| Beat Phenomenon |
| |
When a two degree-of-freedom system
has two closely spaced natural frequencies, wn1 and wn2, vibration
kinetic energy will transfer from one degree-of-freedom
to the other in a periodic fashion. The frequency of
this transfer is known as the beat frequency, given by
(wn1 - wn2) /
2. | |
| Critical Damping |
| |
The minimum damping that results in
non-periodic motion of a system under free
vibration. | |
| Damping Ratio |
| |
The ratio of a system's actual
damping to its critical damping. When less than 1, the
system in underdamped and will exhibit ringing when
disturbed. When larger than 1, the system is overdamped
and disturbances will die out without
ringing. | |
| Degree-of-Freedom |
| |
In the simplest of cases, a
degree-of-freedom is an independent displacement or
rotation that a system may exhibit. A degree-of-freedom
for a system is analogous to an independent variable for
a mathematical function. All system degrees-of-freedom
must be specified to fully characterize the system at
any given time. | |
| Free Body Diagram |
| |
A schematic isolating an object (or
part of an object) from its environment for the purpose
of revealing all external forces and moments acting on
the object. Free body diagrams are helpful in applying
Newton’s 2nd Law of motion to
objects. | |
| Maxwell's Reciprocity
Theorem |
| |
For two identically-sized forces
applied at the distinct points A and B on a linear
structure, Maxwell’s Reciprocity Theorem states that the
displacement at A caused by the force at B is the same
as the displacement at B caused by the force at A. As a
result, the flexibility matrix (and its inverse, the
stiffness matrix) of linear systems is
symmetric. | |
| Natural Frequency |
| |
A frequency where a system resonance
exists. If excited at this frequency, the system will
exhibit very large displacements (for low damping
levels). If the system is undamped, then vibrations can
occur at the natural frequency without any external
excitation indefinitely. | |
| Resonance |
| |
A condition where very little energy
input into a structure results in a very large
displacement (for low damping levels). By definition,
resonances occur at the natural frequencies of a
system. | |
