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E-raamat: Linear and Nonlinear Waves in Microstructured Solids: Homogenization and Asymptotic Approaches [Taylor & Francis e-raamat]

(Prydniprovska State Academy, Ukraine), (Lodz University, Poland), (RWTH Aachen, Germany)
  • Formaat: 232 pages, 112 Line drawings, black and white; 1 Halftones, black and white; 113 Illustrations, black and white
  • Ilmumisaeg: 23-Apr-2021
  • Kirjastus: CRC Press
  • ISBN-13: 9781003146162
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  • Taylor & Francis e-raamat
  • Hind: 193,88 €*
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Linear and Nonlinear Waves in Microstructured Solids: Homogenization and Asymptotic ApproachesSuurem pilt
  • Formaat: 232 pages, 112 Line drawings, black and white; 1 Halftones, black and white; 113 Illustrations, black and white
  • Ilmumisaeg: 23-Apr-2021
  • Kirjastus: CRC Press
  • ISBN-13: 9781003146162
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003146162
This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials.

Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The books cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices.

The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.
Preface xi
Permissions xvii
Chapter 1 Models and Methods to Study Elastic Waves 1(22)
1.1 Brief literature overview
1(6)
1.2 Small "tutorial"
7(12)
1.3 Analytical and numerical solutions in the theory of composite materials
19(1)
1.4 Some general results of the homogenization theory
20(3)
Chapter 2 Waves in Layered Composites: Linear Problems 23(16)
2.1 One-dimensional (1D) dynamic problem
23(1)
2.2 Higher-order homogenization method
24(5)
2.3 The Bloch-Floquet method and exact dispersion equation
29(5)
2.4 Numerical results
34(5)
Chapter 3 Waves in Fiber Composites: Linear Problems 39(24)
3.1 Two-dimensional (2D) dynamic problem
39(1)
3.2 Method of higher-order homogenization
40(6)
3.3 The Bloch-Floquet method and solution based on Fourier series
46(2)
3.4 Numerical results
48(2)
3.5 Shear waves dispersion in cylindrically structured cancellous viscoelastic bones
50(13)
Chapter 4 Longitudinal Waves in Layered Composites 63(18)
4.1 Fundamental relations of nonlinear theory of elasticity
63(2)
4.2 Input boundary value problems
65(1)
4.3 Macroscopic wave equation
66(6)
4.4 Analytical solution for stationary waves
72(4)
4.5 Analysis of solution and numerical results
76(5)
Chapter 5 Antiplane Shear Waves in Fiber Composites with Structural Nonlinearity 81(20)
5.1 Boundary value problem for imperfect bonding conditions
81(3)
5.2 Macroscopic wave equation
84(8)
5.3 Analytical solution for stationary waves
92(4)
5.4 Analysis of solution and numerical result
96(5)
Chapter 6 Formation of Localized Nonlinear Waves in Layered Composites 101(10)
6.1 Initial model and pseudo-spectral method
101(2)
6.2 The Fourier-Pade approximation
103(3)
6.3 Numerical modeling of non-stationary nonlinear waves
106(5)
Chapter 7 Vibration Localization in 1D Linear and Nonlinear Lattices 111(18)
7.1 Introduction
111(1)
7.2 Monatomic lattice with a perturbed mass
112(2)
7.3 Monatomic lattice with a perturbed mass - the continuous approximation
114(1)
7.4 Diatomic lattice
115(2)
7.5 Diatomic lattice with a perturbed mass
117(4)
7.6 Diatomic lattice with a perturbed mass - the continuous approximation
121(2)
7.7 Vibrations of a lattice on the support with a defect
123(1)
7.8 Nonlinear vibrations of a lattice
123(3)
7.9 Effect of nonlinearity on pass bands and stop bands
126(3)
Chapter 8 Spatial Localization of Linear Elastic Waves in Composite Materials with Defects 129(12)
8.1 Introduction
129(1)
8.2 Wave localization in a layered composite material: transfer-matrix method
130(6)
8.3 Wave localization in a layered composite material: lattice approach
136(1)
8.4 Antiplane shear waves in a FIBER composite
137(4)
Chapter 9 Nonlinear Vibrations of Viscoelastic Heterogeneous Solids of Finite Size 141(12)
9.1 Introduction
141(1)
9.2 Input problem and homogenized dynamical equation
142(3)
9.3 Discretization procedure
145(2)
9.4 Method of multiple time scales
147(2)
9.5 Numerical simulation of the modes coupling
149(2)
9.6 Concluding remarks
151(2)
Chapter 10 Nonlocal, Gradient and Local Models of Elastic Media: 1D Case 153(40)
10.1 Introduction
153(2)
10.2 A chain of elastically coupled masses
155(2)
10.3 Classical continuous approximations
157(2)
10.4 "Splashes"
159(2)
10.5 Envelope continualization
161(1)
10.6 Intermediate continuous models
162(2)
10.7 Using of Pade approximations
164(3)
10.8 Normal modes expansion
167(2)
10.9 Theories of elasticity with couple-stresses
169(1)
10.10 Correspondence between functions of discrete arguments and approximating analytical functions
170(1)
10.11 The kernels of integro-differential equations of the discrete and continuous systems
171(4)
10.12 Dispersive wave propagation
175(1)
10.13 Green's function
176(1)
10.14 Double- and triple-dispersive equations
176(3)
10.15 Toda lattice
179(2)
10.16 Discrete kinks
181(2)
10.17 Continualization of β-FPU lattice
183(3)
10.18 Acoustic branch of α-FPU lattice
186(1)
10.19 Anti-continuum limit
186(1)
10.20 2D lattice
186(3)
10.21 Molecular dynamics simulations and continualization: handshake
189(1)
10.22 Continualization and discretization
190(1)
10.23 Possible generalization and applications and open problems
190(3)
Chapter 11 Regular and Chaotic Dynamics Based on Continualization and Discretization 193(14)
11.1 Introduction
193(2)
11.2 Integrable ODE
195(1)
11.3 Continualization with Pade approximants
196(1)
11.4 Numerical results
197(10)
References 207(22)
Index 229
Igor Andrianov is Professor with 25 years of experience in Mathematics, Applied Mechanics and Mechanics of Solids. Researcher with 41 years of experience in Applied Mathematics and Mechanics of Solids. Supervisor of 18 Ph.D. students. Research interests: Asymptotic Approaches, Nonlinear Dynamics, Composite Materials, Theory of Plates and Shells.

Jan Awrejcewicz is a Head of the Department of Automation, Biomechanics and Mechatronics at Lodz University of Technology, Head of Ph.D. School on 'Mechanics' (since 1996) and of graduate/postgraduate programs on Mechatronics (since 2006). He is also recipient of Doctor Honoris Causa (Honorary Professor) of Academy of Arts and Technology (Poland, Bielsko-Biala, 2014) and of Czestochowa University of Technology (Poland, Czestochowa, 2014), Kielce University of Technology (2019), National Technical University "Kharkiv Polytechnic Institute" (2019), and Gdask University of Technology (2019). His papers and research cover various disciplines of mechanics, material science, biomechanics, applied mathematics, automation, physics and computer oriented sciences, with main focus on nonlinear processes.

Vladyslav V Danishevskyy is Professor at Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine. His research area includes mechanical and physical properties of composite materials, metamaterials and heterogeneous structures; non-linear dynamics; waves in heterogeneous media; asymptotic methods.
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