Danilo Karlicic, Tony Murmu, Sondipon Adhikari

Non-Local Structural Mechanics

Collab.: Michael McCarthy

• Gebundenes Buch

Produktbeschreibung

This book gives science and engineering graduates and researchers a detailed understanding of the methods of

non-local analysis necessary for nanoscale structures.

The conventional local elasticity theory has underpinned the majority of applications of continuum mechanics in applied science and engineering since its inception in the early 19th Century. The application of the local elasticity theory in the context of nanoscale objects has been repeatedly questioned in various research articles over the past decade. Non-local elasticity theory, pioneered from the 1970s, is a scale-dependent theory and is considered to be more suitable for analyzing nanoscale objects such as carbon nanotubes and graphene sheets.

This book is the first comprehensive text to cover non-local elasticity theory for static, dynamic and stability analysis of wide-ranging nanostructures. The authors draw on their considerable research experience in this field. The text will be written from a mechanics standpoint, with numerous worked examples relevant across a wide range of nanomechanical systems.

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Serving as a review on non-local mechanics, this book provides an introduction to non-local elasticity theory for static, dynamic and stability analysis in a wide range of nanostructures. The authors draw on their own research experience to present fundamental and complex theories that are relevant across a wide range of nanomechanical systems, from the fundamentals of non-local mechanics to the latest research applications.

Produktdetails

• ISTE
• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 374
• Erscheinungstermin: 10. November 2014
• Englisch
• Abmessung: 240mm x 161mm x 25mm
• Gewicht: 727g
• ISBN-13: 9781848215221
• ISBN-10: 1848215223
• Artikelnr.: 36726236

Autorenporträt

Danilo Karlicic is a Lecturer at the Mechanical Engineering Faculty at the University of Nis, Serbia. Tony Murmu is a Lecturer of Mechanical Engineering at the University of the West of Scotland, United Kingdom. Sondipon Adhikari is the Chair of Aerospace Engineering at the College of Engineering at Swansea University, United Kingdom. Michael McCarthy is Professor of Aeronautical Engineering at the University of Limerick, Ireland.

