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vibration of mechanical systems pdf

This book is intended for a vibration course in an undergraduate
Mechanical Engineering curriculum. It is based on my lecture notes
of a course (ME370) that I have been teaching for many years at The
Pennsylvania State University (PSU), University Park. This vibration
course is a required core course in the PSU mechanical engineering
curriculum and is taken by junior-level or third-year students.

Textbooks that have been used at PSU are as follows: Hutton (1981) and
Rao (1995, First Edition 1986).

In addition, I have used the book by
Thomson and Dahleh (1993, First Edition 1972) as an important reference book while teaching this course. It will be a valid question if one asks why I am writing another book when there are already a large number of excellent textbooks on vibration since Den Hartog wrote
the classic book in 1956. One reason is that most of the books are
intended for senior-level undergraduate and graduate students. As a
result, our faculties have not found any book that can be called ideal
for our junior-level course.

 Another motivation for writing this book is
that I have developed certain unique ways of presenting vibration concepts in response to my understanding of the background of a typical undergraduate student in our department and the available time during a semester. Some of the examples are as follows: review of selected topics in mechanics; the description of the chapter on single-degreeof-freedom (SDOF) systems in terms of equivalent mass, equivalent stiffness, and equivalent damping; unified treatment of various forcedresponse problems such as base excitation and rotating balance; introduction of system thinking, highlighting the fact that SDOF analysis is a building block for multi-degree-of-freedom (MDOF) and continuous system analyses via modal analysis; and a simple introduction
of finite element analysis to connect continuous system and MDOF
analyses.

As mentioned before, there are a large number of excellent books
on vibration. But, because of a desire to include everything, many of
these books often become difficult for undergraduate students. In this
book, all the basic concepts in mechanical vibration are clearly identified and presented in a simple manner with illustrative and practical examples. I have also attempted to make this book self-contained as much as possible; for example, materials needed from previous
courses, such as differential equation and engineering mechanics, are
presented. At the end of each chapter, exercise problems are included.
The use of MATLAB software is also included.

In Chapter 1, the degrees of freedom and the basic elements of
a vibratory mechanical system are presented. Then the concepts
of equivalent mass, equivalent stiffness, and equivalent damping
are introduced to construct an equivalent single-degree-of-freedom
model. Next, the differential equation of motion of an undamped
SDOF spring–mass system is derived along with its solution. Then the
solution of the differential equation of motion of an SDOF spring–
mass–damper system is obtained. Three cases of damping levels –
underdamped, critically damped, and overdamped – are treated in
detail. Last, the concept of stability of an SDOF spring–mass–damper
system is presented.

In Chapter 2, the responses of undamped and damped SDOF
spring–mass systems are presented. An important example of input shaping is shown. Next, the complete solutions of both undamped anddamped spring–mass systems under sinusoidal excitation are derived. Amplitudes and phases of steady-state responses are examined along
with force transmissibility, quality factor, and bandwidth. Then the solutions to rotating unbalance and base excitation problems are provided. Next, the basic principles behind the designs of a vibrometer and an accelerometer are presented. Last, the concept of equivalent
viscous damping is presented for nonviscous energy dissipation.