16-08-2012, 01:24 PM
VIBRATION
1VIBRATION.pdf (Size: 315.99 KB / Downloads: 37)
CONCEPT OF VIBRATION
Any repetitive motion is called vibration or oscillation. The motion of a guitar string,
motion felt by passengers in an automobile traveling over a bumpy road, swaying of
tall buildings due to wind or earthquake, and motion of an airplane in turbulence are
typical examples of vibration. The theory of vibration deals with the study of oscillatory
motion of bodies and the associated forces. The oscillatory motion shown in Fig. 1.1(a)
is called harmonic motion and is denoted as
x(t) = X cos ωt (1.1)
where X is called the amplitude of motion, ω is the frequency of motion, and t is the time.
The motion shown in Fig. 1.1(b) is called periodic motion, and that shown in Fig. 1.1©
is called nonperiodic or transient motion. The motion indicated in Fig. 1.1(d) is random
or long-duration nonperiodic vibration.
The phenomenon of vibration involves an alternating interchange of potential
energy to kinetic energy and kinetic energy to potential energy. Hence, any vibrating
system must have a component that stores potential energy and a component that
stores kinetic energy. The components storing potential and kinetic energies are called
a spring or elastic element and a mass or inertia element, respectively. The elastic
element stores potential energy and gives it up to the inertia element as kinetic energy,
and vice versa, in each cycle of motion. The repetitive motion associated with vibration
can be explained through the motion of a mass on a smooth surface, as shown in
Fig. 1.2. The mass is connected to a linear spring and is assumed to be in equilibrium
or rest at position 1.
IMPORTANCE OF VIBRATION
Any body having mass and elasticity is capable of oscillatory motion. In fact, most
human activities, including hearing, seeing, talking, walking, and breathing, also involve
oscillatory motion. Hearing involves vibration of the eardrum, seeing is associated with
the vibratory motion of light waves, talking requires oscillations of the laryng (tongue),
walking involves oscillatory motion of legs and hands, and breathing is based on the
periodic motion of lungs. In engineering, an understanding of the vibratory behavior of
mechanical and structural systems is important for the safe design, construction, and
operation of a variety of machines and structures.
The failure of most mechanical and structural elements and systems can be associated
with vibration. For example, the blade and disk failures in steam and gas turbines
and structural failures in aircraft are usually associated with vibration and the resulting
fatigue. Vibration in machines leads to rapid wear of parts such as gears and bearings,
loosening of fasteners such as nuts and bolts, poor surface finish during metal cutting,
and excessive noise. Excessive vibration in machines causes not only the failure of
components and systems but also annoyance to humans. For example, imbalance in
diesel engines can cause ground waves powerful enough to create a nuisance in urban
areas. Supersonic aircraft create sonic booms that shatter doors and windows. Several
spectacular failures of bridges, buildings, and dams are associated with wind-induced
vibration, as well as oscillatory ground motion during earthquakes.
AND VIBRATION
The earliest human interest in the study of vibration can be traced to the time when the
first musical instruments, probably whistles or drums, were discovered. Since that time,
people have applied ingenuity and critical investigation to study the phenomenon of
vibration and its relation to sound. Although certain very definite rules were observed
in the art of music, even in ancient times, they can hardly be called science. The ancient
Egyptians used advanced engineering concepts such as the use of dovetailed cramps
and dowels in the stone joints of major structures such as the pyramids during the third
and second millennia b.c.
As far back as 4000 b.c., music was highly developed and well appreciated in
China, India, Japan, and perhaps Egypt [1, 6]. Drawings of stringed instruments such
as harps appeared on the walls of Egyptian tombs as early as 3000 b.c. The British
Museum also has a nanga, a primitive stringed instrument from 155 b.c. The present
system of music is considered to have arisen in ancient Greece.