Non-local continuum modeling of carbon nanotubes: Physical interpretation of non-local kernels using atomistic simulations

The longitudinal, transverse and torsional wave dispersion curves in single walled carbon nanotubes (SWCNT) are used to estimate the non-local kernel for use in continuum elasticity models of nanotubes. The dispersion data for an armchair (10,10) SWCNT was obtained using lattice dynamics of SWNTs while accounting for the helical symmetry of the tubes. In our approach, the Fourier transformed kernel of non-local linear elastic theory is directly estimated by matching the atomistic data to the dispersion curves predicted from non-local 1D rod theory and axisymmetric shell theory. We found that gradient models incur significant errors in both the phase and group velocity when compared to the atomistic model. Complementing these studies, we have also performed detailed tests on the effect of length of the nanotube on the axial and shear moduli to gain a better physical insight on the nature of the true non-local kernel. We note that unlike the kernel from gradient theory, the numerically fitted kernel becomes negative at larger distances from the reference point. We postulate and confirm that the fitted kernel changes sign close to the inflection point of the interatomic potential. The numerically computed kernels obtained from this study will aid in the development of improved and efficient continuum models for predicting the mechanical response of CNTs.     

Finite element modeling of interfacial forces and contact stresses of pneumatic tire on fresh snow for combined longitudinal and lateral slips

Significant challenges exist in the prediction of interaction forces generated from the interface between pneumatic tires and snow-covered terrains due to the highly non-linear nature of the properties of flexible tires, deformable snow cover and the contact mechanics at the interface of tire and snow. Operational conditions of tire-snow interaction are affected by many factors, especially interfacial slips, including longitudinal slip during braking or driving, lateral slip (slip angle) due to turning, and combined slip (longitudinal and lateral slips) due to brake-and-turn and drive-and-turn maneuvers, normal load applied on the wheel, friction coefficient at the interface and snow depth. This paper presents comprehensive three-dimensional finite element simulations of tire-snow interaction for low-strength snow under the full-range of controlled longitudinal and lateral slips for three vertical loads to gain significant mechanistic insight. The pneumatic tire was modeled using elastic, viscoelastic and hyperelastic material models; the snow was modeled using the modified Drucker-Prager Cap material model (MDPC). The traction, motion resistance, drawbar pull, tire sinkage, tire deflection, snow density, contact pressure and contact shear stresses were obtained as a function of longitudinal slip and lateral slip. Wheel states - braked, towed, driven, self-propelled, and driving - have been identified and serve as key classifiers of discernable patterns in tire-snow interaction such as zones of contact shear stresses. The predicted results can be applied to analytical deterministic and stochastic modeling of tire-snow interaction.     

Measurements of dynamic properties of concrete structures using flexural wave propagation characteristics

Flexural wave propagation characteristics influence the impact noise generation of concrete structures that are found in building floors, railroads, bridges, and many other engineering structures. The flexural vibration of the structure is affected by concrete dynamic properties. The purpose of this study is to measure the concrete dynamic characteristics using a wave propagation approach. The flexural wave speeds, bending stiffness and their loss factors were measured. The measured characteristics are essential for understanding sound radiation and vibration dissipation capabilities of the concrete structures. Various concrete beam structures were made and tested. The dynamic stiffness and loss factor were influenced by its components and showed frequency-dependent variation, especially for the measured loss factor.     

Effect of axial load on the propagation of elastic waves in helical beams

Helical structures are designed to support heavy loads, which can significantly affect the dynamic behaviour. This paper proposes a physical analysis of the effect of axial load on the propagation of elastic waves in helical beams. The model is based on the equations of motion of loaded helical Timoshenko beams. An eigensystem is obtained through a Fourier transform along the axis. The equations are made dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain). A parametric study is conducted. The effect of loading is quantified in high, medium and low-frequency ranges. Noting that the effect is significant in low frequencies, dispersion curves of stretched and compressed helical beams are presented for different helix angles and radii. This effect is greater as the helix angle increases. Both the effects of stress and geometry deformation are shown to be non-negligible on elastic wave propagation.     

The formation of hydrodynamic slugs by the interaction of waves in gas–liquid two-phase pipe flow

This paper examines the effects of wave interaction on the formation of hydrodynamic slugs in two-phase pipe flow at relatively low gas and liquid superficial velocities. The experiments were conducted using a horizontal 31 m long, D = 10 cm internal diameter transparent pipe at atmospheric pressure. High resolution photography allowed the location of the gas–liquid interface to be measured with a high degree of accuracy at 5 Hz. Image analysis allowed individual waves to be tracked over a 14D section of the pipe. Regular waves having similar properties such as speed, amplitude and length were seen far from the region of slug formation. However, near the transition region, where hydrodynamic slugs were formed, significant differences between wave properties were observed which resulted in wave interaction leading to a type of sub-harmonic resonance and slug formation. The formation of hydrodynamic slugs due to wave interaction differs from predictions for slug formation using long wavelength stability theory. The properties of the waves were quantified which gave detailed information on the resonance mechanism found near the transition to slugging.     

