4
1 Introduction
down the theory of random vibrations [9–12]. A number of monographs on the topic
are now available.
Vibrations and structural dynamics have made rapid strides in last few decades.
The advent of computer has brought in a revolution in this area like many others.
As a result of which new numerical techniques have been developed, out of which
the finite element method has proved to be most versatile [13]. These newly developed methods of analysis permit the structural analyst to formulate the increasingly
complex problems [13].
1.3 Comparison Between Static and Dynamic Analysis
The prime difference between static and dynamic analysis lies in the interpretation
of the load considered. Dynamic means time varying. As such, time is the additional
parameter in the dynamic analysis.
What is the difference between the two regarding the interpretation of forces?
A block resting on the ground is shown in Fig. 1.1. The ground reactions can be
evaluated for the following conditions from elementary knowledge of statics:
(a) When the block is at rest,
(b) When the block is on the verge of incipient motion,
(c) When it is moving with a uniform velocity.
The forces that may arise in the above three conditions have been indicated in
Fig. 1.1. If the block now starts moving with acceleration a, then it will experience
an inertia force which is equal to mass times acceleration. By applying Newton’s
second law, one obtains
P − R = ma
(1.1)
Fig. 1.1 A block resting on
the ground
1 Introduction
down the theory of random vibrations [9–12]. A number of monographs on the topic
are now available.
Vibrations and structural dynamics have made rapid strides in last few decades.
The advent of computer has brought in a revolution in this area like many others.
As a result of which new numerical techniques have been developed, out of which
the finite element method has proved to be most versatile [13]. These newly developed methods of analysis permit the structural analyst to formulate the increasingly
complex problems [13].
1.3 Comparison Between Static and Dynamic Analysis
The prime difference between static and dynamic analysis lies in the interpretation
of the load considered. Dynamic means time varying. As such, time is the additional
parameter in the dynamic analysis.
What is the difference between the two regarding the interpretation of forces?
A block resting on the ground is shown in Fig. 1.1. The ground reactions can be
evaluated for the following conditions from elementary knowledge of statics:
(a) When the block is at rest,
(b) When the block is on the verge of incipient motion,
(c) When it is moving with a uniform velocity.
The forces that may arise in the above three conditions have been indicated in
Fig. 1.1. If the block now starts moving with acceleration a, then it will experience
an inertia force which is equal to mass times acceleration. By applying Newton’s
second law, one obtains
P − R = ma
(1.1)
Fig. 1.1 A block resting on
the ground