6
1 Introduction
1.5.1 Vibration and Oscillation
If the motion of the body is oscillating or reciprocating in character, it is called
vibration if it involves deformation of the body. In case the reciprocating motion
involves only the rigid body movement without involving its deformation, then it is
called oscillation. The motion of a pendulum is simple harmonic oscillation and so
is the case of a ship if considered as a rigid body moving over waves.
1.5.2 Free Vibration
Vibration of an elastic system may be initiated by the application of the external force,
which may subsequently be withdrawn. The resulting vibration, where no external
force is present, is referred to as free vibration.
1.5.3 Forced Vibration
If the external force is considered to be operative during the vibratory motion of the
body, such a motion is referred to as forced vibration.
1.5.4 Damping
For all practical structures, resistance is encountered during vibration. As a result
of which, the amplitude will not remain constant, but will gradually go on reducing
with time in case of free vibration, till a time comes when all the motion will be
damped out.
Damping forces may depend on the vibrating system, as also on factors outside it.
Damping in a system arises due to the internal friction of the material, or due to drag
effects of surrounding air or other fluids, in which the structure is immersed. The
exact representation of them involves difficulties. However, as to its nature, damping
is of following four types:
(a) Structural damping,
(b) Viscous damping,
(c) Coulomb damping, and
(d) Negative damping.
Structural damping is due to the internal molecular friction of the material of the
structure, or due to the connections inherent in a structural system.
Viscous damping occurs in a system vibrating in a fluid. The damping force in
this case is proportional to the velocity and is given by
1 Introduction
1.5.1 Vibration and Oscillation
If the motion of the body is oscillating or reciprocating in character, it is called
vibration if it involves deformation of the body. In case the reciprocating motion
involves only the rigid body movement without involving its deformation, then it is
called oscillation. The motion of a pendulum is simple harmonic oscillation and so
is the case of a ship if considered as a rigid body moving over waves.
1.5.2 Free Vibration
Vibration of an elastic system may be initiated by the application of the external force,
which may subsequently be withdrawn. The resulting vibration, where no external
force is present, is referred to as free vibration.
1.5.3 Forced Vibration
If the external force is considered to be operative during the vibratory motion of the
body, such a motion is referred to as forced vibration.
1.5.4 Damping
For all practical structures, resistance is encountered during vibration. As a result
of which, the amplitude will not remain constant, but will gradually go on reducing
with time in case of free vibration, till a time comes when all the motion will be
damped out.
Damping forces may depend on the vibrating system, as also on factors outside it.
Damping in a system arises due to the internal friction of the material, or due to drag
effects of surrounding air or other fluids, in which the structure is immersed. The
exact representation of them involves difficulties. However, as to its nature, damping
is of following four types:
(a) Structural damping,
(b) Viscous damping,
(c) Coulomb damping, and
(d) Negative damping.
Structural damping is due to the internal molecular friction of the material of the
structure, or due to the connections inherent in a structural system.
Viscous damping occurs in a system vibrating in a fluid. The damping force in
this case is proportional to the velocity and is given by