLINEAR PROBLEMS; OSCILLATION MODES; RESONANCE; RESONATORS; SIGNALS