Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro-or nanostructures.This paper deals with the lateral-torsional buckling of elastic n...Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro-or nanostructures.This paper deals with the lateral-torsional buckling of elastic nonlocal small-scale beams.Eringen’s model is chosen for the nonlocal constitutive bendingcurvature relationship.The effect of prebuckling deformation is taken into consideration on the basis of the Kirchhoff-Clebsch theory.It is shown that the application of Eringen’s model produces small-length scale terms in the nonlocal elastic lateraltorsional buckling moment of a hinged-hinged strip beam.Clearly,the non-local parameter has the effect of reducing the critical lateral-torsional buckling moment.This tendency is consistent with the one observed for the in-plane stability analysis,for the lateral buckling of a hinged-hinged axially loaded column.The lateral buckling solution can be derived from a physically motivated variational principle.展开更多
In this paper,we study the flexural vibration behavior of single-walled carbon nanotubes(SWCNTs)for the assessment of Timoshenko beam models.Extensive molecular dynamics(MD)simulations based on second-generation reac...In this paper,we study the flexural vibration behavior of single-walled carbon nanotubes(SWCNTs)for the assessment of Timoshenko beam models.Extensive molecular dynamics(MD)simulations based on second-generation reactive empirical bond-order(REBO)potential and Timoshenko beam modeling are performed to determine the vibration frequencies for SWCNTs with various length-todiameter ratios,boundary conditions,chiral angles and initial strain.The effectiveness of the local and nonlocal Timoshenko beam models in the vibration analysis is assessed using the vibration frequencies of MD simulations as the benchmark.It is shown herein that the Timoshenko beam models with properly chosen parameters are applicable for the vibration analysis of SWCNTs.The simulation results show that the fundamental frequencies are independent of the chiral angles,but the chirality has an appreciable effect on higher vibration frequencies.The SWCNTs is very sensitive to the initial strain even if the strain is extremely small.展开更多
A quantized Hall conductance(not conductivity)in three dimensions has been searched for more than 30 years.Here we explore it in 3D topological nodal-ring semimetals,by employing a minimal model describing the essenti...A quantized Hall conductance(not conductivity)in three dimensions has been searched for more than 30 years.Here we explore it in 3D topological nodal-ring semimetals,by employing a minimal model describing the essential physics.In particular,the bulk topology can be captured by a momentum-dependent winding number,which confines the drumhead surface states in a specific momentum region.This confinement leads to a surface quantum Hall conductance in a specific energy window in this 3D system.The winding number for the drumhead surface states and Chern number for their quantum Hall effect form a two-fold topological hierarchy.We demonstrate the one-to-one correspondence between the momentum-dependent winding number and wavefunction of the drumhead surface states.More importantly,we stress that breaking chiral symmetry is necessary for the quantum Hall effect of the drumhead surface states.The analytic theory can be verified numerically by the Kubo formula for the Hall conductance.We propose an experimental setup to distinguish the surface and bulk quantum Hall effects.The theory will be useful for ongoing explorations on nodal-ring semimetals.展开更多
文摘Nonlocal continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with micro-or nanostructures.This paper deals with the lateral-torsional buckling of elastic nonlocal small-scale beams.Eringen’s model is chosen for the nonlocal constitutive bendingcurvature relationship.The effect of prebuckling deformation is taken into consideration on the basis of the Kirchhoff-Clebsch theory.It is shown that the application of Eringen’s model produces small-length scale terms in the nonlocal elastic lateraltorsional buckling moment of a hinged-hinged strip beam.Clearly,the non-local parameter has the effect of reducing the critical lateral-torsional buckling moment.This tendency is consistent with the one observed for the in-plane stability analysis,for the lateral buckling of a hinged-hinged axially loaded column.The lateral buckling solution can be derived from a physically motivated variational principle.
文摘In this paper,we study the flexural vibration behavior of single-walled carbon nanotubes(SWCNTs)for the assessment of Timoshenko beam models.Extensive molecular dynamics(MD)simulations based on second-generation reactive empirical bond-order(REBO)potential and Timoshenko beam modeling are performed to determine the vibration frequencies for SWCNTs with various length-todiameter ratios,boundary conditions,chiral angles and initial strain.The effectiveness of the local and nonlocal Timoshenko beam models in the vibration analysis is assessed using the vibration frequencies of MD simulations as the benchmark.It is shown herein that the Timoshenko beam models with properly chosen parameters are applicable for the vibration analysis of SWCNTs.The simulation results show that the fundamental frequencies are independent of the chiral angles,but the chirality has an appreciable effect on higher vibration frequencies.The SWCNTs is very sensitive to the initial strain even if the strain is extremely small.
基金supported by the National Key R&D Program of China(2022YFA1403700)the Innovation Program for Quantum Science and Technology(2021ZD0302400)+3 种基金the National Natural Science Foundation of China(11925402,11534001,and 11974249)Guangdong province(2020KCXTD001 and 2016ZT06D348)the Natural Science Foundation of Shanghai(19ZR1437300)supported by Center for Computational Science and Engineering of SUSTech.
文摘A quantized Hall conductance(not conductivity)in three dimensions has been searched for more than 30 years.Here we explore it in 3D topological nodal-ring semimetals,by employing a minimal model describing the essential physics.In particular,the bulk topology can be captured by a momentum-dependent winding number,which confines the drumhead surface states in a specific momentum region.This confinement leads to a surface quantum Hall conductance in a specific energy window in this 3D system.The winding number for the drumhead surface states and Chern number for their quantum Hall effect form a two-fold topological hierarchy.We demonstrate the one-to-one correspondence between the momentum-dependent winding number and wavefunction of the drumhead surface states.More importantly,we stress that breaking chiral symmetry is necessary for the quantum Hall effect of the drumhead surface states.The analytic theory can be verified numerically by the Kubo formula for the Hall conductance.We propose an experimental setup to distinguish the surface and bulk quantum Hall effects.The theory will be useful for ongoing explorations on nodal-ring semimetals.