基于ABAQUS的小尺度桩柱波浪力计算方法

基于达索公司开发的ABAQUS有限元分析软件,利用ABAQUS提供的用户子程序编制程序,计算分析风电机组在海洋环境中受到的波浪力.在计算中,使用了三维梁单元和壳单元建模,应用线性波模拟海洋环境中的波浪.基于莫里森方程和数值积分的方法,分析桩柱形支撑结构上的波浪载荷,计算支撑结构的位移,应力变化等,得到了较好的结果.     

On calculation of hydrodynamic forces for steady flows in unbounded domains

This note addresses the question why the “impulse formula”, often employed to compute hydrodynamic forces in vortex-dominated time-dependent flows, is not applicable to steady flows in unbounded domains. By analyzing the asymptotic structure of steady and unsteady flow solutions in unbounded domains, it is demonstrated that one assumption made in the derivation of the impulse formula is in fact not satisfied in the steady case. This result also highlights the special character of steady flows in unbounded domains.     

Three-component conformational equilibria of some flexible pyrrolidin-2-(thi)ones in solution by NMR data (δC, δH, and JHH) and their DFT predictions: a confrontation of different approaches

Three standard gas-phase B3LYP/6-31G(d) methods of the analysis of δ_C, δ_H, and J_HH NMR data for solutions initially used for the title γ-lactams 1a-c led to conflicting findings on fractional populations ηs of their fast interconverting conformers A-C, which were also inconsistent with energy data. In order to find the source(s) of these discrepancies, several additional DFT computations were carried out at the double- and triple-zeta theory level with simultaneous modeling of the solutions in explicit solvents with the COSMO or IEF-PCM technique. The WC04/WP04 functionals and IGLO-II (or IGLO-III) basis set were applied for predicting δ_C/δ_H, and J_HH data, respectively. The limits of efficiency and accuracy of a few current NMR-oriented computational protocols were determined by their specific use to the main forms of 1a-c treated as test cases. Thus, an unreliability of the modified Karplus-type equation for this purpose was shown. In turn, only the use of DFT-D3 corrections for the attractive van der Waals dispersion interactions (London forces) not present in conventional DFT, to Gibbs free energies (ΔG) estimated for the forms A-C of 1a-c in solution, yielded energetics and so populations (η_Gs) compatible within ±15% (only ±2%, for 1a) with the best results found by considering the ¹H NMR data. These η_Hs were found by a linear regression of GIAO-predicted δ_H sets reproducing experiment in the best way (r²>0.9996, for 1a and 1b, r²=0.9970, for 1c with strongly degenerated δ_Hs). As for η_Js, they permitted only for evaluations of the ratios (A+B)/C, excepting sufficiently differentiated J_HHs (1b in acetone). In contrast, an application of δ_Cs for assessing η_Cs was unsuccessful. Selected findings were finally compared with the DP4-probability results (η_DP4s) and fairly good agreement was found. The greatest divergence in ηs exists for the CS bond-containing object 1b, what suggests a large effect of the intramolecular London forces on its structure and properties. The present results should be useful guidelines for NMR studies on the other multi-conformer systems in rapid equilibrium between more than two energetically feasible forms.     

Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

Solutions of the scalar Helmholtz wave equation are derived for the analysis of the transport and thermodynamic properties of the two-dimensional disk and three-dimensional infinitely long straight wire in the external uniform longitudinal magnetic field B under the assumption that the Robin boundary condition contains extrapolation length Λ with nonzero imaginary part Λ_i. As a result of this complexity, the self-adjointness of the Hamiltonian is lost, its eigenvalues E become complex too and the discrete bound states of the disk characteristic for the real Λ turn into the corresponding quasibound states with their lifetime defined by the eigenenergies imaginary parts E_i. Accordingly, the longitudinal flux undergoes an alteration as it flows along the wire with its attenuation/amplification being E_i-dependent too. It is shown that, for zero magnetic field, the component E_i as a function of the Robin imaginary part exhibits a pronounced sharp extremum with its magnitude being the largest for the zero real part Λ_r of the extrapolation length. Increasing magnitude of Λ_r quenches the E_i − Λ_i resonance and at very large Λ_r the eigenenergies E approach the asymptotic real values independent of Λ_i. The extremum is also wiped out by the magnetic field when, for the large B, the energies tend to the Landau levels. Mathematical and physical interpretations of the obtained results are provided; in particular, it is shown that the finite lifetime of the disk quasibound states stems from the Λ_i-induced currents flowing through the sample boundary. Possible experimental tests of the calculated effect are discussed; namely, it is argued that it can be observed in superconductors by applying to them the external electric field E normal to the surface.