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.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.

This book deals with fundamental problems, concepts, and methods ofmultiparameter stability theory with applications in mechanics. Itpresents recent achievements and knowledge of bifurcation theory, sensitivity analysis of stability characteristics, general aspects ofnonconservative stability problems, analysis of singularities ofboundaries for the stability domains, stability analysis ofmultiparameter linear periodic systems, and optimization of structuresunder stability constraints

Compared to other books devoted to matrices, this volume is unique in covering the whole of a triptych consisting of algebraic theory, algorithmic problems and numerical applications, all united by the essential use and urge for development of matrix methods. This was the spirit of the 2nd International Conference on Matrix Methods and Operator Equations from 23-27 July 2007 in Moscow that was organized by Dario Bini, Gene Golub, Alexander Guterman, Vadim Olshevsky, Stefano Serra-Capizzano, Gilbert Strang and Eugene Tyrtyshnikov.Matrix methods provide the key to many problems in pure and applied mathematics. However, linear algebra theory, numerical algorithms and matrices in FEM/BEM applications usually live as if in three separate worlds. In this volume, maybe for the first time ever, they are compiled together as one entity as it was at the Moscow meeting, where the algebraic part was impersonated by Hans Schneider, algorithms by Gene Golub, and applications by Guri Marchuk. All topics intervened in plenary sessions are specially categorized into three sections of this volume.The soul of the meeting was Gene Golub, who rendered a charming “Golub's dimension” to the three main axes of the conference topics. This volume is dedicated in gratitude to his memory.

This book presents inductive and hybrid levitation micro-systems and their applications in micro-sensors and –actuators. It proposes and discusses analytical and quasi-finite element techniques for modeling levitation micro-systems based on the Lagrangian formalism. In particular, micro-bearings, -actuators, -accelerators and –accelerometers based on inductive levitation are comprehensively described with accompanying experimental measurements.

This unique book presents an analytical uniform design methodology of continuous-time or discrete-time nonlinear control system design which guarantees desired transient performances in the presence of plant parameter variations and unknown external disturbances. All results are illustrated with numerical simulations, their practical importance is highlighted, and they may be used for real-time control system design in robotics, mechatronics, chemical reactors, electrical and electro-mechanical systems as well as aircraft control systems. The book is easy reading and is suitable for teaching.

The contributions in this volume are written by well-known specialists in the fields of mechanics, materials modeling and analysis. They comprehensively address the core issues and present the latest developments in these and related areas. In particular, the book demonstrates the breadth of current research activity in continuum mechanics. A variety of theoretical, computational, and experimental approaches are reported, covering finite elasticity, vibration and stability, and mechanical modeling. The coverage reflects the extent and impact of the research pursued by Professor Haseganu and her international colleagues.

This book presents a systematic description and case studies of chemical engineering modelling and simulation based on the MATLAB/FEMLAB tools, in support of selected topics in undergraduate and postgraduate programmes that require numerical solution of complex balance equations (ordinary differential equations, partial differential equations, nonlinear equations, integro-differential equations). These systems arise naturally in analysis of transport phenomena, process systems, chemical reactions and chemical thermodynamics, and particle rate processes. Templates are given for modelling both state-of-the-art research topics (e.g. microfluidic networks, film drying, multiphase flow, population balance equations) and case studies of commonplace design calculations -- mixed phase reactor design, heat transfer, flowsheet analysis of unit operations, flash distillations, etc. The great strength of this book is that it makes modelling and simulating in the MATLAB/FEMLAB environment approachable to both the novice and the expert modeller.

