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This book presents a selection of contributions from the 4th International Conference on Structural Nonlinear Dynamics and Diagnostics, reflecting diverse aspects of nonlinear and complex dynamics. Fifteen chapters discuss the latest findings and applications in active research areas in nonlinear mechanics and physics. These includes the dynamics of ships with liquid sloshing interaction, dynamics of drops and bubbles, nonlinear drying processes, suppression of time-delayed induced vibrations, dynamics of robotic systems, chaos detection in rolling element, dynamics of a planetary gear system with faults, vibro-impact systems, complex fractional moments for nonlinear systems, oscillations under hysteretic conditions, as well as topics in nonlinear energy harvesting and control.
In their prior Dover book, the authors provided a self-contained account of classical mechanics; this supplement/update offers a bridge to contemporary mechanics. Topics include nonlinear continuous systems. 2006 edition.
This book covers different topics of nonlinear mechanics in complex structures, such as the appearance of new nonlinear phenomena and the behavior of finite-dimensional and distributed nonlinear systems, including numerous systems directly connected with important technological problems.
This book offers a recipe for constructing the numerical models for representing the complex nonlinear behavior of structures and their components, represented as deformable solid bodies. Its appeal extends to those interested in linear problems of mechanics.
Through a series of examples from physics, engineering, biology and economics, this book illustrates the enormous potential for application of ideas and concepts from nonlinear dynamics and chaos theory. The overlap with examples published in other books is virtually equal to zero. The book takes the reader from detailed studies of bifurcation structures of relativity simple models to pattern formation in spatially extended systems. The book also discusses the different perspectives that nonlinear dynamics brings to different fields of science.
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.
Providing a modern and comprehensive coverage of continuum mechanics, this volume includes information on "variational principles"--Significant, as this is the only method by which such material is actually utilized in engineering practice.
This two-part text fills what has often been a void in the first-year graduate physics curriculum. Through its examination of particles and continua, it supplies a lucid and self-contained account of classical mechanics — which in turn provides a natural framework for introducing many of the advanced mathematical concepts in physics. The text opens with Newton's laws of motion and systematically develops the dynamics of classical particles, with chapters on basic principles, rotating coordinate systems, lagrangian formalism, small oscillations, dynamics of rigid bodies, and hamiltonian formalism, including a brief discussion of the transition to quantum mechanics. This part of the book also considers examples of the limiting behavior of many particles, facilitating the eventual transition to a continuous medium. The second part deals with classical continua, including chapters on string membranes, sound waves, surface waves on nonviscous fluids, heat conduction, viscous fluids, and elastic media. Each of these self-contained chapters provides the relevant physical background and develops the appropriate mathematical techniques, and problems of varying difficulty appear throughout the text.
The aim of this book is to develop a unified approach to nonlinear science, which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate both the development of the subject and the mathematical techniques, by reference to simple models. Each chapter concludes with a set of problems. This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications.