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MULTIPARAMETER STABILITY THEORY WITH MECHANICAL APPLICATIONS Alexander
P. Seyranian & Alexei A. Mailybaev
(Moscow State
Lomonosov University, Russia) |
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This book deals with
fundamental problems, concepts, and methods of multiparameter stability
theory with applications in mechanics. It presents recent achievements
and knowledge of bifurcation theory, sensitivity analysis of stability
characteristics, general aspects of nonconservative stability problems,
analysis of singularities of boundaries for the stability domains,
stability analysis of multiparameter linear periodic systems, and
optimization of structures under stability constraints. Systems with
finite degrees of freedom and with continuous models are both
considered. The book combines mathematical foundation with interesting
classical and modern mechanical problems.
A number of mechanical
problems illustrating how bifurcations and
singularities change the behavior of systems and lead to new physical
phenomena are discussed. Among these problems, the authors consider
systems of rotating bodies, tubes conveying fluid, elastic columns
under the action of periodic and follower forces, optimization problems
for conservative systems, etc. The methods presented are constructive
and easy to implement in computer programs.
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Contents:
- Introduction to Stability Theory
- Bifurcation Analysis of Eigenvalues
- Stability Boundary of General System Dependent on Parameters
- Bifurcation Analysis of Roots and Stability of Characteristic Polynomial Dependent on Parameters
- Vibrations and Stability of Conservative System
- Gyroscopic Stabilization
- Linear Hamiltonian Systems
- Mechanical Effects Associated with Bifurcations and Singularities
- Stability of Periodic Systems Dependent on Parameters
- Stability Boundary of General Periodic System
- Instability Domains of Oscillatory System with Small Parametric Excitation and Damping
- Stability Domains of Non-Conservative System under Small
Parametric Excitation
Readership:
This book is addressed to graduate students, academics, researchers and practitioners in aerospace, naval, civil and mechanical engineering. No special background is needed; just a basic knowledge of mathematics and mechanics."The book is an excellent
and most valuable contribution, which I warmly recommend to graduate
students and university professors, as well as to researchers and
industrial engineers interested in multiparameter stability theory and
its applications in mechanics. I expect that this book will serve as an
inspiration for studies of new problems, effects, and phenomena
associated with instabilities, and that it will provide a new entry to
classical problems as well." Read
Full
Review
| Professor Niels Olhoff Structural and Multidisciplinary Optimization |
"... it is a very important
and high-quality book. It represents a major contribution to the
multi-parameter bifurcation theory of eigenvalues. Since Bolotin's
pioneering book on nonconservation problems on the theory of elastic
stability, not many books appeared at such a high level, such as this
one. It beautifully summarizes the results of the authors'
investigations performed for decades. The authors successfully analyze
singularities of stability boundaries and provide consistent and
in-depth descriptions of several most interesting mechanical effects.
These include gyroscopic stabilization, instability transfer between
the eigenvalue branches, paradox of destabilization by a small damping,
disappearance of flutter instability, parametric resonance in
periodically excited systems, to name a few." Read Full
Review
| Professor Isaac Elishakoff Meccanica |
“This book is highly
recommended for researchers involved in the stability investigation of
physical systems, because it explains the theory from the basic facts
up to a sophisticated level.” Read Full
Review
| Professor Alois
Steindl Zentralblatt MATH |
“The material covered
in the book could be used as a basis for a graduate course in
mechanical, aerospace or civil engineering, as well as in applied
mathematics courses on stability. Researchers in those fields will also
find this book an important addition to the existing literature. To all
those the book is warmly recommended. It is my opinion that it will
become a classic in the field.” Read Full
Review
| Professor Teodor M
Atanackovic Theoretical and Applied Mechanics |
“This book succeeds in
bringing qualitative results of the famous Russian school of applied
mathematics to stability theory, making these results quantitative and
applicable ... applications play a major role in this book. This
feature makes it of great value, especially for graduate students and
engineers ... Without hesitation I can warmly recommend the
book.” Read Full
Review
| Professor Wolfhard
Kliem Mathematical Reviews |
“This book reviewed is
an excellent representative both of the mathematical outlook just
described and of the close Russian-style interaction between abstract
geometrical thinking and specific engineering applications ... The text
is clearly written and the mathematics attractively set out with plenty
of clear and instructive diagrams: an enjoyable book to read.” Read Full
Review
| Professor
D.R.J.Chillingworth Journal of Sound and Vibration |