Inhaltsangabe

Preface xi Chapter 1. Introduction to Non
Local Elasticity 1 1.1. Why the non
local elasticity method for nanostructures? 1 1.2. General modeling of nanostructures 3 1.3. Overview of popular nanostructures 4 1.4. Popular approaches for understanding nanostructures 8 1.5. Experimental methods 9 1.6. Molecular dynamics simulations 9 1.7. Continuum mechanics approach 9 1.8. Failure of classical continuum mechanics 10 1.9. Size effects in properties of small
scale structures 11 1.10. Evolution of size
dependent continuum theories 12 1.11. Concept of non
local elasticity 14 1.12. Mathematical formulation of non
local elasticity 15 1.12.1. Integral form 15 1.12.2. Non
local modulus 17 1.12.3. Differential form equation of non
local elasticity 17 1.13. Non
local parameter 18 1.14. Non
local elasticity theory versus molecular dynamics 19 Chapter 2. Non
local Elastic Rod Theory 21 2.1.Background 21 2.2. Governing equation of motion of the nanorod 24 2.3.Results and discussions 29 Chapter 3. Non
local Elastic Beam Theories 33 3.1. Background 33 3.2. Non
local nanobeam model 36 3.2.1. Non
local Euler
Bernoulli beam theory 36 3.2.2. Non
local Timoshenko beam theory 43 3.2.3. Non
local Reddy beam theory 51 3.3. Torsional vibration of nanobeam 60 3.4. Comparison of the non
local beam theories 64 Chapter 4. Non
local Elastic Plate Theories 69 4.1. Non
local plate for graphene sheets 69 4.2. Non
local plate constitutive relations 69 4.3. Free vibration of single
layer graphene sheets 72 4.3.1. Transverse
free vibration 73 4.3.2. Graphene sheets embedded in an elastic medium 75 4.4. Axially stressed nanoplate non
local theory 78 4.5. In
plane vibration 79 4.6. Buckling of graphene sheets 80 4.6.1. Uniaxial buckling 81 4.6.2. Graphene sheets embedded in an elastic medium 82 4.7. Summary 84 Chapter 5. One
Dimensional Double
Nanostructure
Systems 87 5.1. Background 87 5.2. Revisiting non
local rod theory 90 5.2.1. Equations of motion of double
nanorod
system 91 5.2.2. Solution methodology 94 5.2.3. Clamped
clamped boundary condition 95 5.2.4. Clamped
free (cantilever) boundary condition 96 5.2.5. Longitudinal vibration of auxiliary (secondary) nanorod 98 5.3. Axial vibration of double
rod system 99 5.3.1. Effect of the non
local parameter in the clamped
type DNRS 100 5.3.2. Coupling spring stiffness in DNRS 102 5.3.3. Higher modes of vibration in DNRS 102 5.3.4. Effect of non
local parameter, spring stiffness and higher modes in cantilever
type
DNRS 103 5.4. Summary 104 5.5. Transverse vibration of double
nanobeam
systems 104 5.5.1. Background 105 5.5.2. Non
local double
nanobeam
system 107 5.6. Vibration of non
local double
nanobeam
system 110 5.7. Boundary conditions in non
local double
nanobeam
system 111 5.8. Exact solutions of the frequency equations 113 5.9. Discussions 116 5.9.1. Effect of small scale on vibrating NDNBS 117 5.9.2. Effect of the stiffness of the coupling springs on NDNBS 120 5.9.3. Analysis of higher modes of NDNBS 120 5.10. Summary 121 5.11. Axial instability of double
nanobeam
systems 122 5.11.1. Background 123 5.11.2. Buckling equations of non
local doublenanobeam
systems 124 5.12. Non
local boundary conditions of NDNBS 126 5.13. Buckling states of double
nanobeam
system 128 5.13.1. Out
of
phase buckling load: (w1
w20) 128 5.13.2. In
phase buckling state: (w1
w2=0) 129 5.13.3. One nanobeam is fixed 130 5.14. Coupled carbon nanotube systems 130 5.15. Results and discussions on the scale
dependent buckling phenomenon 131 5.15. Summary 136 Chapter 6. Double
Nanoplate
Systems 137 6.1. Double
nanoplate
system 137 6.2. Vibration of double
nanoplate
system 139 6.3. Equations of motion for non
local doublenanoplate
system 139 6.4. Boundary conditions in non
local doublenanoplate
system 142 6.5. Exact solutions of the frequency equations 144 6.5.1. Both nanoplates of NDNPS are vibrating out
of
phase 144 6.5.2. Both nanoplates of NDNPS are vibrating in
phase 146 6.5.3. One nanoplate of NDNPS is stationary 147 6.5.4. Discussions 148 6.5.5. Non
local double
nanobeam
system versus non
local double
nanoplate
system 156 6.5.6. Summary 157 6.6. Buckling behavior of double
nanoplate
systems 158 6.6.1. Background 159 6.6.2. Uniaxially compressed double
nanoplate
system 160 6.6.3. Buckling states of double
nanoplate
system 163 6.7. Results and discussion 167 6.7.1. Coupled double
graphene
sheet
system 167 6.7.2. Effect of small scale on NDNPS undergoing compression 168 6.7.3. Effect of stiffness of coupling springs in NDNPS 170 6.7.4. Effect of aspect ratio on NDNPS 173 6.8. Summary 177 Chapter 7. Multiple Nanostructure Systems 179 7.1. Longitudinal vibration of a multi
nanorod system 180 7.1.1. The governing equations of motion 182 7.1.2. Exact solution 185 7.1.3. Asymptotic analysis 191 7.1.4. Numerical examples and discussions 192 7.2. Transversal vibration and stability of a multiplenanobeam system 197 7.2.1. The governing equations of motion 199 7.2.2. Exact solution 202 7.2.3. Asymptotic analysis 209 7.2.4. Numerical examples and discussions 210 7.3. Transversal vibration and buckling of the multinanoplate system 215 7.3.1. The governing equations of motion 217 7.3.2. Exact solutions 221 7.3.3 Asymptotic analysis 227 7.3.4. Numerical results and discussions 227 7.4. Summary 232 Chapter 8. Finite Element Method for Dynamics of Nonlocal Systems 235 8.1. Introduction 236 8.2. Finite element modeling of non
local dynamic systems 239 8.2.1. Axial vibration of nanorods 239 8.2.2. Bending vibration of nanobeams 241 8.2.3. Transverse vibration of nanoplates 243 8.3. Modal analysis of non
local dynamical systems 247 8.3.1. Conditions for classical normal modes 248 8.3.2. Non
local normal modes 250 8.3.3. Approximate non
local normal modes 251 8.4. Dynamics of damped non
local systems 254 8.5. Numerical examples 256 8.5.1. Axial vibration of a single
walled carbon nanotube 256 8.5.2. Bending vibration of a double
walled carbon nanotube 261 8.5.3. Transverse vibration of a single
layer graphene sheet 265 8.6. Summary 269 Chapter 9. Dynamic Finite Element Analysis of Nonlocal Rods: Axial Vibration 271 9.1. Introduction 272 9.2. Axial vibration of damped non
local rods 275 9.2.1. Equation of motion 275 9.2.2. Analysis of damped natural frequencies 277 9.2.3. Asymptotic analysis of natural frequencies 279 9.3. Dynamic finite element matrix 281 9.3.1. Classical finite element of non
local rods 281 9.3.2. Dynamic finite element for damped non
local rod 282 9.4. Numerical results and discussions 285 9.5. Summary 291 Chapter 10. Non
local Nanosensor Based on Vibrating Graphene Sheets 293 10.1. Introduction 294 10.2. Free vibration of graphene sheets 295 10.2.1. Vibration of SLGS without attached mass 297 10.3. Natural vibration of SLGS with biofragment 299 10.3.1. Attached masses are at the cantilever tip 301 10.3.2. Attached masses arranged in a line along the width 301 10.3.3. Attached masses arranged in a line along the length 302 10.3.4. Attached masses arranged with arbitrary angle 302 10.4. Sensor equations and sensitivity analysis 303 10.5. Analysis of numerical results 305 10.6. Summary 311 Chapter 11. Introduction to Molecular Dynamics for Small
scale Structures 313 11.1. Background 313 11.2. Overview of the molecular dynamics simulation method 314 11.3. Acknowledgement 325 Bibliography 327 Index 353