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

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.

Experiments match simulations in a multiple post reentrant cavity.

Microwave reentrant cavities are used for many applications in science and engineering. The potential for both high mechanical tunability and high electric quality factors make them important tools in many areas. They are usually resonant cylindrical cavities with a central post, which makes a small gap spacing with the cavity wall. By adding an arbitrary number of extra posts, they are generalized to a type of multiple post reentrant cavity. This new approach has been theoretically studied but no experimental results have been presented. The main purpose of this work was to compare experimental modes with simulated ones from a reentrant cavity made of forty nine cylindrical posts. Each post could be moved using a screw in order to make tunable gap spacing between the post top and the cavity cover. Eight different gap setups were made making it possible to investigate thirty six different reentrant modes at room temperature. The lowest frequency percentage agreement between experiment and simulation was 91.31%, and the best one was 99.92%. Taking into account all the modes, 94.44% of them agreed above 96%. Thus, we have determined an experimental procedure suitable to investigate the reentrant modes from multiple post cavities. There is a wide range of potential applications for such cavities due to their unique features compared to conventional ones.