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This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Zusammenfassung: This volume aims to present the latest advancements in experimental, analytical, and numerical methodologies aimed at exploring the nonlinear dynamics of diverse systems across varying length and time scales. It delves into the following topics: Methodologies for nonlinear dynamic analysis (harmonic balance, asymptotic techniques, enhanced time integration) Data-driven dynamics, machine learning techniques Exploration of bifurcations and nonsmooth systems Nonlinear phenomena in mechanical systems and structures Experimental dynamics, system identification, and monitoring techniques Fluid-structure interaction Dynamics of multibody systems Turning processes, rotating systems, and systems with time delays
Provides the basic background needed by engineers to determine experimentally and interpret the rheological behavior of polymer melts--including not only traditional pure melts but also solutions and compounds containing anisotropic (fiber or disc) or colloidal particles--and apply it to analyze flow in processing operations. Experimental foundations of modern rheology and rheo-optics and the interpretation of experimental data are covered, which also develops the fundamentals of continuum mechanics and shows how it may be applied to devise methods for measurement of rheological properties, formulation of three-dimensional stress-deformation relationships, and analysis of flow in processing operations. Also discusses the structure of polymers and considers rheological behavior in terms of structure. Constitutive equations relating stress to deformation history in non-Newtonian fluids and their applications are discussed. Each chapter presents an overview of the subject matter and then develops the material in a pedagogical manner.
The science of rheology remains a mystery to most people, even to some scientists. Some respectable dictionaries have been quite cavalier in their attitude to the science, the small Collins Gem dictionary, for example, being quite happy to inform us that a Rhea is an three-toed South American ostrich, whilst at the same time offering no definition of rheology. This maybe due to the fact that the science is interdisciplinary and does not fit well into any one of the historical disciplines. This book contains an in-depth study of the history of rheology, beginning with the statements of Heraclitus, Confucius and the prophetess Deborah. It also emphasises the distinctive contributions of Newton, Hooke, Boltzmann, Maxwell, Kelvin and others, and culminates in the flourishing activity in the second half of this century. Features of this book: . Is the only book on the subject . Prevents the rediscovery of results already made . Will educate newcomers to the field to the rich heritage in even a relatively recent science like rheology. The book will be invaluable for science and scientific history libraries and will also be of interest to rheologists, and scientists working in the polymer processing, food, lubrication, detergent and similar industries.
Instability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
Modern day high-performance computers are making available to 21st-century scientists solutions to rheological flow problems of ever-increasing complexity. Computational rheology is a fast-moving subject — problems which only 10 years ago were intractable, such as 3D transient flows of polymeric liquids, non-isothermal non-Newtonian flows or flows of highly elastic liquids through complex geometries, are now being tackled owing to the availability of parallel computers, adaptive methods and advances in constitutive modelling.Computational Rheology traces the development of numerical methods for non-Newtonian flows from the late 1960's to the present day. It begins with broad coverage of non-Newtonian fluids, including their mathematical modelling and analysis, before specific computational techniques are discussed. The application of these techniques to some important rheological flow problems of academic and industrial interest is then treated in a detailed and up-to-date exposition. Finally, the reader is kept abreast of topics at the cutting edge of research in computational applied mathematics, such as adaptivity and stochastic partial differential equations.All the topics in this book are dealt with from an elementary level and this makes the text suitable for advanced undergraduate and graduate students, as well as experienced researchers from both the academic and industrial communities.