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The aim of this International Symposium on Dynamics of
Vibro-Impact Systems is to provide a forum for the discussion of
recent developments in the theory and industrial applications of
vibro-impact ocean systems. A special effort has been made to
invite active researchers from engineering, science, and applied
mathematics communities. This symposium has indeed updated
engineers with recent analytical developments of vibro-impact
dynamics and at the same time allowed engineers and industrial
practitioners to alert mathematicians with their unresolved issues.
The symposium was held in Troy, Michigan, during the period October
1-3, 2008. It included 28 presentations grouped as follows: The
first group comprises of nine papers dealing with the interaction
of ocean systems with slamming waves and floating ice. It also
covers related topics such as sloshing-slamming dynamics, and
non-smooth dynamics associated with offshore structures. Moreover,
it includes control issues pertaining to marine surface vessels.
The second group consists of fifteen papers treats the interaction
of impact systems with friction and their control, Hertzian contact
dynamics, parameter variation in vibro-impact oscillators, random
excitation of vibro-impact systems, vibro-impact dampers,
oscillators with a bouncing ball, limiting phase trajectory
corresponding to energy exchange between the oscillator and
external source, frequency-energy distribution in oscillators with
impacts, and discontinuity mapping. The third group is covered in
four papers and addresses some industrial applications such as
hand-held percussion machines, rub-impact dynamics of rotating
machinery, impact fatigue in joint structures.
Vibro-impact dynamics has occupied a wide spectrum of studies by
dyn- icists, physicists, and mathematicians. These studies may be
classi?ed into three main categories: modeling, mapping and
applications. The main te- niques used in modeling of vibro-impact
systems include phenomenological modelings, Hertzian models, and
non-smooth coordinate transformations- velopedbyZhuravlevandIvanov.
Oneofthemostcriticalsituationsimpeded
invibro-impactsystemsisthegrazingbifurcation.
Grazingbifurcationisu- ally studied through discontinuity mapping
techniques, which are very useful to uncover the rich dynamics in
the process of impact interaction. Note the availablemappings
arevalidonly intheabsenceofnon-impactnonlinearities. Complex
dynamic phenomena of vibro-impact systems include subharmonic
oscillations, chaotic motion, and coexistence of di?erent
attractors for the sameexcitationand systemparametersbut under
di?erent initial conditions.
Selectedapplicationsofvibro-impactdynamics. Theseincludelumpedand
continuous systems. Lumped systems cover a bouncing ball on an
oscillating barrier, mass-spring-dashpot systems, normal and
inverted pendulums, the spherical pendulum, the ship roll motion
against icebergs, joints with fr- play, rotor-stator rubbing in
rotating machinery, vocal folds, microactuators, strings, beams,
pipes conveying ?uids with end-restraints, nuclear reactors and
heat exchangers, and plates. These applications are discussed
within the framework of the deterministic theory. Under random
excitation the tre- ment requires special tools. The techniques of
equivalent linearization and stochastic averaging have been applied
to limited number of problems. One of the most bene?cial outcomesof
vibro-impact dynamics is the development of impact dampers, which
have witnessed signi?cant activities over the last four decades and
have been used in several applications. On the other hand,
vibro-impacthas detrimental e?ects on the operationsof
mechanicalsystems and damage of pipes and rods in nuclear reactors.
Vibro-impact dynamics has occupied a wide spectrum of studies by
dyn- icists, physicists, and mathematicians. These studies may be
classi?ed into three main categories: modeling, mapping and
applications. The main te- niques used in modeling of vibro-impact
systems include phenomenological modelings, Hertzian models, and
non-smooth coordinate transformations- velopedbyZhuravlevandIvanov.
Oneofthemostcriticalsituationsimpeded
invibro-impactsystemsisthegrazingbifurcation.
Grazingbifurcationisu- ally studied through discontinuity mapping
techniques, which are very useful to uncover the rich dynamics in
the process of impact interaction. Note the availablemappings
arevalidonly intheabsenceofnon-impactnonlinearities. Complex
dynamic phenomena of vibro-impact systems include subharmonic
oscillations, chaotic motion, and coexistence of di?erent
attractors for the sameexcitationand systemparametersbut under
di?erent initial conditions.
