Dynamic Response of Rock-like Materials Based on SHPB Pulse Waveform Characteristics

Rock-like brittle materials under dynamic load will show more complex dynamic mechanical properties than those under static load. The relationship between pulse waveform characteristics and strain rate effect and inertia effect is rarely discussed in the split-Hopkinson pressure bar (SHPB) numerical simulation research. In response to this problem, this paper discusses the effects of different pulse types and pulse waveforms on the incident waveform and dynamic response characteristics of specimens based on particle flow code (PFC). The research identifies a critical interval of rock dynamic strength, where the dynamic strength of the specimen is independent of the strain rate but increases with the amplitude of the incident stress wave. When the critical interval is exceeded, the dynamic strength is determined by the strain rate and strain rate gradient. The strain rate of the specimen is only related to the slope of the incident stress wave and is independent of its amplitude. It is also determined that the inertia effect cannot be eliminated in the SHPB. The slope of the velocity pulse waveform determines the strain rate of the specimen, the slope of the force pulse waveform determines the strain rate gradient of the specimen, and the upper bottom time determines the strain rate of the specimen. It provides a reference for SHPB numerical simulation. A dynamic strength prediction model of rock-like materials is then proposed, which considers the effects of strain rate and strain rate gradient.

The Effect of Micro-Inertia and Flexoelectricity on Love Wave Propagation in Layered Piezoelectric Structures

The non-classical linear governing equations of strain gradient piezoelectricity with micro-inertia effect are used to investigate Love wave propagation in a layered piezoelectric structure. The influence of flexoelectricity and micro-inertia effect on the phase wave velocity in a thin homogeneous flexoelectric layer deposited on a piezoelectric substrate is investigated. The dispersion relation for Love waves is obtained. The phase velocity is numerically calculated and graphically illustrated for the electric open-circuit and short-circuit conditions and for distinct material properties of the layer and substrate. The influence of direct flexoelectricity, micro-inertia effect, as well as the layer thickness on Love wave propagation is studied individually. It is found that flexoelectricity increases the Love-wave phase velocity, while the micro-inertia effect reduces its value. These effects become more significant for Love waves with shorter wavelengths and small guiding layer thicknesses.

Static and dynamic characteristics and stability analysis of high-speed water-lubricated hydrodynamic journal bearings

The purpose of this paper is to analyze the influence of turbulent, inertia, and misaligned effects on the static and dynamic characteristics and stability of high-speed water-lubricated hydrodynamic journal bearings. Based on the Navier–Stokes equation, the mixing-length theory, and the essential assumption that the velocity profile is not strongly affected by inertia force, the fluid lubrication model with turbulent, inertia, and misaligned effects is established, and then the stability analysis of bearings is carried out based on the equation of motion with four degrees of freedom. The model is solved by the finite difference method and the numerical results are compared under different operating conditions. The results show that the turbulent effect greatly increases the load capacity, power consumption, stiffness and damping coefficients, and stability of bearings, and the inertia effect significantly increases the volume flow rate of bearings, and the misaligned effect increases the load capacity, stiffness and damping coefficients, and stability of bearings. In high rotary speed and moderate eccentricity ratios, the influence of the inertia effect on the load capacity, stiffness coefficients, and stability cannot be neglected.

Dynamic finite element simulation of wheel–rail contact response for the straight track case

The dynamic effects, mainly including the inertia effect and strain-rate effect, on the dynamic wheel–rail contact behavior become more and more serious as the train speed increases. The inertia effect can be automatically taken into account in explicit finite element analysis codes, while the strain-rate effect needs to be considered via inputting the related material parameters. In the present paper, the influence of strain rate on the dynamic wheel–rail contact response for the straight track case was explored, based on a 3D wheel–rail rolling contact finite element model, via LS-DYNA/explicit algorithm. Effects of the axle load and train speed on typical dynamic wheel–rail responses were discussed, and the results indicate that the coupled train speed with strain rate has a non-negligible influence on dynamic contact responses. The strain rate hardening effect increases the maximum contact pressure and stress, and inhibits the plastic deformation of the wheel–rail system. A rate-sensitive factor (RSF) was then introduced to describe the strain rate hardening effect, confirming that the rail is more sensitive to strain rate compared to the wheel. Finally, an error analysis of the wheel–rail Hertz contact theory was conducted, which further verify the differences between elastic and elastic-plastic contact solutions.

Higher order and scale-dependent micro-inertia effect on the longitudinal dispersion based on the modified couple stress theory

The conventional modified couple stress theory cannot model the correct behavior of the longitudinal dispersion and acts the same as the classical theory in the face of such problems. In this paper, the micro-inertia-based couple stress theory is used to triumph over this deficiency. The developed theory is imposed to tackle the longitudinal dispersion of aluminum beams in two distinct scales. Convenient available experimental data obtained for a macro-scale aluminum rod and aluminum crystals are utilized to determine the corresponding micro-inertia length scale parameters and show the scale-dependent nature of this parameter for the first time. In addition, a higher order micro-rotation relation is employed to describe the higher order micro-inertia effects. This relation leads to a developed equation of motion containing an additional term compared with the first-order relation. The obtained results indicate that only higher order micro-inertia effect that is proposed in this study for the first time is able to capture the highly nonlinear behavior of dispersion curves (including an extremum/inflection point), which has experimentally been observed for phonons propagating in the longitudinal direction in an aluminum crystal.

Correction of Young’s Modulus Calculation in the Flexural Mode of Resonant Column Test

The resonant column test includes torsional and flexural modes that can be used to obtain reduction curves for the shear modulus and Young’s modulus of the soil, respectively. When the resonant column test is performed under flexural mode, Young’s modulus is calculated mainly using the measured resonant frequency following the formula proposed by Cascante et al. However, this formula does not consider the rotational inertia effect of the electromagnetic drive disk of the resonant column apparatus and thus may inaccurately calculate Young’s modulus. In this study, the formula was modified by considering the rotational inertia effect of the electromagnetic drive disk, and its accuracy was verified by using three aluminum calibration rods with different diameters as a dummy specimen for the resonant tests in flexural and torsional modes.