dimensional analysis with case studies in mechanics

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Dimensional Analysis

Author : Qing-Ming Tan
ISBN : 3642192343
Genre : Technology & Engineering
File Size : 20. 83 MB
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Dimensional analysis is an essential scientific method and a powerful tool for solving problems in physics and engineering. This book starts by introducing the Pi Theorem, which is the theoretical foundation of dimensional analysis. It also provides ample and detailed examples of how dimensional analysis is applied to solving problems in various branches of mechanics. The book covers the extensive findings on explosion mechanics and impact dynamics contributed by the author’s research group over the past forty years at the Chinese Academy of Sciences. The book is intended for research scientists and engineers working in the fields of physics and engineering, as well as graduate students and advanced undergraduates of the related fields. Qing-Ming Tan is a former Professor at the Institute of Mechanics, the Chinese Academy of Sciences, China.

Advances In Mechanics Theoretical Computational And Interdisciplinary Issues

Author : Michał Kleiber
ISBN : 9781315645063
Genre : Computers
File Size : 47. 62 MB
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Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues covers the domain of theoretical, experimental and computational mechanics as well as interdisciplinary issues, such as industrial applications. Special attention is paid to the theoretical background and practical applications of computational mechanics. This volume contains 132 contributions presented at the PCM-CMM-2015 Congress held on 8-11 September, 2015 in Gdańsk, Poland. The Congress is a joint scientific event of the 3rd Polish Congress of Mechanics (PCM) and the 21st International Conference on Computer Methods in Mechanics (CMM). Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues will be of interest to researchers and designers dealing with mechanics and its applications.

Dimensional Analysis Beyond The Pi Theorem

Author : Bahman Zohuri
ISBN : 9783319457260
Genre : Mathematics
File Size : 53. 99 MB
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Dimensional Analysis and Physical Similarity are well understood subjects, and the general concepts of dynamical similarity are explained in this book. Our exposition is essentially different from those available in the literature, although it follows the general ideas known as Pi Theorem. There are many excellent books that one can refer to; however, dimensional analysis goes beyond Pi theorem, which is also known as Buckingham’s Pi Theorem. Many techniques via self-similar solutions can bound solutions to problems that seem intractable. A time-developing phenomenon is called self-similar if the spatial distributions of its properties at different points in time can be obtained from one another by a similarity transformation, and identifying one of the independent variables as time. However, this is where Dimensional Analysis goes beyond Pi Theorem into self-similarity, which has represented progress for researchers. In recent years there has been a surge of interest in self-similar solutions of the First and Second kind. Such solutions are not newly discovered; they have been identified and named by Zel’dovich, a famous Russian Mathematician in 1956. They have been used in the context of a variety of problems, such as shock waves in gas dynamics, and filtration through elasto-plastic materials. Self-Similarity has simplified computations and the representation of the properties of phenomena under investigation. It handles experimental data, reduces what would be a random cloud of empirical points to lie on a single curve or surface, and constructs procedures that are self-similar. Variables can be specifically chosen for the calculations.

Dimensional Analysis And Self Similarity Methods For Engineers And Scientists

Author : Bahman Zohuri
ISBN : 9783319134765
Genre : Technology & Engineering
File Size : 58. 79 MB
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This ground-breaking reference provides an overview of key concepts in dimensional analysis, and then pushes well beyond traditional applications in fluid mechanics to demonstrate how powerful this tool can be in solving complex problems across many diverse fields. Of particular interest is the book’s coverage of dimensional analysis and self-similarity methods in nuclear and energy engineering. Numerous practical examples of dimensional problems are presented throughout, allowing readers to link the book’s theoretical explanations and step-by-step mathematical solutions to practical implementations.

Back Of The Envelope Quantum Mechanics

Author : Maxim Olshanii
ISBN : 9789814508476
Genre : Differential equations, Partial
File Size : 64. 60 MB
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Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that something else is needed to quickly gain insight into the system they are going to study. Qualitative methods are this something else, but typically, students have never heard of them before. The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pi ce de r(r)sistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori . Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear SchrAdinger breather as a function of its widt

Mathematics Applied To Deterministic Problems In The Natural Sciences

Author : C. C. Lin
ISBN : 0898712297
Genre : Mathematics
File Size : 69. 23 MB
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This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.

Mechanical Systems Classical Models

Author : Petre P. Teodorescu
ISBN : 9781402054426
Genre : Science
File Size : 63. 61 MB
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This book examines the study of mechanical systems as well as its links to other sciences of nature. It presents the fundamentals behind how mechanical theories are constructed and details the solving methodology and mathematical tools used: vectors, tensors and notions of field theory. It also offers continuous and discontinuous phenomena as well as various mechanical magnitudes in a unitary form by means of the theory of distributions.

Engineering Fluid Mechanics

Author : William Graebel
ISBN : 1560327111
Genre : Technology & Engineering
File Size : 33. 80 MB
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Fluid mechanics is a core component of many undergraduate engineering courses. It is essential for both students and lecturers to have a comprehensive, highly illustrated textbook, full of exercises, problems and practical applications to guide them through their study and teaching. Engineering Fluid Mechanics By William P. Grabel is that book The ISE version of this comprehensive text is especially priced for the student market and is an essential textbook for undergraduates (particularly those on mechanical and civil engineering courses) designed to emphasis the physical aspects of fluid mechanics and to develop the analytical skills and attitudes of the engineering student. Example problems follow most of the theory to ensure that students easily grasp the calculations, step by step processes outline the procedure used, so as to improve the students' problem solving skills. An Appendix is included to present some of the more general considerations involved in the design process. The author also links fluid mechanics to other core engineering courses an undergraduate must take (heat transfer, thermodynamics, mechanics of materials, statistics and dynamics) wherever possible, to build on previously learned knowledge.

Fracture Processes Of Concrete

Author : Jan G.M. van Mier
ISBN : 0849391237
Genre : Technology & Engineering
File Size : 27. 16 MB
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Despite tremendous advances made in fracture mechanics of concrete in recent years, very little information has been available on the nature of fracture processes and on reliable test methods for determining parameters for the different models. Moreover, most texts on this topic discuss numerical modeling but fail to consider experimentation. This book fills these gaps and synthesizes progress in the field in a simple, straightforward manner geared to practical applications.

Mechanical Engineering Design Education

Author :
ISBN : UOM:39015047823821
Genre : Engineering design
File Size : 52. 46 MB
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