Selectedapplicationsofvibro-impactdynamics. Theseincludelumpedand
continuous systems. Lumped systems cover a bouncing ball on an
oscillating barrier, mass-spring-dashpot systems, normal and
inverted pendulums, the spherical pendulum, the ship roll motion
against icebergs, joints with fr- play, rotor-stator rubbing in
rotating machinery, vocal folds, microactuators, strings, beams,
pipes conveying ?uids with end-restraints, nuclear reactors and
heat exchangers, and plates. These applications are discussed
within the framework of the deterministic theory. Under random
excitation the tre- ment requires special tools. The techniques of
equivalent linearization and stochastic averaging have been applied
to limited number of problems. One of the most bene?cial outcomesof
vibro-impact dynamics is the development of impact dampers, which
have witnessed signi?cant activities over the last four decades and
have been used in several applications. On the other hand,
vibro-impacthas detrimental e?ects on the operationsof
mechanicalsystems and damage of pipes and rods in nuclear reactors.
The aim of this International Symposium on Dynamics of
Vibro-Impact Systems is to provide a forum for the discussion of
recent developments in the theory and industrial applications of
vibro-impact ocean systems. A special effort has been made to
invite active researchers from engineering, science, and applied
mathematics communities. This symposium has indeed updated
engineers with recent analytical developments of vibro-impact
dynamics and at the same time allowed engineers and industrial
practitioners to alert mathematicians with their unresolved issues.
The symposium was held in Troy, Michigan, during the period October
1-3, 2008. It included 28 presentations grouped as follows: The
first group comprises of nine papers dealing with the interaction
of ocean systems with slamming waves and floating ice. It also
covers related topics such as sloshing-slamming dynamics, and
non-smooth dynamics associated with offshore structures. Moreover,
it includes control issues pertaining to marine surface vessels.
The second group consists of fifteen papers treats the interaction
of impact systems with friction and their control, Hertzian contact
dynamics, parameter variation in vibro-impact oscillators, random
excitation of vibro-impact systems, vibro-impact dampers,
oscillators with a bouncing ball, limiting phase trajectory
corresponding to energy exchange between the oscillator and
external source, frequency-energy distribution in oscillators with
impacts, and discontinuity mapping. The third group is covered in
four papers and addresses some industrial applications such as
hand-held percussion machines, rub-impact dynamics of rotating
machinery, impact fatigue in joint structures.
Coherent and systematic, this text explores the behavior of linear
and nonlinear dynamical systems subject to parametric random
vibrations, by means of the theory of stochastic processes,
stochastic differential equations, and applied dynamics. It
distills decades of research to formulate new stochastic stability
theorems and analytical techniques for determining the random
response of nonlinear systems. In addition, it resolves
controversies and paradoxes related to the interpretation of
certain stochastic processes and the use of analytical
methods.
After a brief overview of parametric vibration and its subclasses,
the text surveys the fundamental concepts of random processes and
their calculus rules, emphasizing the main elements necessary for
the analysis of parametric vibration problems. Subsequent chapters
address the stability and response analyses of linear and nonlinear
systems with random coefficients. The final chapter presents an
extensive compilation of experimental results from the literature
of the field.
The problem of liquid sloshing in moving or stationary containers
remains of great concern to aerospace, civil, and nuclear
engineers; physicists; designers of road tankers and ship tankers;
and mathematicians. Beginning with the fundamentals of liquid
sloshing theory, this book takes the reader systematically from
basic theory to advanced analytical and experimental results in a
self-contained and coherent format. The book is divided into four
sections. Part I deals with the theory of linear liquid sloshing
dynamics; Part II addresses the nonlinear theory of liquid sloshing
dynamics, Faraday waves, and sloshing impacts; Part III presents
the problem of linear and nonlinear interaction of liquid sloshing
dynamics with elastic containers and supported structures; and Part
IV considers the fluid dynamics in spinning containers and
microgravity sloshing. This book will be invaluable to researchers
and graduate students in mechanical and aeronautical engineering,
designers of liquid containers, and applied mathematicians.
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