• Nonlinearities may quantitatively alter the response of a system. Students should
know the most common methods of perturbation analysis and acquire considerable working experience with at least one method.
• Modern mechanical structures are often flexible, lightweight, operate at a high
speed or are dynamically controlled. Such structures are more easily forced into
a nonlinear regime than are traditional stiff, heavy, and passive structures.
• Nonlinear problems can no longer be considered intractable, as was often the
only reason for linearization in the past. Using mathematics, computers, and
experience with commonly encountered types of nonlinearities—we are now in
a much better position to analyze nonlinear systems.
• There is currently a significant interest in the subject, as browsing any scientific
journal or conference program on dynamics and vibrations will show. To keep
pace with the rapid evolution in vibration research, one has to know about
nonlinear models, phenomena, and tools.
Why a New Book on Such an Old Topic? (Glimpse of Vibration History). Much
research and teaching in mechanical vibrations concentrates on describing, understanding, predicting, measuring, and possibly controlling the free vibrations of
mechanical system, or their response to resonant or near-resonant periodic excitation. In fact, this has been the case since Pythagoras (570–497 b.c.) quantified the
theory of music and related it to his theory of numbers. It continued via Galileo’s
(1564–1642) work on pendulum oscillations (Galilei 1638) and Sir Isaac Newton’s
(1642–1727) subsequent formulation of his laws of motion (Newton 1696) to
Robert Hooke’s (1635–1703) formulation of the relationship between stress and
strain in elastic bodies and the subsequent solution of the differential equation for a
vibrating beam by Leonard Euler (1707–1783) and Daniel Bernoulli (1700–1782)
(see Shabana 1996; Dimarogonas and Haddad 1992). A major culmination occurred
in 1877 with Lord Rayleigh’s masterpiece The Theory of Sound (Rayleigh 1877).
Since Rayleigh, the character of problems facing the vibration theoretician or
practitioner has hardly changed (which perhaps explains why Rayleigh’s books
appear surprisingly modern even today). But, the tools for solving vibration
problems have improved immensely by the emergence of (1) computers and software that can be used to simulate the behavior of virtually any dynamic system;
(2) new or improved mathematical tools for solving nonlinear differential equations
approximately; and (3) computerized and miniaturized measurement equipment for
experimentally based testing and improvement of theories. These corners of the
‘mechanicians triangular toolbox’ are centers of fields (numerical/theoretical/
experimental analysis) that are all expanding significantly in these years, seemingly
in a mutually fertilizing manner. New or updated books are needed to reflect these
developments and explain them to students.
Why This Book? There is, in fact, a plenitude of good books on nonlinear
dynamics/vibrations. Many of these are on my shelf. I use them heavily, and had no
intention of writing a competitor. Though, for my course in advanced vibration
analysis, I found that none of them treated the relevant range of subjects in the way
Preface
vii
know the most common methods of perturbation analysis and acquire considerable working experience with at least one method.
• Modern mechanical structures are often flexible, lightweight, operate at a high
speed or are dynamically controlled. Such structures are more easily forced into
a nonlinear regime than are traditional stiff, heavy, and passive structures.
• Nonlinear problems can no longer be considered intractable, as was often the
only reason for linearization in the past. Using mathematics, computers, and
experience with commonly encountered types of nonlinearities—we are now in
a much better position to analyze nonlinear systems.
• There is currently a significant interest in the subject, as browsing any scientific
journal or conference program on dynamics and vibrations will show. To keep
pace with the rapid evolution in vibration research, one has to know about
nonlinear models, phenomena, and tools.
Why a New Book on Such an Old Topic? (Glimpse of Vibration History). Much
research and teaching in mechanical vibrations concentrates on describing, understanding, predicting, measuring, and possibly controlling the free vibrations of
mechanical system, or their response to resonant or near-resonant periodic excitation. In fact, this has been the case since Pythagoras (570–497 b.c.) quantified the
theory of music and related it to his theory of numbers. It continued via Galileo’s
(1564–1642) work on pendulum oscillations (Galilei 1638) and Sir Isaac Newton’s
(1642–1727) subsequent formulation of his laws of motion (Newton 1696) to
Robert Hooke’s (1635–1703) formulation of the relationship between stress and
strain in elastic bodies and the subsequent solution of the differential equation for a
vibrating beam by Leonard Euler (1707–1783) and Daniel Bernoulli (1700–1782)
(see Shabana 1996; Dimarogonas and Haddad 1992). A major culmination occurred
in 1877 with Lord Rayleigh’s masterpiece The Theory of Sound (Rayleigh 1877).
Since Rayleigh, the character of problems facing the vibration theoretician or
practitioner has hardly changed (which perhaps explains why Rayleigh’s books
appear surprisingly modern even today). But, the tools for solving vibration
problems have improved immensely by the emergence of (1) computers and software that can be used to simulate the behavior of virtually any dynamic system;
(2) new or improved mathematical tools for solving nonlinear differential equations
approximately; and (3) computerized and miniaturized measurement equipment for
experimentally based testing and improvement of theories. These corners of the
‘mechanicians triangular toolbox’ are centers of fields (numerical/theoretical/
experimental analysis) that are all expanding significantly in these years, seemingly
in a mutually fertilizing manner. New or updated books are needed to reflect these
developments and explain them to students.
Why This Book? There is, in fact, a plenitude of good books on nonlinear
dynamics/vibrations. Many of these are on my shelf. I use them heavily, and had no
intention of writing a competitor. Though, for my course in advanced vibration
analysis, I found that none of them treated the relevant range of subjects in the way
Preface
vii