Electrostatic frequency reduction: A negative stiffness mechanism for measuring dissipation in a mechanical oscillator at low frequency

• Published in: Review of scientific instruments 2021-01, Vol.92 (1), p.015101-015101
• Main Authors: Erwin, A., Stone, K. J., Shelton, D., Hahn, I., Huie, W., de Paula, L. A. N., Schmerr, N. C., Paik, H. J., Chui, T. C. P.
• Format: Article
• Language: English
• Subjects: Broadband; Brownian motion; Damping; Electrical noise; Frequency ranges; Friction; Gravitational waves; Helical springs; Internal friction; Low frequencies; Mechanical oscillators; Noise; Noise reduction; Q factors; Resonance; Scientific apparatus & instruments; Seismographs; Springs (elastic); Stiffness; White noise
• ISSN: 0034-6748; 1089-7623
• DOI: 10.1063/5.0019351

Broadband seismometers and gravitational wave detectors make use of mechanical resonators with a high quality factor to reduce Brownian noise. At low frequency, Brownian noise is ultimately dominated by internal friction in the suspension, which has a 1/f noise compared with the white noise arising from viscous dissipation. Internal friction is typically modeled as a frequency-dependent loss and can be challenging to measure reliably through experiment. In this work, we present the physics and experimental implementation of electrostatic frequency reduction (EFR) in a mechanical oscillator—a method to measure dissipation as a function of frequency. By applying a high voltage to two parallel capacitor plates, with the center plate being a suspended mass, an electrostatic force is created that acts as a negative stiffness mechanism to reduce the system’s resonance frequency. Through EFR, the loss angle can be measured as a function of frequency by measuring amplitude decay response curves for a range of applied voltages. We present experimental measurements of the loss angle for three metal helical extension springs in the nominal frequency range 0.7–2.9 Hz at 0.2 Hz intervals, demonstrating the possibility for fine adjustment of the resonance frequency for loss angle measurements. A quality factor proportional to the resonance frequency squared was measured, an indication that internal friction and other non-viscous dissipation elements, such as electrostatic damping, were the prominent loss mechanisms in our experiments. Finally, we consider the implications of Brownian noise arising from internal friction on a low 1/f noise seismometer.