The intersection of noise, amplitude, and nonlinearity in a high-Q micromechanical torsion pendulum

Published

May 6, 2024

Author(s)

Jon R. Pratt, Stephan Schlamminger, Dalziel Wilson, Charles Condos, Aman Rajendra Agrawal, Christian Pluchar

Abstract

We derive a nonlinear equation of motion for a chip-scale pendulum comprising a thick plate suspended from a tensioned nanoribbon. Recently we explored the use of such a device as a clock gravimeter, exploiting the parametric coupling of its frequency to the local acceleration of gravity, and demonstrating micro-$g$ resolution with a silicon nitride prototype. Here we consider the restoring torque arising from the mid-plane stretching of the nanoribbon, finding it is a hardening spring that can be used to counteract the softening of gravitational torques, reducing parametric frequency noise and extending the range of isochronous pendulation. Using the method of multiple scales, we predict that parametric frequency-amplitude coupling can be driven to zero by exploiting fabrication tolerances available using modern nanolithography.

Proceedings Title

Advances in Nonlinear Dynamics: Proceedings of the 3rd International Nonlinear Dynamics Conference (NODYCON 2023)

Conference Dates

June 18-22, 2023

Conference Location

Rome, IT

Conference Title

NODYCON 2023 third International Nonlinear Dynamics Conference

Pub Type

Conferences

Download Paper

https://doi.org/10.1007/978-3-031-50635-2

Local Download

Keywords

micromechanical torsion pendulum, dissipation dilution, gravimeter

Citation

Pratt, J. , Schlamminger, S. , Wilson, D. , Condos, C. , Agrawal, A. and Pluchar, C. (2024), The intersection of noise, amplitude, and nonlinearity in a high-Q micromechanical torsion pendulum, Advances in Nonlinear Dynamics: Proceedings of the 3rd International Nonlinear Dynamics Conference (NODYCON 2023), Rome, IT, [online], https://doi.org/10.1007/978-3-031-50635-2, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=936199 (Accessed December 24, 2024)