Figure 6. Typical tensile stress-strain curves of the
catalytically-grown multi-walled carbon nanotube-reinforced epoxy
composite.
The effect of temperature on the loss factor is illustrated in Figure 7
for the catalytically-grown multi-walled carbon nanotube-reinforced
epoxy composite. Carbon nanotubes are the subject of intense theoretical
and technological interest in materials science because of their extreme
characteristics. Their theoretically-predicted and
experimentally-measured mechanical properties, including high strength,
high stiffness, toughness, and low density, should make them ideal
strengthening material in advanced fiber-reinforced composites. Carbon
nanotubes are produced in primarily two configurations; single-walled
carbon nanotubes and multi-walled carbon nanotubes, and can be twisted
or woven into carbon nanotube fibers. Parallel-aligned carbon nanotube
fibers form hexagonal closest packed fibers because of the van der Waals
forces of attraction between the individual carbon nanotubes. Vibration
is a physical phenomenon characterized by oscillatory deformation of an
elastic body about a position of equilibrium. The basic physical
concepts involved in vibratory motion are fairly simple. Deformation of
an elastic body in a first direction by the application of an external
force provides the elastic body with an initial amount of mechanical
energy in the form of potential energy. Removal of the external force
results in movement of the deformed elastic body from the high-energy
deformed position towards the low-energy equilibrium position. Movement
of the elastic body from the deformed position to the equilibrium
position intrinsically results in the irreversible dissipation of a
portion of the mechanical energy and conversion of the remaining
mechanical energy from potential energy to kinetic energy. The thus
converted kinetic energy causes the elastic body to move past the
equilibrium position and result in deformation of the elastic body in a
second direction. Deformation of the elastic body in the second
direction intrinsically results in the irreversible dissipation of a
second portion of the mechanical energy and reconversion of the
remaining mechanical energy from kinetic energy back into potential
energy. Movement of the elastic body reverses when the kinetic energy is
completely converted to potential energy. The thus deformed elastic body
possess an amount of potential energy equal to the initial amount of
potential energy minus the amount of energy irreversibly dissipated.
Oscillation of the elastic body about the equilibrium position continues
until the cumulative amounts of energy irreversibly dissipated equals
the amount of mechanical energy originally provided to the elastic body.
Vibration of a deformed elastic body can be perpetuated by periodically
adding sufficient mechanical energy to the vibrating body to compensate
for the energy lost through intrinsic dissipation. The irreversible
dissipation of mechanical energy from a vibrating elastic body is an
intrinsic phenomenon commonly referred to as damping. Damping is
believed to result from a variety of energy loss mechanisms such as the
conversion of mechanical energy to heat through internal friction within
the elastic body, the conversion of mechanical energy to heat through
friction caused by the rubbing of one component of the elastic body
against another, the transfer of mechanical energy from the vibrating
elastic body to adjacent structural components, the transfer of
mechanical energy from the vibrating elastic body to the environment
through acoustic radiation, the conversion of mechanical energy to heat
through a viscous response either inherent in the system or subsequently
added to the system. The energy dissipation mechanisms themselves are
very complex and dependent upon a great number of factors including
specifically, but not exclusively: the composition of the elastic body,
the crystallinity of the elastic body, the geometry of the elastic body,
the temperature of the elastic body, the initial strain placed upon the
elastic body, the amount of any preload placed upon the elastic body,
the interrelationship between the elastic body and other bodies, the
amplitude and frequency of the vibration, and the amount of viscous
response. Due to the variety of dissipative mechanisms and the internal
complexity of those mechanism, it is extremely difficult to accurately
predict the damping effect of a given material. The damping behavior of
a material is dependent upon the modulus and loss factor of the
material. Hence, knowledge of the modulus and loss factor of a material
permits an assessment of the damping behavior of a material. The modulus
and loss factor variables of a damping material are highly dependent
upon the temperature of the damping material and the vibration
frequency. Advent of the reduced temperature nomograph constitutes a
tremendous advancement over the previously employed method of
determining modulus and loss factor based upon separate temperature and
frequency graphs. However, even with the increased simplicity offered by
reduced-temperature nomographs, many individuals, particularly those
with a limited scientific background, still find it difficult to
determine the modulus and loss factor of a material.