2
1 Introduction
systems having internal intricacies and huge dimensions are now daringly attempted.
The increasing interest in the vibrations and dynamics of structures and machines is
thus only natural.
1.2 Brief History of Vibrations
During the period of development of basic science in Greece, the birth of vibration
theory and its subsequent growth was a natural process. The Ionion School of natural
philosophy introduced the scientific methods of dealing with natural phenomena.
Vibration theory was initiated by Pythagoras in the fifth century B.C. By establishing a rational method of measuring sound frequencies, Pythagoras quantified
the theory of acoustics. He conducted several experiments with hammers, strings,
pipes and shells for determining fundamental frequency. He proved with his hammer
experiments that natural frequencies are system properties and they do not depend
on the magnitude of excitation [1, 2].
Aristotle and his Peripatetic School founded mechanics and developed an understanding between statics and dynamics. The basics were attempted to be implanted
on fundamental philosophical ideas, instead of empirically founded axioms [3]. In
the Hellenistic period, there were substantial engineering developments in the field
of mechanical design and vibration.
The pendulum as a time and vibration measuring device was known in antiquity
to the extent that by the end of first millennium A.D., it was used by astronomers as
a vibrating and perhaps, time measuring device.
Galileo experimented with pendulum in the seventeenth century. He observed that
there exists a relationship between the length and the frequency of a pendulum. He
further noticed that the density, tension, frequency and length of a vibrating string are
related to each other. The relationship between sound and vibration of mechanical
system was understood for a long time, but Galileo was the first to prove that pitch
is determined from the frequency of vibration.
In the development of vibration theory, Taylor, Bernoulli, D’Alembert, Euler,
Lagrange, Duhamel, Hertz and Fourier are the names to conjure with. Thomas Young
was the first to show how important dynamical effect of load can be [4]. Poncelet
demonstrated analytically that a suddenly applied load produces twice the stress the
same load would produce if applied gradually. From experiments, Savart noted the
mode shapes from the study of nodal lines in aelotropic circular plates. He also coined
the term fundamental for the lowest natural frequency and harmonics for the other.
The concept of the principle of linear superposition of harmonics was put forward
by Bernoulli.
Coulomb carried out theoretical and experimental studies of torsional oscillation
of a metal cylinder suspended by a wire in 1784.
By covering a plate with fine sand, Chladni proved the existence of nodal lines for
various modes of vibration. The French Emperor Napoleon was very impressed by
Chladni’s experiments. At his suggestion, the French Academy announced in 1811
1 Introduction
systems having internal intricacies and huge dimensions are now daringly attempted.
The increasing interest in the vibrations and dynamics of structures and machines is
thus only natural.
1.2 Brief History of Vibrations
During the period of development of basic science in Greece, the birth of vibration
theory and its subsequent growth was a natural process. The Ionion School of natural
philosophy introduced the scientific methods of dealing with natural phenomena.
Vibration theory was initiated by Pythagoras in the fifth century B.C. By establishing a rational method of measuring sound frequencies, Pythagoras quantified
the theory of acoustics. He conducted several experiments with hammers, strings,
pipes and shells for determining fundamental frequency. He proved with his hammer
experiments that natural frequencies are system properties and they do not depend
on the magnitude of excitation [1, 2].
Aristotle and his Peripatetic School founded mechanics and developed an understanding between statics and dynamics. The basics were attempted to be implanted
on fundamental philosophical ideas, instead of empirically founded axioms [3]. In
the Hellenistic period, there were substantial engineering developments in the field
of mechanical design and vibration.
The pendulum as a time and vibration measuring device was known in antiquity
to the extent that by the end of first millennium A.D., it was used by astronomers as
a vibrating and perhaps, time measuring device.
Galileo experimented with pendulum in the seventeenth century. He observed that
there exists a relationship between the length and the frequency of a pendulum. He
further noticed that the density, tension, frequency and length of a vibrating string are
related to each other. The relationship between sound and vibration of mechanical
system was understood for a long time, but Galileo was the first to prove that pitch
is determined from the frequency of vibration.
In the development of vibration theory, Taylor, Bernoulli, D’Alembert, Euler,
Lagrange, Duhamel, Hertz and Fourier are the names to conjure with. Thomas Young
was the first to show how important dynamical effect of load can be [4]. Poncelet
demonstrated analytically that a suddenly applied load produces twice the stress the
same load would produce if applied gradually. From experiments, Savart noted the
mode shapes from the study of nodal lines in aelotropic circular plates. He also coined
the term fundamental for the lowest natural frequency and harmonics for the other.
The concept of the principle of linear superposition of harmonics was put forward
by Bernoulli.
Coulomb carried out theoretical and experimental studies of torsional oscillation
of a metal cylinder suspended by a wire in 1784.
By covering a plate with fine sand, Chladni proved the existence of nodal lines for
various modes of vibration. The French Emperor Napoleon was very impressed by
Chladni’s experiments. At his suggestion, the French Academy announced in 1811