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Mathematical models of waves linked consistently to physical effects
Emphasis is on the nonclassical models of wave motion
Step-by-step approach from simple to complex
Includes supplementary material: sn.pub/extras
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Table of contents (8 chapters)
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Front Matter
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Back Matter
About this book
This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua.
With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.
Reviews
“This book contains a description of basic ideas on wave motion in elastic media starting from a simple to a more complex stage. … This book will be useful to researchers in physical and engineering sciences interested in wave mechanics. The book presents the material from modelling to the construction of solutions in a variety of situations.” (Fiazud Din Zaman, zbMATH, Vol. 1325.74001, 2016)
“The book covers the most important topics and equations of the field, sometimes briefly and sometimes at length, with supporting references. It should be useful as a reference for scholars and graduate students and also might serve as a textbook for special courses. … Figures are generally of high quality, with many reproduced from prior journal publications.” (John D. Clayton, Mathematical Reviews, December, 2015)
Authors and Affiliations
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Centre for Nonlinear Studies (CENS), Tallinn University of Technology Institute of Cybernetics, Tallinn, Estonia
Jüri Engelbrecht
About the author
Bibliographic Information
Book Title: Questions About Elastic Waves
Authors: Jüri Engelbrecht
DOI: https://doi.org/10.1007/978-3-319-14791-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-14790-1Published: 25 March 2015
Softcover ISBN: 978-3-319-36699-9Published: 06 October 2016
eBook ISBN: 978-3-319-14791-8Published: 05 March 2015
Edition Number: 1
Number of Pages: XIV, 196
Number of Illustrations: 64 b/w illustrations, 10 illustrations in colour
Topics: Applications of Mathematics, Numerical and Computational Physics, Simulation, Partial Differential Equations, Mathematical Modeling and Industrial Mathematics, Computational Mathematics and Numerical Analysis