research. Necessarily incomplete in covering a very wide and active field, its
purpose remains to try cover some of the gap between a typical elementary-level
vibration course and interesting and relevant real vibration problems in engineering
science and applications.
The Second Edition (2003) was a revised and expanded version of the first edition
published by McGraw-Hill in 1997, reflecting the experience gathered during its six
years in service as a classroom or self-study text for students and researchers. The
second edition added a major new chapter (Chap. 7), three new appendices, many
new exercise problems, more than 120 new and updated bibliographic references,
and hundreds of minor updates, corrections, and clarifications. Also, the subtitle
was changed to better reflect the scope and intended readership of the book. In
deciding what to change or include, I have drew partly on a large number of inputs
from students and other readers to improve it as a textbook and partly on a selfish
wish to make it a self-contained handbook for use in my own work with vibration
problems. Examples of the latter are the inclusion of lists of expressions of natural
frequencies and mode shapes for basic structures such as rods, beams, plates, and
membranes; tables of constants for engineering materials (elasticity, density, friction); and mathematical topics such as stability criteria for Mathieu’s equation and
the Routh–Hurwitz stability criterion.
Why Learn About Nonlinear Vibrations? Many do not bother with this question at
all, once they caught by the delights and horrors of nonlinear phenomena. However,
there are sound reasons for bothering engineers-to-be with this knowledge:
• Real systems are nonlinear. Nevertheless, we attempt linearizing whenever
possible, because linear theory is well established and rather straightforward.
However, when we linearize, we also lose essential information. Thus, students
should be capable of recognizing nonlinear mechanisms and understand their
possible significance.
• Nonlinearities may account for significant deviations between experimental
observations and linear model predictions. Students should be trained to recognize significant nonlinear phenomena as these show up in experiments and
computer simulations.
• Using nonlinear computer models without the analyst, possessing a firm theoretical background is meaningless, at best. One cannot, as with linear systems,
obtain a general ‘feel’ for the dynamics of a nonlinear system simply by running
the model with a few sets of parameters. There can be multiple solution branches, extreme sensitivity to initial conditions, discontinuities in response, special
high-frequency effects, and several other non-trivial effects. Output from computers (and experiments) is always viewed in the light of the theoretical
knowledge and expectations. Thus, students should know what to expect from
nonlinear systems and be well prepared for the unexpected.
• Nonlinearities may qualitatively alter the response of a system. Students should
know the universal nonlinear bifurcations.
vi
Preface
purpose remains to try cover some of the gap between a typical elementary-level
vibration course and interesting and relevant real vibration problems in engineering
science and applications.
The Second Edition (2003) was a revised and expanded version of the first edition
published by McGraw-Hill in 1997, reflecting the experience gathered during its six
years in service as a classroom or self-study text for students and researchers. The
second edition added a major new chapter (Chap. 7), three new appendices, many
new exercise problems, more than 120 new and updated bibliographic references,
and hundreds of minor updates, corrections, and clarifications. Also, the subtitle
was changed to better reflect the scope and intended readership of the book. In
deciding what to change or include, I have drew partly on a large number of inputs
from students and other readers to improve it as a textbook and partly on a selfish
wish to make it a self-contained handbook for use in my own work with vibration
problems. Examples of the latter are the inclusion of lists of expressions of natural
frequencies and mode shapes for basic structures such as rods, beams, plates, and
membranes; tables of constants for engineering materials (elasticity, density, friction); and mathematical topics such as stability criteria for Mathieu’s equation and
the Routh–Hurwitz stability criterion.
Why Learn About Nonlinear Vibrations? Many do not bother with this question at
all, once they caught by the delights and horrors of nonlinear phenomena. However,
there are sound reasons for bothering engineers-to-be with this knowledge:
• Real systems are nonlinear. Nevertheless, we attempt linearizing whenever
possible, because linear theory is well established and rather straightforward.
However, when we linearize, we also lose essential information. Thus, students
should be capable of recognizing nonlinear mechanisms and understand their
possible significance.
• Nonlinearities may account for significant deviations between experimental
observations and linear model predictions. Students should be trained to recognize significant nonlinear phenomena as these show up in experiments and
computer simulations.
• Using nonlinear computer models without the analyst, possessing a firm theoretical background is meaningless, at best. One cannot, as with linear systems,
obtain a general ‘feel’ for the dynamics of a nonlinear system simply by running
the model with a few sets of parameters. There can be multiple solution branches, extreme sensitivity to initial conditions, discontinuities in response, special
high-frequency effects, and several other non-trivial effects. Output from computers (and experiments) is always viewed in the light of the theoretical
knowledge and expectations. Thus, students should know what to expect from
nonlinear systems and be well prepared for the unexpected.
• Nonlinearities may qualitatively alter the response of a system. Students should
know the universal nonlinear bifurcations.
vi
Preface