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2005 Measurements on Elastic Vibrations of Tubes
This page archives strain data for elastic vibrations excited in
tubes by propagating detonations. The facility is described in the
thesis of Tong Wa Chao. The experiments were carried out by Florian Pintgen
using an optical vibrometer in addition to strain gages. The key results from
these tests were
- Under repeated dynamic loading with strain reversal conditions, the strain gage response degraded rapidly, the
data were not repeatable, and also showed significant artifacts.
- The vibrometer data were very repeatable.
- The tube wall thickness varied significantly with angle and this was
quantified by destructive testing.
Presentations
The experimental setup, data from strain and pressure, and conclusions about repeatability are given
in the slides presented at LLNL in June. Some revisions were made to update the plots describing
the tube thickness variation effect.
- June 2005 LLNL 'roadshow' presentation (revised 8/23/2005) (pdf)
- Detonation-driven fracture experiments: Flexural wave validation exercise (pdf)
Setup
The specimen tube is 6061T6 alumminum, the same type as used in previous studies.
Outer diameter is 41.28 mm (1.625 in). The thickness
of the tube is nominally 0.89 mm (0.035 in) but actual dimensions vary by +/- 10% due to the
manufacturing technique. See the data at the bottom of this page for the measured
tube thickness of this specimen.
Data
Description summary file
All shots used an identical mixture: 3O2+C2H4. Two initial pressures were
used: 1 bar and 0.5 bar. The CJ conditions and parameters for the loading model
of Beltman and Shepherd (see Appendix B, Journal of Sound and Vibration, 252(4):617-655, 2002) are:
| P_0 | U_CJ | P_CJ | P_3 | T |
| (bar) | (m/s) | (bar) | (bar) | (ms) |
| 1.0 | 2375 | 33.3 | 11.65 | 0.240 |
| 0.5 | 2342 | 16.2 | 5.67 | 0.243 |
The decay time constant T was computed using a distance of 1.9 m
between the orgin (ignition location) of the detonation wave and the
measurement location. The time is given in units of millisecond (ms),
1 ms = .001 s.
The measured velocity is about 1% lower than
the CJ values in the last half of the detonation tube. The
corresponding peak pressure (P_2 in the model) will be about 2% lower
than the CJ value. You will get slightly better agreement with the
vibrometer data by adjusting the peak pressure and velocity downward
to account for this. The actual values at the measurement location
might even be slightly lower, as much as 1.5 to 2% for the velocity
and 3-4% for the pressure.
Strain Gage location in degrees
Strain Gage axial location and effective tube length
The gage axial location and position position relative to the fixture
were slightly different than in Tony's thesis. The effective length of
the tube is defined by the total distance between collets that grip the
tube. In the present experiments, the collets were spaced about 420 mm apart. The
collets very tightly grip the tube and are rigidly attached to the stiff
fixture frame; this makes a good approximation to a built-in boundary condition
at these loations.
The strain gages S1, S2, S3 and the vibrometer were located half-way between
the collets, 210 mm from the first collet (at the ignition end of the fixture).
The gage S4 was located 20 mm ahead (closer to the ignition end)
of the tube midpoint and the gage S5 was located 20 mm behind (closer to the tail
end of the fixture) the midpoint.
Shot conditions, vibrometer location, and data files
The data files are in asci format with space separators. The columns in
the vibrometer data files are time (s), velocity (m/s), displacement (mm), and strain.
The columns in the stain gage data file (labeled by location as given above)
are time (s) and strain. Encapsulated postscript (eps) files of the strain time history
are given for each gage. Only a limited number of oscillation cycles (about 8-10) are given for each test. Only
one set of strain gage data is given. The vibrometer data was very repeatable and high quality, the strain
gages less so.
Peak strains from vibrometer measurements are given in the text files in this directory
The text files contain columnar asci data, space separated. The first column is time (s), the second column is
normalized time (s), and the third column is the peak strain. The normalized time is the time relative to first
peak; both positive and negative peaks are given.
Tube thickness measurements (file)
(eps)
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