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

Abstract

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.