Self Adjoint Problems For An Ideal Fluid
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Self Adjoint Problems For An Ideal Fluid
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Author : Nikolay D. Kopachevsky
language : en
Publisher:
Release Date : 2001
Self Adjoint Problems For An Ideal Fluid written by Nikolay D. Kopachevsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Fluid dynamics categories.
Operator Approach To Linear Problems Of Hydrodynamics
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Author : Nikolay D. Kopachevskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-09-01
Operator Approach To Linear Problems Of Hydrodynamics written by Nikolay D. Kopachevskii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-01 with Mathematics categories.
The main topics presented in this book deal with methods from functional analysis applied to the study ofsmall movements and normal oscillations ofhydrome- chanical systems having cavities filled with either ideal or viscous fluids. The book is a sequel to and at the same time substantially extends the volume entitled "Opera- tor Methods in Linear Hydrodynamics: Evolution and Spectral Problems," by N. D. Kopachevsky, S.G. Krein, and Ngo Zuy Kan that was published in 1989 by the Nauka publishing house in Moscow. The present book includesseveral new problems on the oscillations ofpartially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The contents of this book do not overlap almost at all with the ones in the following volumes: "Mathematical Problems of the Motion of Viscous Incopressible Fluids," by O. A. Ladyzhenskaya, "The Dynamics ofBodies with Cavities Filled with Fluids," by N. N. Moiseev and V. V. Rumiantzev, "Navier-Stokes Equations," by R. Temam, and "Boundary Problems for Navier-Stokes Equations," by S. M. Belonosov and K. A. Chernous. Mainly, the contents of the present book rely on the authors' and their students' works. We would like to express our gratitude to I. T. Gohberg and A. S. Markus, who encouraged us to publish the book and who offered many helpful suggestions. Our gratidude goes also to our colleagues T. Ya. Azizov, O. A. Ladyzhenskaya, N. N.
Operator Approach To Linear Problems Of Hydrodynamics
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Author : Nikolay D. Kopachevskii
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Approach To Linear Problems Of Hydrodynamics written by Nikolay D. Kopachevskii and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume "Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems" by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students' works of the last 30-40 years. The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils. The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems.
Operator Approach To Linear Problems Of Hydrodynamics
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Author : Nikolay D. Kopachevsky
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Operator Approach To Linear Problems Of Hydrodynamics written by Nikolay D. Kopachevsky and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is the second volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The second part of the present volume collects nonself-adjoint problems on small motions and normal oscillations of a viscous fluid filling a bounded region.
Sloshing In Upright Circular Containers
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Author : Ihor Raynovskyy
language : en
Publisher: CRC Press
Release Date : 2020-10-08
Sloshing In Upright Circular Containers written by Ihor Raynovskyy and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-08 with Technology & Engineering categories.
This book presents mathematical fundaments and results on sloshing in an upright circular cylindrical tank with semi-analytical solutions. The book outlines generic mathematical and physical aspects of the multimodal method, describes milestones, and presents several versions of modal systems for an upright circular tank, both linear and nonlinear. The book offers an extended description of the state-of-the-art theoretical sloshing with more than 200 references. It presents mathematical fundamentals of free-surface sloshing problems, details linear and nonlinear modal equations, provides analytical estimates of viscous damping, and covers stability analysis of steady-state solution. The book is for engineers dealing with sloshing, applied mathematicians working on free-surface problems, and lecturers in fluid mechanics that need to know the fundamentals and analytical solutions from surface wave theory.
Nonlinear Dynamics
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Author : Ivan A. Lukovsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-04-24
Nonlinear Dynamics written by Ivan A. Lukovsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-24 with Mathematics categories.
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities (containers) partly filled by a liquid. The methods are normally based on the Bateman-Luke variational formalism combined with perturbation theory. The derived approximate equations of spatial motions of the body-liquid mechanical system (these equations are called mathematical models in the title) take the form of a finite-dimensional system of nonlinear ordinary differential equations coupling quasi-velocities of the rigid body motions and generalized coordinates responsible for displacements of the natural sloshing modes. Algorithms for computing the hydrodynamic coefficients in the approximate mathematical models are proposed. Numerical values of these coefficients are listed for some tank shapes and liquid fillings. The mathematical models are also derived for the contained liquid characterized by the Newton-type dissipation. Formulas for hydrodynamic force and moment are derived in terms of the solid body quasi-velocities and the sloshing-related generalized coordinates. For prescribed harmonic excitations of upright circular (annular) cylindrical and/or conical tanks, the steady-state sloshing regimes are theoretically classified; the results are compared with known experimental data. The book can be useful for both experienced and early-stage mechanicians, applied mathematicians and engineers interested in (semi-)analytical approaches to the “fluid-structure” interaction problems, their fundamental mathematical background as well as in modeling the dynamics of complex mechanical systems containing a rigid tank partly filled by a liquid.
Dynamic Stability And Bifurcation In Nonconservative Mechanics
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Author : Davide Bigoni
language : en
Publisher: Springer
Release Date : 2018-07-09
Dynamic Stability And Bifurcation In Nonconservative Mechanics written by Davide Bigoni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Science categories.
The book offers a unified view on classical results and recent advances in the dynamics of nonconservative systems. The theoretical fundamentals are presented systematically and include: Lagrangian and Hamiltonian formalism, non-holonomic constraints, Lyapunov stability theory, Krein theory of spectra of Hamiltonian systems and modes of negative and positive energy, anomalous Doppler effect, reversible systems, sensitivity analysis of non-self-adjoint operators, dissipation-induced instabilities, local and global instabilities. They are applied to engineering situations such as the coupled mode flutter of wings, flags and pipes, flutter in granular materials, piezoelectric mechanical metamaterials, wave dynamics of infinitely long structures, radiative damping, stability of high-speed trains, experimental realization of follower forces, soft-robot locomotion, wave energy converters, friction-induced instabilities, brake squeal, non-holonomic sailing, dynamics of moving continua, and stability of bicycles and walking robots. The book responds to a demand in the modern theory of nonconservative systems coming from the growing number of scientific and engineering disciplines including physics, fluid and solids mechanics, fluid-structure interactions, and modern multidisciplinary research areas such as biomechanics, micro- and nanomechanics, optomechanics, robotics, and material science. It is targeted at both young and experienced researchers and engineers working in fields associated with the dynamics of structures and materials. The book will help to get a comprehensive and systematic knowledge on the stability, bifurcations and dynamics of nonconservative systems and establish links between approaches and methods developed in different areas of mechanics and physics and modern applied mathematics.
Trend And Applications Of Mathematics To Mechanics
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Author : S. Rionero
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-11
Trend And Applications Of Mathematics To Mechanics written by S. Rionero and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-11 with Technology & Engineering categories.
The book provides a collection of recent theoretical and methodological advances which can provide support and stimulus to scientists and scholars involved in research activity in the fields of interest.
Spectral Analysis Of Differential Operators Interplay Between Spectral And Oscillatory Properties
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Author : Fedor S Rofe-beketov
language : en
Publisher: World Scientific
Release Date : 2005-08-29
Spectral Analysis Of Differential Operators Interplay Between Spectral And Oscillatory Properties written by Fedor S Rofe-beketov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-29 with Mathematics categories.
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic Schrödinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals).The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators.
New Difference Schemes For Partial Differential Equations
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Author : Allaberen Ashyralyev
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
New Difference Schemes For Partial Differential Equations written by Allaberen Ashyralyev and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.