8
1 Introduction
Fig. 1.4 Single degree of freedom system
has a single degree of freedom. If one is interested only in the flexural vibration of the
structure, then the x-coordinate displacement describes the motion and the system
still is of single degree of freedom. But if one intends to study the axial and flexural
vibration in a combined manner, then the problem at hand becomes a two-degree of
freedom system (the x and y displacements of the mass).
Depending on the independent coordinates required to describe the motion, the
vibratory system is divided into the following categories:
(a) Single degree of freedom system (SDF system),
(b) Multiple degrees of freedom system (MDF system),
(c) Continuous system.
If a single coordinate is sufficient to define at any instant of time the position of the
mass of the system, it is referred to as a single degree of freedom system (Fig. 1.4).
If more than one independent coordinate is required to define at any instant of time
the position of different masses of the system, it is referred to as multiple degrees of
freedom system. A few examples of multiple degrees of freedom system have been
shown in Fig. 1.5. If a system requires three independent coordinates as shown in
Fig. 1.5a and d, it is called three degrees of freedom system.
The mass of a system, such as the beam of Fig. 1.6, may be considered to be
distributed over its length, in which case the mass is considered to have infinite
degrees of freedom. Such a system is referred to as a continuous system.
1.6 Dynamic Loading
Dynamic load is that in which its magnitude, direction or position vary with time.
Almost all structures are subjected to dynamic load sometime or other during its
lifespan. They are the result of various manmade and natural causes. The particulars
of the load vary with time for different sources from which they are generated. Some
common types of influences resulting in the disturbance are due to initial conditions,
applied actions and support motions.
A few cases of dynamic loads acting on different systems are shown in Fig. 1.7. In
general, the deterministic loading that acts on different systems can be divided into
two basic categories: periodic and non-periodic. In periodic loading, the variation of
1 Introduction
Fig. 1.4 Single degree of freedom system
has a single degree of freedom. If one is interested only in the flexural vibration of the
structure, then the x-coordinate displacement describes the motion and the system
still is of single degree of freedom. But if one intends to study the axial and flexural
vibration in a combined manner, then the problem at hand becomes a two-degree of
freedom system (the x and y displacements of the mass).
Depending on the independent coordinates required to describe the motion, the
vibratory system is divided into the following categories:
(a) Single degree of freedom system (SDF system),
(b) Multiple degrees of freedom system (MDF system),
(c) Continuous system.
If a single coordinate is sufficient to define at any instant of time the position of the
mass of the system, it is referred to as a single degree of freedom system (Fig. 1.4).
If more than one independent coordinate is required to define at any instant of time
the position of different masses of the system, it is referred to as multiple degrees of
freedom system. A few examples of multiple degrees of freedom system have been
shown in Fig. 1.5. If a system requires three independent coordinates as shown in
Fig. 1.5a and d, it is called three degrees of freedom system.
The mass of a system, such as the beam of Fig. 1.6, may be considered to be
distributed over its length, in which case the mass is considered to have infinite
degrees of freedom. Such a system is referred to as a continuous system.
1.6 Dynamic Loading
Dynamic load is that in which its magnitude, direction or position vary with time.
Almost all structures are subjected to dynamic load sometime or other during its
lifespan. They are the result of various manmade and natural causes. The particulars
of the load vary with time for different sources from which they are generated. Some
common types of influences resulting in the disturbance are due to initial conditions,
applied actions and support motions.
A few cases of dynamic loads acting on different systems are shown in Fig. 1.7. In
general, the deterministic loading that acts on different systems can be divided into
two basic categories: periodic and non-periodic. In periodic loading, the variation of