A quasi-complete mechanical model for a double torsion pendulum

TL;DR

This paper develops a quasi-complete dynamical model for a double torsion pendulum system, capturing low-frequency torsional resonance and higher-frequency swinging and bouncing modes to accurately predict its response to external disturbances.

Contribution

It introduces a simplified yet comprehensive model considering 8 degrees of freedom for the double torsion pendulum, improving understanding of its dynamics and noise response.

Findings

Model accurately predicts the system's response to external forces.

Seismic tilt noise significantly affects low-frequency signals.

8 degrees of freedom suffice for an accurate dynamic description.

Abstract

We present a dynamical model for the double torsion pendulum nicknamed PETER, where one torsion pendulum hangs in cascade, but off-axis, from the other. The dynamics of interest in these devices lies around the torsional resonance, that is at very low frequencies (mHz). However, we find that, in order to properly describe the forced motion of the pendulums, also other modes must be considered, namely swinging and bouncing oscillations of the two suspended masses, that resonate at higher frequencies (Hz). Although the system has obviously 6+6 Degrees of Freedom, we find that 8 are sufficient for an accurate description of the observed motion. This model produces reliable estimates of the response to generic external disturbances and actuating forces or torques. In particular, we compute the effect of seismic floor motion (tilt noise) on the low frequency part of the signal spectra and show that it properly accounts for most of the measured low frequency noise.