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Researchers, scientists and design engineers always try to know
about first few modes of vibrations before finalizing any design of
machine or structure so that they can save the money & time of
the nation. For these two fold requirements i.e. money and time,
they can get a lot of help from the contents of this book.
Actually, deeply analysis of the graphs in each chapter or model
can provide them the required or desired values of frequency
parameters & surely, they can get the same with the proper
choice of varying parameters i.e. thermal gradient, taper
parameters, non-homogeneity constant, aspect ratio and skew angles.
I assure them that if they use the findings of these models in
practical manner, it will definitely help to provide more reliable,
durable and efficient mechanical structures or machines
In the modern epoch of science and technology; scientists,
engineers & practitioners have become more interested to
analyze the vibrational characteristics of structural components
which are mainly operated under elevated temperature i.e. space
technology, nuclear energy applications, high speed atmospheric
flights etc. Due to the influence of temperature, the physical
properties of materials change significantly. Further, the use of
various plate type structural elements under high temperature
environments, particularly in space vehicles and modern missiles,
demand that non-homogeneity of the material should be taken into
account to predict their natural frequencies. The book is mainly
the collection of theoretical mathematical models about the effect
of bi-dimensional temperature variations on vibrations of four
sided clamped square plate with bi-dimensional thickness
variability. Numeric values of natural frequencies are calculated
for both the modes of vibrations for different values of taper
parameters & thermal gradient. We hope that the content of the
book will definitely help the readers as well scientists to fulfill
their requirements.
In the course of time, the study of vibration of plates with
thickness variability has acquired great importance in nuclear
reactor technology, earth-quake resistant structures, aeronautical
field, naval structures and machine designs etc. Plates of variable
thickness are mainly used for two fold requirements of safety and
economy. Therefore, it becomes the need of the hour to provide some
authentic theoretical mathematical models for the help of
mechanical/design engineers & scientists so that before
finalizing any design or mechanical structure, they can use of them
with practical approach and provide much better design and
structures with more durability, reliability & strength. In the
present work, some mathematical models on vibrational behaviour of
visco-elastic homogeneous rectangular plates with bi-directional
thickness variability are deeply discussed for fixed boundary
conditions. Numeric values of time period, deflection and
logarithmic decrement are given in tabular and graphical forms
both. I hope that the engineers/scientists may develop a
qualitative understanding of plate vibrational behaviour by using
these findings.
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