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E-raamat: Wave Propagation in Nanostructures: Nonlocal Continuum Mechanics Formulations

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  • Formaat: PDF+DRM
  • Sari: NanoScience and Technology
  • Ilmumisaeg: 10-Sep-2013
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319010328
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Wave Propagation in Nanostructures: Nonlocal Continuum Mechanics FormulationsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: NanoScience and Technology
  • Ilmumisaeg: 10-Sep-2013
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319010328
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This book covers nonlocal continuum mechanics methods applied to nanostructures. It takes readers from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes and nanotubes with magnetic field and surface effects.

Wave Propagation in Nanostructures describes the fundamental and advanced concepts of waves propagating in structures that have dimensions of the order of nanometers. The book is fundamentally based on non-local elasticity theory, which includes scale effects in the continuum model. The book predominantly addresses wave behavior in carbon nanotubes and Graphene structures, although the methods of analysis provided in this text are equally applicable to other nanostructures.The book takes the reader from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes, coupled nanotubes, and nanotubes with magnetic field and surface effects. The first few chapters cover the basics of wave propagation, different modeling schemes for nanostructures and introduce non-local elasticity theories, which form the building blocks for understanding the material provided in later chapters. A number of interesting examples are provided to illustrate the important features of wave behavior in these low dimensional structures.
1 Introduction to Nanostructures 1(18)
1.1 Historical Perspectives
3(1)
1.2 Hybridization of Carbon Nanostructures
4(9)
1.2.1 Nanotubes
7(1)
1.2.2 Structure of Carbon Nanotubes
8(2)
1.2.3 Properties of Carbon Nanotubes
10(3)
1.3 Need for Wave Propagation Analysis in Nanostructures
13(2)
1.4 Outline and Scope of the Book
15(1)
1.5 Summary
15(1)
References
16(3)
2 Introductory Concepts of Wave Propagation Analysis in Structures 19(12)
2.1 Introduction to Wave Propagation
20(1)
2.2 Spectral Analysis
21(1)
2.3 Wave Propagation Terminologies
21(2)
2.4 Spectrum and Dispersion Relations
23(6)
2.4.1 Second-Order PDE
24(2)
2.4.2 Fourth Order PDE
26(3)
2.5 Summary
29(1)
References
29(2)
3 Various Modeling Techniques for Nanostructures 31(28)
3.1 First-Principles Methods (Atomistic Simulations)
32(4)
3.1.1 Density Functional Theory
34(1)
3.1.2 Ab initio Pseudopotentials
35(1)
3.2 Molecular Dynamics
36(2)
3.2.1 Potential Functions
37(1)
3.3 Molecular Dynamics for Wave Propagation in CNT
38(3)
3.4 Molecular Dynamics Simulation for Wave Propagation in Graphene
41(1)
3.5 Monte Carlo Methods
42(1)
3.5.1 The Metropolis Algorithms
42(1)
3.5.2 Kinetic Monte Carlo Simulations
42(1)
3.6 Continuum Modeling
43(3)
3.7 Methods of Multiscale Modeling
46(1)
3.8 Overview on Length Scales
47(2)
3.9 Nonlocal Theories in Continuum Mechanics
49(6)
3.9.1 Strain-Gradient Elasticity
50(1)
3.9.2 Models with Mixed Spatial-Temporal Derivatives
51(1)
3.9.3 Integral-Type Nonlocal Elasticity
52(3)
3.10 Summary
55(1)
References
56(3)
4 Theory of Nonlocal Elasticity 59(12)
4.1 Need for Nonlocal Elasticity for Nanostructures
59(1)
4.2 Introduction to Nonlocal Elasticity
60(3)
4.3 Types of Nonlocality
63(4)
4.3.1 Properties of the Kernels
65(2)
4.4 Nonlocal Constitutive Relations
67(2)
4.4.1 Nonlocal Constitutive Relation for 1D Problems
67(1)
4.4.2 Nonlocal Constitutive Relations for 2D Problems
67(1)
4.4.3 Nonlocal Constitutive Relations for 3D Problems
68(1)
4.4.4 Nonlocal Constitutive Relations for Cylindrical Shell Problems
68(1)
4.5 Summary
69(1)
References
69(2)
5 Material Property and Nonlocal Scale Parameter Estimation for Carbon Nanotubes 71(50)
5.1 Length-Dependent In-plane Stiffness of Carbon Nanotubes
72(7)
5.1.1 Governing Equations for SWCNT
72(2)
5.1.2 Solution of Governing Equations
74(1)
5.1.3 In-plane Stiffness Ratio Estimation
75(2)
5.1.4 Numerical Results and Discussion
77(2)
5.2 Material Property Estimation: A Comparison with Nonlocal Rod Model
79(5)
5.2.1 Numerical Results and Discussions
81(3)
