Has somebody ever tried to measure the gravity oscillations of nearby rotating masses? I'd like to extend this question:
Are Newton's gravity waves detectable by a laser interferometer?
but with some changes. 
Has somebody ever tried to measure the gravity oscillations nearby (< some meters) of such rotating masses (as in Carl Brannens question)?
Say some kgs or grams rotating on a beam with the highest rpm technically possible? 
(In a vacuum chamber of course!)
I dont know what will "radiate" stronger , 
some grams at 100 000 rpm or some kg at say, 5000 rpm (and some cm distance), therefore, has anybody ever tried something like that in lab? 
I am aware, that such a experiment is plagued by mechanical (elastic) coupling through 
air, supporting structures etc, but I think that one can make use of mechanical resonance 
in the detecting device, helping a lot for selectivity. The fact that the oscillations come from a quadrupole(frequency doubling) , whereas mechanical coupling is not at double frequency, might help to "see" something. As often, its a question of signal/noise ratio :=(
 A: The near-field effect (of Newtonian gravity) can be measured by a gravimeter (which you might say was invented by Cavendish at the end of the 18th century).  Here's a quote from the Wikipedia page:

The superconducting gravimeter achieves extraordinary sensitivities of one nanogal, one thousandth of one billionth (10-12) of the Earth surface gravity. In a dramatic demonstration of the sensitivity of the superconducting gravimeter, Virtanen (2006), describes how an instrument at Metsähovi, Finland, detected the gradual increase in surface gravity as workmen cleared snow from its laboratory roof.

It is left as an exercise for the reader to calculate what system of rotating masses will generate 1 nanogal at the sensor.
On the other hand, suppose you want to measure the far-field effect (gravitational waves).  This turns out to be completely impractical.  See section 2.1 ("Laboratory generators of gravitational waves") of Peter Saulson's note "Physics of Gravitational Wave Detection", or take a look at his book. 
A: There are no gravitational waves in the Newtonian gravity.
A wave is defined by its shape: it is something that depends on space like $\cos(kx)$ but nothing like that can be produced by Newton's gravity whose action is instantaneous. In the standard Ansatz for a wave,
$$\exp(-i\omega t +i k x),$$
one has $k=\omega/c$ but if $c$ is sent to infinity, $k$ goes to zero and the space dependence disappears. So you can't really be talking about waves - something that has a periodic dependence on the spatial coordinates. There aren't any.
Also, for equivalent reasons, according to non-relativistic mechanics, an orbiting binary star isn't losing any energy by the emission of gravitational waves because there aren't any. If there are extra objects in space besides the binary star, they will influence the internal motion of the binary star (a three-body problem) but this is in no way equivalent to the effect of gravitational waves. In particular, there's no "guaranteed sign" that would ensure that the internal energy of the binary stars decreases. It would go up and down equally often. The energy is only carried by the "point masses" and not by "gravitational waves" because there aren't any.
In non-relativistic mechanics, you may only talk about time-dependent gravitational fields. But it's only the quadrupole moment that may be periodically changing if the source of gravity is changing. And the gravitational force from an oscillating quadrupole goes like
$$ \cos(\omega t)/r^4.$$
I added two powers of $1/r$ to the Newton's $1/r^2$ inverse square law. On the other hand, if there are gravity waves, they - e.g. the magnitude of $\delta g_{\mu\nu}(x,y,z,t)$ - depend on the location as
$$\cos(\omega t-kr) / r$$
because the density of energy goes like the square of the amplitude above and $1/r^2$ is the right way how energy spreads in space (gets distributed over the spherical area of $4\pi r^2$). Note that the multiplicative difference between the true gravitational waves in general relativity - that go like $1/r$ - and the time-dependent quadrupole in Newtonian gravity - that goes like $1/r^4$ - is $1/r^3$. That's a huge difference, especially if the distances are very large.
Consequently, the effect of the quadrupole decreases much more quickly with the distance from the source than the intensity of the gravitational waves. Obviously, one can't measure the former if we can't even measure latter - the latter, gravitational waves, is incomparably larger than its Newtonian artifact, but we still haven't managed to measure it.
So the whole idea that there is something like "gravitational waves" in non-relativistic gravity is totally misguided. This comment is not meant to say that one can't measure time dependence of gravitational fields. Of course that one can. Ocean tides that change twice a day are exactly an example of a periodic change of the higher moments from other celestial bodies - the Moon and the Sun. 
But they're not "waves" in any sense because the energy isn't carried away by those would-be waves, and it isn't distributed over the sphere as the energy of waves would. It's up to you whether you consider ocean tides to be an example of "measured gravity oscillations of nearby rotating masses" - I think that you should. But this observation only means a tautologically trivial thing - that changing configurations of matter produce changing gravitational forces - and this trivial thing is in no way analogous to gravitational waves which are independent objects that exist according to general relativity.
A: The nearby effect of rotating masses are detectable and Joe Weber (who I took general relativity from) measured this effect in the 1950s. It's how he calibrated his gravity wave detectors. This is old technology and largely forgotten now. For example, see:
Jpn. J. Appl. Phys. 19, pp. L123-L125, (1980), Katsunobu Oide, Kimio Tsubono and Hiromasa Hirakawa, The Gravitational Field of a Rotating Bar

The dynamic gravitational field around
  a rotating bar, and the forced
  oscillation of a resonant antenna
  located in this field, are treated in
  terms of the quadrupole-quadrupole
  interaction. Some of these
  calculations have been confirmed by
  observation of the resonant
  oscillation of a quadrupole antenna in
  several orientations.

http://jjap.jsap.jp/link?JJAP/19/L123/
Another reference:
Proceedings of Space Technology and Applications International Forum 2000, STAIF2000, Giorgio Fontana, Gravitational Radiation and its Application to Space Travel, principles and required scientific developments

Historically, the emission of
  gravitational radiation has been
  studied in astrophysical systems, as
  reported in the second section of this
  paper, and a quite large literature
  exists on the subject. Instead, the
  laboratory generation of gravitational
  radiation is still in its theoretical
  stage of development except, perhaps,
  the rotor employed for the calibration
  of a GW antenna (Astone, 1991), which
  has indeed produced experimental
  results for a near field detection.

The above were found by googling "Weber bar"+calibration
A: Despite the calibration procedure mentioned above, the Weber bars (deployed at the University of Maryland at about the time I received my physics degree there) were never definitively demonstrated to be able to detect any gravity waves.  Neither has the LIGO gravity wave detector, despite repeated adjustments and upgrades to the sensitivity of the interferometer mirror apparatus.
For an experiment with some more interesting (quasi-local) rotating masses, see:
http://www.eclipse2006.boun.edu.tr/sss/paper02.pdf
There was a lot of hype about possible solutions and controversy surrounding the gravimetric effects observed during this event.  The idea was to use a very sensitive microgravimeter (of LaCoste-Romberg design) to determine effects on terrestrial gravity during a total solar eclipse.  The experiment yielded a surprise: gravimeter peaks which appeared one hour before, and one hour after the total solar eclipse event.  Great care was taken to assure that the temperature fluctuations during the eclipse event did not perturb the gravimeter.
Although the results of this observation are hotly contested, this might just be the first terrestrial observation of gravitational interaction with halos of dark matter surrounding bodies in our own solar system.  Halos of DM are routinely observed to effect gravitational lensing around galaxies.  DM is affected by gravity in terms of creating in a halo surrounding ordinary matter, but does not gravitate further inward or otherwise interact with baryionic matter.
