Table of Contents -- Title -- Copyright -- Preface -- 1 Introduction to Non-local Elasticity -- 1.1. Why the non-local elasticity method for nanostructures? -- 1.2. General modeling of nanostructures -- 1.3. Overview of popular nanostructures -- 1.4. Popular approaches for understanding nanostructures -- 1.5. Experimental methods -- 1.6. Molecular dynamics simulations -- 1.7. Continuum mechanics approach -- 1.8. Failure of classical continuum mechanics -- 1.9. Size effects in properties of small-scale structures -- 1.10. Evolution of size-dependent continuum theories -- 1.11. Concept of non-local elasticity -- 1.12. Mathematical formulation of non-local elasticity -- 1.13. Non-local parameter -- 1.14. Non-local elasticity theory versus molecular dynamics -- 2 Non-local Elastic Rod Theory -- 2.1. Background -- 2.2. Governing equation of motion of the nanorod -- 2.3. Results and discussions -- 3 Non-local Elastic Beam Theories -- 3.1. Background -- 3.2. Non-local nanobeam model -- 3.3. Torsional vibration of nanobeam -- 3.4. Comparison of the non-local beam theories -- 4 Non-local Elastic Plate Theories -- 4.1. Non-local plate for graphene sheets -- 4.2. Non-local plate constitutive relations -- 4.3. Free vibration of single-layer graphene sheets -- 4.4. Axially stressed nanoplate non-local theory -- 4.5. In-plane vibration -- 4.6. Buckling of graphene sheets -- 4.7. Summary -- 5 One-Dimensional Double-Nanostructure-Systems -- 5.1. Background -- 5.2. Revisiting non-local rod theory -- 5.3. Axial vibration of double-rod system -- 5.4. Summary -- 5.5. Transverse vibration of double-nanobeam-systems -- 5.6. Vibration of non-local double-nanobeam-system -- 5.7. Boundary conditions in non-local double-nanobeam-system -- 5.8. Exact solutions of the frequency equations -- 5.9. Discussions -- 5.10. Summary.

5.11. Axial instability of double-nanobeam-systems -- 5.12. Non-local boundary conditions of NDNBS -- 5.13. Buckling states of double-nanobeam-system -- 5.14. Coupled carbon nanotube systems -- 5.15. Results and discussions on the scale-dependent buckling phenomenon -- 5.15. Summary -- 6 Double-Nanoplate-Systems -- 6.1. Double-nanoplate-system -- 6.2. Vibration of double-nanoplate-system -- 6.3. Equations of motion for non-local double-nanoplate-system -- 6.4. Boundary conditions in non-local double-nanoplate-system -- 6.5. Exact solutions of the frequency equations -- 6.6. Buckling behavior of double-nanoplate-systems -- 6.7. Results and discussion -- 6.8. Summary -- 7 Multiple Nanostructure Systems -- 7.1. Longitudinal vibration of a multi-nanorod system -- 7.2. Transversal vibration and stability of a multiple-nanobeam system -- 7.3. Transversal vibration and buckling of the multi-nanoplate system -- 7.4. Summary -- 8 Finite Element Method for Dynamics of Non-local Systems -- 8.1. Introduction -- 8.2. Finite element modeling of non-local dynamic systems -- 8.3. Modal analysis of non-local dynamical systems -- 8.4. Dynamics of damped non-local systems -- 8.5. Numerical examples -- 8.6. Summary -- 9 Dynamic Finite Element Analysis of Non-local Rods: Axial Vibration -- 9.1. Introduction -- 9.2. Axial vibration of damped non-local rods -- 9.3. Dynamic finite element matrix -- 9.4. Numerical results and discussions -- 9.5. Summary -- 10 Non-local Nanosensor Based on Vibrating Graphene Sheets -- 10.1. Introduction -- 10.2. Free vibration of graphene sheets -- 10.3. Natural vibration of SLGS with biofragment -- 10.4. Sensor equations and sensitivity analysis -- 10.5. Analysis of numerical results -- 10.6. Summary -- 11 Introduction to Molecular Dynamics for Small-scale Structures -- 11.1. Background.

11.2. Overview of the molecular dynamics simulation method -- 11.3. Acknowledgement -- Bibliography -- Index -- End User License Agreement.