Frequency division using a micromechanical resonance cascade
Abstract
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:⋯:2N. 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 2j 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 15, 2014
- Source ID
- 10.1063/1.4904465
Entities
People
- Alice Ma
- B. Gibson
- B. S. Strachan
- K. L. Turner
- Kamala Qalandar
- Maitreyee Sharma Priyadarshini
- Steven W. Shaw
Organizations
- Defense Advanced Research Projects Agency
- Michigan State University
- National Science Foundation
- University of California, Santa Barbara