Dynamic measurement of gravitational coupling between resonating beams in the hertz regime

Dynamic gravitational excitation of structural resonances in the hertz regime using two rotating bars

“…This is illustrated in Table 1 showing an overview of the few dynamic gravitational experiments reported during the last 50 years. To fill this gap, we presented in a previous work the dynamical gravitational coupling between two parallel beams vibrating in their first bending resonance at 42 Hz [1]. This setup allowed for a quantitative investigation of the distance behavior and the estimation of the gravitational constant G. Although this setup allowed for important advances in dynamic gravitation measurements, it features some drawbacks, such as the need for matching transmitter and detector resonance frequency or the generation of very low detector amplitudes.…”

“…These advantages, however, come at the expense of high requirements on the balancing of the rotors and their motion control, in particular their phase accuracy and phase jitter. To demonstrate the potential of this new setup, we use the same detector beam as in [1] and the same measurement procedure. Thus we obtain the detector resonance amplitude and phase at different distances, as well as an estimation of the gravitational constant G. While the motion of the rotating bars is trivial to model, its interaction with the detector beam is categorized as a nonstandard moving load problem [9] with varying speed and shape of the moving force pulse.…”

“…1. The detector's bending movement can then be calculated using an Euler-Bernoulli beam model and a modal approach [1,10], in which the distributed force is reduced to the effective modal excitation force F y,b of the first bending mode via…”

“…By averaging the last 16 min of each step, a signal-to-noise ratio (SNR) ratio of up to 500 can be achieved. After fitting the frequency response of a single-degree-of freedom (SDOF) oscillator [1], the following parameters are obtained: amplitude and phase at resonance, resonance frequency, the detector's Q factor, and a complex offset constant. The low bandwidth of the detector and the need for synchronization of both beams imposes extremely high requirements on the resolution and stability of the rotation frequencies.…”

The Nonlinear Influence of Large Celestial Bodies on Earthquakes—Short Commentary

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A new study on the nonlinear interaction of the fluctuating planetary gravitational field with the lithosphere suggests that not only the directly acting gravitational forces are of influence, but mainly higher harmonics of the celestial bodies considered as oscillators on large scales [1]. In the meantime, resonances caused by fluctuating gravity can also be detected on small scales in the laboratory [2].

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