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Suppose you wanted to detect gravitational waves from a lab source (I know, any reasonable man-made source will be several orders of magnitude below detection technology, but humor me for a second). The first thing you will want to make sure is that any mechanical signal from the source gets attenuated at the detector below the expected level of the gravitational wave. Assume the detector itself is sensitive enough to detect whatever gravitational signal is received at its end

So I've seen that some experiments reduce noise by placing equipment into granular support that efficiently disperses mechanical energy.

But also it seems (to me) that a single material would behave worse than multiple layers of different materials that make multiple scatterings of any leftover waves at each interface.

What is the optimal mechanical insulator infrastructure required for a gravitational experiment on the range of frequencies where a mechanical source can typically spin? (i.e up to a few kHz)

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The miniGRAIL attempts to do this using a series of 7 shields.

minigrail

The MiniGRAIL attenuation system consists of a room temperature part and a cryogenic part. The cryostat is suspended from a concrete support, which is built on specially designed low vibration islands. The concrete platform, which holds the dewar rests on a stack of rubber and wooden rings that works as a low frequency absorber. The low pass mechanical filter, consisting of a stack of masses and springs, is mounted inside of the cryostat. Seven masses and springs are suspended from the top flange of the cryostat with three stainless steel cables, hanging from three helical springs meant to damp low frequency vibrations. The stack is inserted in the neck of the cryostat. The stainless steel cables hold the upper mass (number one), while the other masses hang from each other by means of stainless steel springs and copper rods. Ten radiation shields are mounted between the upper mass and the top flange. The fifth intermediate shield is thermally anchored to the nitrogen reservoir of the cryostat and the last shield is coupled to the helium reservoir. The stainless steel cables are thermally anchored to both shields with flexible copper braid.

There are only a few points in the spectrum where they approach the sensitivity available in the space-based LIGO system. While not quite good enough to rival LIGO (or other space based systems) it could detect larger gravitational waves from non-axis-symmetric instabilities in rotating single and binary neutron stars, small black-hole or neutron-star mergers.

sensitivity

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In addition to the direct ground vibration and acoustic transmission paths into the detector, for most low frequency motions, you will be most sensitive to the near-field gravitational force (i.e. not the radiation, but just the usual "Newtonian" change in the potential).

Assuming that you locate the detector far enough away that the radiation term is dominant, its likely that the mechanical transmission paths will also be small.

The key technique used in the LIGO-like detectors (which are not in space) is mechanical impedance mis-match. The vibrations are kept from travelling down to the mirror by a series of mass-spring sets. The specific choice of material is not the main concern, but rather making the resonant frequency of the mechanical oscillators much lower than the gravitational wave frequency.

There was an article written on using nuclear warheads to produce detectable gravitational radiation, but this is probably not legal since the Comprehensive Test Ban.

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