Bringing together 18 chapters written by leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics, this book presents state-of-the-art approaches to a wide spectrum of new and challenging stability problems. Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations focuses on problems of spectral analysis, stability and bifurcations arising in the nonlinear partial differential equations of modern physics. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics, and dissipation-induced instabilities are treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches. Each chapter contains mechanical and physical examples, and the combination of advanced material and more tutorial elements makes this book attractive for both experts and non-specialists keen to expand their knowledge on modern methods and trends in stability theory. Contents 1. Surprising Instabilities of Simple Elastic Structures, Davide Bigoni, Diego Misseroni, Giovanni Noselli and Daniele Zaccaria. 2. WKB Solutions Near an Unstable Equilibrium and Applications, Jean-François Bony, Setsuro Fujiié, Thierry Ramond and Maher Zerzeri, partially supported by French ANR project NOSEVOL. 3. The Sign Exchange Bifurcation in a Family of Linear Hamiltonian Systems, Richard Cushman, Johnathan Robbins and Dimitrii Sadovskii. 4. Dissipation Effect on Local and Global Fluid-Elastic Instabilities, Olivier Doaré. 5. Tunneling, Librations and Normal Forms in a Quantum Double Well with a Magnetic Field, Sergey Yu. Dobrokhotov and Anatoly Yu. Anikin. 6. Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials, Nir Dror and Boris A. Malomed. 7. Representation of Wave Energy of a Rotating Flow in Terms of the Dispersion Relation, Yasuhide Fukumoto, Makoto Hirota and Youichi Mie. 8. Determining the Stability Domain of Perturbed Four-Dimensional Systems in 1:1 Resonance, Igor Hoveijn and Oleg N. Kirillov. 9. Index Theorems for Polynomial Pencils, Richard Kollár and Radomír Bosák. 10. Investigating Stability and Finding New Solutions in Conservative Fluid Flows Through Bifurcation Approaches, Paolo Luzzatto-Fegiz and Charles H.K. Williamson. 11. Evolution Equations for Finite Amplitude Waves in Parallel Shear Flows, Sherwin A. Maslowe. 12. Continuum Hamiltonian Hopf Bifurcation I, Philip J. Morrison and George I. Hagstrom. 13. Continuum Hamiltonian Hopf Bifurcation II, George I. Hagstrom and Philip J. Morrison. 14. Energy Stability Analysis for a Hybrid Fluid-Kinetic Plasma Model, Philip J. Morrison, Emanuele Tassi and Cesare Tronci. 15. Accurate Estimates for the Exponential Decay of Semigroups with Non-Self-Adjoint Generators, Francis Nier. 16. Stability Optimization for Polynomials and Matrices, Michael L. Overton. 17. Spectral Stability of Nonlinear Waves in KdV-Type Evolution Equations, Dmitry E. Pelinovsky. 18. Unfreezing Casimir Invariants: Singular Perturbations Giving Rise to Forbidden Instabilities, Zensho Yoshida and Philip J. Morrison. About the Authors Oleg N. Kirillov has been a Research Fellow at the Magneto-Hydrodynamics Division of the Helmholtz-Zentrum Dresden-Rossendorf in Germany since 2011. His research interests include non-conservative stability problems of structural mechanics and physics, perturbation theory of non-self-adjoint boundary eigenvalue problems, magnetohydrodynamics, friction-induced oscillations, dissipation-induced instabilities and non-Hermitian problems of optics and microwave physics. Since 2013 he has served as an Associate Editor for the journal Frontiers in Mathematical Physics. Dmitry E. Pelinovsky has been Professor at McMaster University in Canada since 2000. His research profile includes work with nonlinear partial differential equations, discrete dynamical systems, spectral theory, integrable systems, and numerical analysis. He served as the guest editor of the special issue of the journals Chaos in 2005 and Applicable Analysis in 2010. He is an Associate Editor of the journal Communications in Nonlinear Science and Numerical Simulations. This book is devoted to the problems of spectral analysis, stability and bifurcations arising from the nonlinear partial differential equations of modern physics. Leading experts in dynamical systems, operator theory, partial differential equations, and solid and fluid mechanics present state-of-the-art approaches to a wide spectrum of new challenging stability problems. Bifurcations and stability of solitary waves, geometrical optics stability analysis in hydro- and magnetohydrodynamics and dissipation-induced instabilities will be treated with the use of the theory of Krein and Pontryagin space, index theory, the theory of multi-parameter eigenvalue problems and modern asymptotic and perturbative approaches. All chapters contain mechanical and physical examples and combine both tutorial and advanced sections, making them attractive both to experts in the field and non-specialists interested in knowing more about modern methods and trends in stability theory.

While the stability theory for systems with bilateral constraints is a well-established field, this monograph represents a systematic study of mechanical systems with unilateral constraints, such as unilateral contact, impact and friction. Such unilateral constraints give rise to non-smooth dynamical models for which stability theory is developed in this work. The book will be of interest to those working in the field of non-smooth mechanics and dynamics.