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E-grāmata: Questions About Elastic Waves

  • Formāts: PDF+DRM
  • Izdošanas datums: 05-Mar-2015
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319147918
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Questions About Elastic WavesPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 05-Mar-2015
  • Izdevniecība: Springer International Publishing AG
  • Valoda: eng
  • ISBN-13: 9783319147918
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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.

1 Introduction What is all that about - 2 What is wave motion.- 3 How to model waves? .- 4 What are internal variables? Arkadi Berezovski answers .- 5 What are evolution equations? . 6 What physical effects are involved? - 7 What physical mechanisms govern waves in non-conservative systems? - 8 What is complexity of waves? - References .- Index

Recenzijas

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)

1 Introduction: What is all that about?
1(8)
2 What is wave motion?
9(10)
2.1 What is a wave?
9(1)
2.2 What is a wave equation?
10(2)
2.3 What is needed for wave motion?
12(2)
2.4 How to measure waves?
14(3)
2.5 Why does the wave equation need to be modified?
17(2)
3 How to model waves?
19(24)
3.1 What must be known before modelling?
19(2)
3.2 What are the general principles for modelling?
21(3)
3.3 How to model waves in homogeneous materials?
24(3)
3.4 How to modify wave equations for homogeneous solids?
27(3)
3.5 How to model waves in heterogeneous materials?
30(13)
4 What are internal variables? A. Berezovski answers
43(28)
4.1 What are internal structures in terms of internal variables?
43(2)
4.2 How to use internal variables in continuum mechanics?
45(10)
4.3 How to model elastic waves using the concept of internal variables?
55(6)
4.4 How to model thermoelastic waves using the concept of internal variables?
61(5)
4.5 How to model the effects of microdeformation and microtemperature simultaneously?
66(5)
5 What are evolution equations?
71(20)
5.1 What is the difference between wave equations and evolution equations?
71(2)
5.2 How to derive evolution equations?
73(7)
5.3 What are examples of evolution equations?
80(11)
6 What physical effects are involved?
91(60)
6.1 What kind of questions should be asked?
91(1)
6.2 Are there analytic solutions to wave or evolution equations?
92(8)
6.3 What is the hierarchy of waves?
100(7)
6.4 What are dispersive effects in wave motion?
107(7)
6.5 How does dispersion affect wave profiles?
114(9)
6.6 What is the result of dispersive and nonlinear effects in wave motion?
123(12)
6.7 What are special features in terms of emergence and interaction of solitons?
135(16)
7 What physical mechanisms govern waves in non-conservative systems?
151(24)
7.1 What kind of models describe non-conservative systems?
151(4)
7.2 What happens with solitons in non-conservative systems?
155(9)
7.3 Are nerve pulses solitary waves?
164(8)
7.4 What is the influence of thermal effects?
172(3)
8 What is complexity of waves?
175(10)
8.1 Why do we need the concept of complexity?
175(5)
8.2 What are further questions to be asked?
180(2)
8.3 What could be noted finally?
182(3)
References 185(10)
Index 195
Jüri Engelbrecht, Prof, DSc, Dr h c is the Head of Centre for Nonlinear Studies (an Estonian Centre for Excellence in Research). His research interest is nonlinear wave motion, mathematical physics and complexity. He is author of several monographs on nonlinear waves (published by Pitman, Longman, Kluwer, World Scientific, Springer), has served Euromech Council and IUTAM Bureau for many years, has been awarded with the Estonian Science Awards (two times) and the Humboldt Research Award, has been the President of the Estonian Academy of Sciences (1994-2004) and the President of ALLEA (2006-2011).
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
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