Page 18 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Oscillatory

Motion

The Study of vibration is concerned with the oscillatory motions of bodies and the
forces associated with them. All bodies possessing mass and elasticity are capable
of vibration. Thus, most engineering machines and structures experience vibration
to some degree, and their design generally requires consideration of their oscilla­
tory behavior.
Oscillatory systems can be broadly characterized as linear or nonlinear. For
linear systems, the principle of superposition holds, and the mathematical tech­
niques available for their treatment are well developed. In contrast, techniques for
the analysis of nonlinear systems are less well known, and difficult to apply.
However, some knowledge of nonlinear systems is desirable, because all systems
tend to become nonlinear with increasing amplitude of oscillation.
There are two general classes of vibrations—free and forced. Free vibration
takes place when a system oscillates under the action of forces inherent in the
system itself, and when external Impressed forces are absent. The system under
free vibration will vibrate at one or more of its natural frequencies, which are
properties of the dynamical system established by its mass and stiffness distribu­
tion.
Vibration that takes place under the excitation of external forces is called
forced vibration. When the excitation is oscillatory, the system is forced to vibrate
at the excitation frequency. If the frequency of excitation coincides with one of the
natural frequencies of the system, a condition of resonance is encountered, and
dangerously large oscillations may result. The failure of major structures such as
bridges, buildings, or airplane wings is an awesome possibility under resonance.
Thus, the calculation of the natural frequencies is of major importance in the study
of vibrations.
Vibrating systems are all subject to damping to some degree because energy
is dissipated by friction and other resistances. If the damping is small, it has very
little influence on the natural frequencies of the system, and hence the calculations