Questions About Elastic Waves [electronic resource] /
Engelbrecht, Jüri.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
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.
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.
Applied mathematics.
Engineering mathematics.
Physics.
Partial differential equations.
Mathematical models.
Computer mathematics.
Applications of Mathematics.
Numerical and Computational Physics, Simulation.
Partial Differential Equations.
Mathematical Modeling and Industrial Mathematics.
Computational Mathematics and Numerical Analysis.