that I wanted to present them, that is: Treating classical as well as modern nonlinear
analysis (excluding texts dealing with only one area), focusing almost exclusively
on mechanical systems (precluding texts on general nonlinear systems), and balancing theory and applications in a way where the latter is the goal and the former is
the tool (excluding excessively mathematical texts).
The book title reflects the intimate connection between a phenomenon (vibrations
or vibration-related) and the presence of this phenomenon as something observable
in reality (stability). Using vibration theory, we are mostly concerned with predicting equilibrium states, dynamical or statical, of mathematical models that are
supposed to model selected aspects of real physical systems. But knowing such
states is not enough: Typically, at least with nonlinear models, there are several
states of equilibrium, some being stable to perturbations, and some being unstable
(think of the down- and up-pointing equilibriums of a pendulum). In reality, and
with computer models, we never observe systems in their unstable states for very
long; they will either reside in a stable state or be on their way to one. So, stability
analysis is an integral and crucial part of vibration analysis, in particular for nonlinear systems, and therefore also forms an important part of the book.
Notes for Teachers The book centers on the analysis of a limited number of
simple generic models, which serve to illustrate qualitative behaviors for a wide
variety of mechanical systems. The students are trained to analyze simple models
and to recognize phenomena associated with them. Also, they are taught how to
extract simple models out of complicated systems. When combined, this will allow
them to appropriately benefit from computer simulations of large-scale systems,
e.g., nonlinear finite element models.
A limited number of nonlinear phenomena are described rather than the rich
variety of nonlinear systems. A few simple systems provide the backbone through
several chapters, illustrating tools such as perturbation analysis and bifurcation
analysis, as well as essential phenomena such as nonlinear frequency response,
chaos, and stabilization by high-frequency fields.
I encourage the use of classroom demonstrations for supporting the examples
given in the book. An instrumented clamped beam and a pair of magnets can be
used for illustrating a whole range of subjects covered, e.g., resonance, mode
shapes, statical buckling, hysteresis, bifurcations, and chaotic motion. Similarly, a
pendulum on vibrating support (a hobby jigsaw, e.g.) can be used for illustrating
parametrical resonance, softening frequency response, chaos, and stabilization
(of the upside-down equilibrium) using high-frequency excitation; and a simple
pendulum, hanging in a spring, illustrates internal resonance and modal interaction.
Also, classroom computer simulations are helpful in illustrating concepts such as
phase planes, Poincaré map and frequency spectra, and for showing animated
models of physical systems while integrating numerically their equations of motion.
Learning advanced vibration and stability analysis is hard work for most students,
viii
Preface
analysis (excluding texts dealing with only one area), focusing almost exclusively
on mechanical systems (precluding texts on general nonlinear systems), and balancing theory and applications in a way where the latter is the goal and the former is
the tool (excluding excessively mathematical texts).
The book title reflects the intimate connection between a phenomenon (vibrations
or vibration-related) and the presence of this phenomenon as something observable
in reality (stability). Using vibration theory, we are mostly concerned with predicting equilibrium states, dynamical or statical, of mathematical models that are
supposed to model selected aspects of real physical systems. But knowing such
states is not enough: Typically, at least with nonlinear models, there are several
states of equilibrium, some being stable to perturbations, and some being unstable
(think of the down- and up-pointing equilibriums of a pendulum). In reality, and
with computer models, we never observe systems in their unstable states for very
long; they will either reside in a stable state or be on their way to one. So, stability
analysis is an integral and crucial part of vibration analysis, in particular for nonlinear systems, and therefore also forms an important part of the book.
Notes for Teachers The book centers on the analysis of a limited number of
simple generic models, which serve to illustrate qualitative behaviors for a wide
variety of mechanical systems. The students are trained to analyze simple models
and to recognize phenomena associated with them. Also, they are taught how to
extract simple models out of complicated systems. When combined, this will allow
them to appropriately benefit from computer simulations of large-scale systems,
e.g., nonlinear finite element models.
A limited number of nonlinear phenomena are described rather than the rich
variety of nonlinear systems. A few simple systems provide the backbone through
several chapters, illustrating tools such as perturbation analysis and bifurcation
analysis, as well as essential phenomena such as nonlinear frequency response,
chaos, and stabilization by high-frequency fields.
I encourage the use of classroom demonstrations for supporting the examples
given in the book. An instrumented clamped beam and a pair of magnets can be
used for illustrating a whole range of subjects covered, e.g., resonance, mode
shapes, statical buckling, hysteresis, bifurcations, and chaotic motion. Similarly, a
pendulum on vibrating support (a hobby jigsaw, e.g.) can be used for illustrating
parametrical resonance, softening frequency response, chaos, and stabilization
(of the upside-down equilibrium) using high-frequency excitation; and a simple
pendulum, hanging in a spring, illustrates internal resonance and modal interaction.
Also, classroom computer simulations are helpful in illustrating concepts such as
phase planes, Poincaré map and frequency spectra, and for showing animated
models of physical systems while integrating numerically their equations of motion.
Learning advanced vibration and stability analysis is hard work for most students,
viii
Preface