5.3 Prediction of Nonlocal Scale Parameter: A Molecular Structural Mechanics and Nonlocal Elasticity Model
84(33)
5.3.1 Armchair SWCNTs
86(8)
5.3.2 Zigzag SWCNTs
94(7)
5.3.3 Chiral SWCNTs
101(16)
5.4 Summary
117(1)
References
118(3)
6 Wave Propagation in 1D-Nanostructures: Nanorods 121(44)
6.1 Axial Wave Propagation in NLSGM Nanorod
122(6)
6.1.1 Governing Equations for NLSGM Nanorods
122(2)
6.1.2 Wave Characteristics in NLSGM Nanorods
124(4)
6.2 Axial Wave Propagation NLStGM Nanorods
128(11)
6.2.1 Governing Equations for Second and Fourth-Order NLStGM Nanorods
129(2)
6.2.2 Uniqueness and Stability of Second-Order NLStGM Nanorods
131(2)
6.2.3 Wave Characteristics of Second-Order NLStGM Nanorods
133(1)
6.2.4 Wave Characteristics of Fourth-Order NLStGM Nanorods
134(1)
6.2.5 Numerical Results and Discussion
135(4)
6.3 Axial Wave Propagation in Nanorods with Lateral Inertia
139(8)
6.3.1 NLSGM-Based Governing Equations for Nanorods with Lateral Inertia
139(3)
6.3.2 Wave Characteristics of Nanorods with Lateral Inertia
142(5)
6.4 Torsional Wave Propagation in NLSGM Nanoshafts
147(5)
6.4.1 Numerical Results and Discussion
150(2)
6.5 Spectral Finite Element Formulation
152(9)
6.5.1 Frequency Dependent Shape Functions
154(2)
6.5.2 Dynamic Stiffness Matrix
156(1)
6.5.3 Numerical Results and Discussion
157(4)
6.6 Summary
161(1)
References
162(3)
7 Wave Propagation in 1D-Nanostructures: Nanobeams 165(50)
7.1 NLSM for Euler-Bernoulli Nanobeams
165(5)
7.1.1 Wave Dispersion Characteristics
167(3)
7.2 NLSGM for Timoshenko Nanobeam
170(7)
7.2.1 Wave Dispersion Characteristics
172(5)
7.3 Rotating Nanotubes: An Introduction
177(10)
7.3.1 Governing Equations for Rotating Nanotube
178(3)
7.3.2 Wave Dispersion Analysis
181(6)
7.4 Fluid Carrying SWCNTs
187(7)
7.4.1 Nonlocal Governing Equations of Motion
187(7)
7.5 Magnetic Field Effects on SWCNT
194(7)
7.5.1 Maxwell's Relations
195(1)
7.5.2 Nonlocal Governing Equations of Motion Including Magnetic Field Effects
196(5)
7.6 Surface Effects on Flexural Wave Propagation in Nanobeams
201(10)
7.6.1 Governing Equation of Motion Including Surface Residual Stress
204(2)
7.6.2 Wave Propagation Analysis
206(5)
7.7 Summary
211(1)
References
212(3)
8 Wave Propagation in Multi-Walled Carbon Nanotubes 215(24)
8.1 van der Waals Forces
217(1)
8.2 Governing Equations for NLSGM MWCNT
218(18)
8.2.1 Generalized Wave Dispersion Analysis in MWCNTs
219(3)
8.2.2 Wave Dispersion in SWCNTs
222(3)
8.2.3 Wave Dispersion in DWCNTs
225(6)
8.2.4 Wave Dispersion in TWCNTs
231(5)
8.3 Summary
236(1)
References
236(3)
9 Wave Propagation in Coupled 1D-Nanosystems 239(30)
9.1 Governing Equations of Motion for Double Nanorod System
240(8)
9.1.1 Wave Propagation Analysis in DNRS
242(6)
9.2 Coupled Nano-Beam System
248(18)
9.2.1 Wave Propagation in Double Euler-Bernoulli Nanobeam System
250(4)
9.2.2 Wave Propagation in Coupled Timoshenko Nanobeam System
254(12)
9.3 Summary
266(1)
References
266(3)
10 Wave Propagation in 2D-Nanostructures 269(54)
10.1 Flexural Wave Propagation in Monolayer Graphene Sheets
271(9)
10.1.1 Governing Equations for Graphene Structures
271(2)
10.1.2 Wave Dispersion Analysis
273(7)
10.2 Modeling of Graphene Layer on Silicon Substrate
280(4)
10.2.1 Potential Energy, Equilibrium and Force Constants
281(3)
10.3 Wave Propagation in Single Graphene Layer on Silicon Substrate
284(11)
10.3.1 Wave Dispersion Analysis
287(8)
10.4 Temperature Effects on Wave Propagation in Nanoplates
295(10)
10.4.1 Governing Equations of Motion Including Thermal Effects
297(3)
10.4.2 Thermo-Elastic Flexural Wave Dispersion Analysis
300(5)
10.5 Surface Effects on Wave Propagation in Nanoplates
305(2)
10.6 Mathematical Modeling of Nanoplate with the Surface Effects
307(10)
10.6.1 Dispersion Characteristics
309(8)
10.7 Summary
317(2)
References
319(4)
11 Wave Propagation in Nanoshells 323(32)
11.1 Wave Propagation in Circular Cylindrical Nanoshells
324(12)
11.1.1 Wave Dispersion Analysis
327(9)
11.2 Fluid-Filled Nanoshells
336(5)
11.2.1 Wave Dispersion Analysis
337(4)
11.3 Wave Propagation in Higher Order Nanoshells
341(11)
11.3.1 Governing Nanoshell Equations Including Shear and Contraction Effects
342(3)
11.3.2 Wave Dispersion Analysis
345(7)
11.4 Summary
352(1)
References
353(2)
Index 355
Srinivasan Gopalakrishnan

Indian Institute of Science

Bangalore

India









S. Narendar

Defence Research and Development Laboratory

Kanchanbagh, Hyderabad

India
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