Date: Thu Apr 1 16:03:10 1999
Posted By: David Ellis, Researcher, NASA Lewis Research Center
Area of science: Engineering
ID: 922669318.EgMessage:
Resonance Frequency Measurement
Importance of Resonance Frequency
Resonance frequency measurements are a major concern to materials, civil
and aerospace engineers as well as others who work with structures.
If a resonance frequency is too low, natural vibrations caused by wind
or people walking can destroy the structure. The classic example
of this is the Tacoma
Narrows Bridge which was torn apart in a 42 mph wind storm. Space
based structures such as the new International
Space Station are particularly susceptible because they are small
structures
with many large, thin sections such as the radiator and photovoltaic
panels.
If the resonance frequency of the station is low enough, astronauts moving
around in the station will start to vibrate the panels
uncontrollably.
They will eventually tear themselves apart just like the Tacoma Narrows
Bridge.
Measuring Resonance Frequency Of A Material
Unless someone is actually trying to destroy an object by putting very
large amounts of sonic energy into a tiny volume, all resonance
measurements
are nondestructive. Materials have a resonance frequency unique to
a material that can be measured by vibrating a sample of the material and
observing the response. Most resonance frequencies of interest occur
between 0 Hz and 20,000 Hz or the audible range for humans. Audio
microphones similar to those used in home stereo systems are used for much
of the testing. Some methods also use voice coils similar to those
found in speakers.
Excitation of the specimen can be done by a vibrating membrane, reed,
tuning fork or by simply striking the specimen with a hammer.
Sensitive
microphones collect the waves (sound) generated within the specimen.
At the resonance frequencies of a material, the amplitude of the measured
sound waves will be greater than that of the supplied excitation.
This is because the waves reinforce each other and essentially build up
one upon another. As with harmonics in music, materials have
resonance
frequencies that go through a progression where the frequencies are
progressively
doubled, i.e., 100 Hz, 200 Hz, 400 Hz, 800 Hz, 1600 Hz, etc.
The resonance frequencies of materials actually reflect on the strength
and distance between atoms in the material. Some elements with very
low symmetry or outright different bonding have different resonance
frequencies
depending on what direction the sound is traveling. Take graphite
for example. Graphite consists of covalently bonded carbon atoms
tightly bound to one another arranged in sheets. These sheets are
held together by very loose Van der Waals bonds. These weak bonds
make graphite useful for pencil leads. The difference in bonds also
means there is one set of resonance frequencies for sound waves traveling
within the sheets along covalent bonds and another set for sound waves
traveling perpendicular to the sheets along the Van der Waals bonds.
Within the sheet the resonance frequencies are significantly higher than
between the sheets.
Since the resonance frequencies reflect directly on the strength of
the bonds of a material, it can be used to measure several elastic
properties
of the material. The dynamic Young's modulus and shear modulus are
the two most common elastic properties measured. Young's modulus
is essentially how stiff a material is when it deforms elastically (like
an elastic band) when pulled or pressed uniaxially. Shear modulus
is similar to the Young's modulus but is in the plane of atoms that gives
the least resistance to deformation. It is a measure of rigidity
or resistance to bending in torsion.
There are at least two standards for testing the resonance frequency
of a material from the American Standard
of Testing and Materials (ASTM). They are ASTM E1259 Standard
Test Method for Dynamic Young's Modulus, Shear Modulus, and Poisson's Ratio
for Advanced Ceramics by Impulse Excitation of Vibration and ASTM E
1876 Standard Test Method for Dynamic Young's Modulus, Shear Modulus,
and Poisson's Ratio by Impulse Excitation of Vibration. These
standards are available through your library and give full details on
instrumentation
and other aspects of testing materials as well as some of the uses of the
results.
Measuring Resonance Frequency Of A Structure
Measuring the resonance frequency of a structure is more difficult but,
as the Tacoma Narrows Bridge illustrates, very important. There are
a variety of physics based computer simulations of varying complexity that
can model the structure. One of the big problems is taking into
account
all the materials that go into a structure like a building (stone, steel,
aluminum, carpeting, etc.). For relatively simple structures such
as truss bridges made from steel and concrete there are very good models
used by civil engineers to use. Considerable advancements in modeling
the response of more complex structures such as skyscrapers to wind are
also being made. The American Society
of Civil Engineers is a good source for further information.
A Practical Use For Resonance Frequencies
In materials science, electron microscopes are used to image details as
fine as individual atoms. As you can well imagine, vibrations are
a disaster, so the microscopes are isolated on air tables. A very
good explanation of these devices is given at the Herzan
Web site.