Non-local structural mechanics:
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| Main Authors: | , , , |
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| Format: | Book |
| Language: | English |
| Published: |
London
ISTE
2016
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| Series: | Mechanical engineering and solid mechanics series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xiv, 354 Seiten Illustrationen |
| ISBN: | 9781848215221 1848215223 |
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| 245 | 1 | 0 | |a Non-local structural mechanics |c Danilo Karličić, Tony Murmu, Sondipon Adhikari, Michael McCarthy |
| 264 | 1 | |a London |b ISTE |c 2016 | |
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| 490 | 0 | |a Mechanical engineering and solid mechanics series | |
| 650 | 4 | |a Nanostructures | |
| 650 | 4 | |a Structural analysis (Engineering) | |
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Record in the Search Index
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| adam_text | Contents
Preface.................................................................... xi
Chapter 1. Introduction to Non-Local Elasticity.......................... I
l. I. 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
vi Non-local Structural Mechanics
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-iocai 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-ffee (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
Contents vii
5.7. Boundary conditions in non-local double-nanobeam-system....... Ill
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 double-
nanobeam-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: (wl-w2 ^ 0) ................... 128
5.13.2. In-phase buckling state: (wl - w2 = 0) .................. 129
5.13.3. One nanobeam is fixed: (w2 = 0) 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 double-
nanoplate-system .................................................... 139
6.4. Boundary conditions in non-local double-
nanoplate-system..................................................... 142
6.5. Exact solutions of the frequency equations...................... 144
6.5.1. Both nanoplates of NDNPS are vibrating
out-of-phase: (wl — w2 ^ 0) 144
6.5.2. Both nanoplates of NDNPS are vibrating
in-phase: (wl - w2 = 0) ......................................... 146
6.5.3. One nanoplate of NDNPS is stationary:
(w2(x,y, t) = 0) ................................................ 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
viii Non-local Structural Mechanics
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 multiple-
nanobeam 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 multi-
nanoplate 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
Contents ix
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
x Non-local Structural Mechantes
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
Serving as a review on non-local mechanics, this book provides
an introduction to the 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.
Presenting the latest developments in the modeling and analysis
of popular nanostructures, this book is relevant to aerospace,
mechanical and civil engineering disciplines and various
subdisciplines within them.
The focus being on the mathematical and computational aspects,
readers who would benefit most include undergraduate and
graduate students with projects or doctoral research in the field of
small-scale structures. Researchers, professors and practicing
engineers working in the field of small-scale structures will also
find this book useful.
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.
www.iste.co.uk
Wiley
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| spelling | Karlicic, Danilo Verfasser aut Non-local structural mechanics Danilo Karličić, Tony Murmu, Sondipon Adhikari, Michael McCarthy London ISTE 2016 xiv, 354 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mechanical engineering and solid mechanics series Nanostructures Structural analysis (Engineering) Nanostructures fast Structural analysis (Engineering) fast Nanostrukturiertes Material (DE-588)4342626-8 gnd rswk-swf Nanostrukturiertes Material (DE-588)4342626-8 s DE-604 Murmu, Tony Verfasser aut Adhikari, Sondipon Verfasser aut McCarthy, Michael Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028715656&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028715656&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Karlicic, Danilo Murmu, Tony Adhikari, Sondipon McCarthy, Michael Non-local structural mechanics Nanostructures Structural analysis (Engineering) Nanostructures fast Structural analysis (Engineering) fast Nanostrukturiertes Material (DE-588)4342626-8 gnd |
| subject_GND | (DE-588)4342626-8 |
| title | Non-local structural mechanics |
| title_auth | Non-local structural mechanics |
| title_exact_search | Non-local structural mechanics |
| title_full | Non-local structural mechanics Danilo Karličić, Tony Murmu, Sondipon Adhikari, Michael McCarthy |
| title_fullStr | Non-local structural mechanics Danilo Karličić, Tony Murmu, Sondipon Adhikari, Michael McCarthy |
| title_full_unstemmed | Non-local structural mechanics Danilo Karličić, Tony Murmu, Sondipon Adhikari, Michael McCarthy |
| title_short | Non-local structural mechanics |
| title_sort | non local structural mechanics |
| topic | Nanostructures Structural analysis (Engineering) Nanostructures fast Structural analysis (Engineering) fast Nanostrukturiertes Material (DE-588)4342626-8 gnd |
| topic_facet | Nanostructures Structural analysis (Engineering) Nanostrukturiertes Material |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028715656&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028715656&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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