Experimental and numerical study on dynamic mechanical behaviors of shale under true triaxial compression at high strain rate

High-energy gas fracturing of shale is a novel,high efficacy and eco-friendly mining technique,which is a typical dynamic perturbing behavior.To effectively extract shale gas,it is important to understand the dynamic mechanical properties of shale.Dynamic experiments on shale subjected to true triaxial compression at different strain rates are first conducted in this research.The dynamic stress-strain curves,peak strain,peak stress and failure modes of shale are investigated.The results of the study indicate that the intermediate principal stress and the minor principal stress have the significant influence on the dynamic mechanical behaviors,although this effect decreases as the strain rate increases.The characteristics of compression-shear failure primarily occur in shale subjected to triaxial compression at high strain rates,which distinguishes it from the fragmentation characteristics observed in shale under dynamic uniaxial compression.Additionally,a numerical three-dimensional Split Hopkinson Pressure Bar(3D-SHPB),which is established by coupling PFC3D and FLAC3D methods,is validated to replicate the laboratory characteristics of shale.The dynamic mechanical characteristics of shale subjected to different confining stresses are systematically investigated by the coupling PFC3D and FLAC3D method.The numerical results are in good agreement with the experimental data.

Effect of diagenetic variation on the static and dynamic mechanical behavior of coral reef limestone

Coral reef limestone at different depositional depths and facies differ remarkably on the textural and mineralogical characteristics,owing to the complex sedimentary diagenesis.To explore the effects of pore structure and mineral composition associated with diagenetic variation on the mechanical behavior of reef limestone,a series of quasi-static and dynamic compression tests along with microscopic examinations were performed on the reef limestone at shallow and deep burial depths.It is revealed that the shallow reef limestone(SRL)is classified as a porous aragonite-type carbonate rock with high porosity(55.3±3.2)%and pore connectivity.In comparison,the deep reef limestone(DRL)is mainly composed of dense calcite-type calcium carbonate with low porosity(4.9±1.6)%and pore connectivity.The DRL strengthened and stiffened by the tight grain framework consistently displays much higher values of the dynamic compressive strength,elastic modulus,brittleness index,and specific energy absorption than those of the SRL.The gap between two types of limestone further increases with an increase in strain rate.It appears that the failure pattern of SRL is dominated by the inherent defects like weak bonding interfaces and growth lines,revealed by the intricate fracturing network and mixed failure.Likewise,although the preexisting megapores in DRL may affect the crack propagation on pore tips to a certain distance,it hardly alters the axial splitting failure of DRL under impacts.The stress wave propagation and attenuation in SRL is primarily controlled by the reflection and diffusion caused by plenty mesopores,as well as an energy dissipation in layer-wise pore collapse and adjacent grain crushing,while the stress wave in DRL is highly hinged on the insulation and diffraction induced by the isolated megapores.This process is accompanied by the energy dissipation behavior of inelastic deformation resulted from the pore-emanated microcracking.

MD Simulation of Diffusion Behaviors in Collision Welding Processes of Al-Cu, Al-Al, Cu-Cu

To investigate the effects of material combinations and velocity conditions on atomic diffusion behavior near collision interfaces,this study simulates the atomic diffusion behavior near collision interfaces in Cu-Al,Al-Al and Cu-Cu combinations fabricated through collision welding using molecular dynamic(MD)simulation.The atomic diffusion behaviors are compared between similar metal combinations(Al-Al,Cu-Cu)and dissimilar metal combinations(Al-Cu).By combining the simulation results and classical diffusion theory,the diffusion coefficients for similar and dissimilar metal material combinations under different velocity conditions are obtained.The effects of material combinations and collision velocity on diffusion behaviors are also discussed.The diffusion behaviors of dissimilar material combinations strongly depend on the transverse velocity,whereas those of the similar material combinations are more dependent on the longitudinal velocity.These findings can provide guidance for optimizing welding parameters.

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

Experimental study and numerical simulation of the impact of under-sleeper pads on the dynamic and static mechanical behavior of heavy-haul railway ballast track

Laying the under-sleeper pad(USP)is one of the effective measures commonly used to delay ballast degradation and reduce maintenance workload.To explore the impact of application of the USP on the dynamic and static mechanical behavior of the ballast track in the heavy-haul railway system,numerical simulation models of the ballast bed with USP and without USP are presented in this paper by using the discrete element method(DEM)-multi-flexible body dynamic(MFBD)coupling analysis method.The ballast bed support stiffness test and dynamic displacement tests were carried out on the actual operation of a heavy-haul railway line to verify the validity of the models.The results show that using the USP results in a 43.01%reduction in the ballast bed support stiffness and achieves a more uniform distribution of track loads on the sleepers.It effectively reduces the load borne by the sleeper directly under the wheel load,with a 7.89%reduction in the pressure on the sleeper.Furthermore,the laying of the USP changes the lateral resistance sharing ratio of the ballast bed,significantly reducing the stress level of the ballast bed under train loads,with an average stress reduction of 42.19 kPa.It also reduces the plastic displacement of ballast particles and lowers the peak value of rotational angular velocity by about 50%to 70%,which is conducive to slowing down ballast bed settlement deformation and reducing maintenance costs.In summary,laying the USP has a potential value in enhancing the stability and extending the lifespan of the ballast bed in heavy-haul railway systems.

Understanding the interfacial behaviors of benzene alkylation with butene using chloroaluminate ionic liquid catalyst: A molecular dynamics simulation

To better understand the benzene alkylation with chloroaluminate ionic liquids(ILs) as catalyst, the interfacial properties between the benzene/butene binary reactants and chloroaluminate ILs with varying cation alkyl chain length and different anions were investigated using molecular dynamics(MD) simulations. The results indicate that ILs can obviously improve the interfacial width, solubility and diffusion of reactants compared to H_(2)SO_(4). The longer alkyl chains of cations present a density enrichment at the interface and protrude into the binary reactants phase. Furthermore, the ILs consisting of 1-octyl-3-methylimidazolium cations([Omim]^(+)) and the stronger acidity heptachlorodialuminate anions([Al_(2)Cl_(7)]^(-)) are more beneficial to promote the interfacial width and facilitate the dissolution and diffusion of benzene in both the IL bulk and the interfacial region in comparison to the ones with shorter alkyl chains cations and weaker acidity anions. The information gives us a better guideline for the design of ILs for benzene alkylation.

RESEARCH ON THE COMPLICATED DYNAMICAL BEHAVIORS OF NONLINEAR ECOSYSTEMS(Ⅱ)

This paper is a further study of reference [1]. In this paper, we mainly discuss the complicated dynamical behaviors resulting from a simple one-dimensional model of nonlinear ecosystems: fixed point motion, periodic motion and chaotic motion etc., and briefly discuss the universality of the complicated dynamical behaviors, which can be described by the first and the second M. Feigenbaun. constants. At last, we discuss the 'one-side lowering phenomenon' due to near unstabilization when the nonlinear ecosystem approaches bifurcation points from unbifurcation side. It is of important theoretical and practical meanings both in the development and utilization of ecological resources ar.d in the design and management of artifilial ecosystems.

Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation

We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the threedimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like（antikink-like） wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves.

Exact explicit solitary wave and periodic wave solutions and their dynamical behaviors for the Schamel–Korteweg–de Vries equation

The Schamel–Korteweg–de Vries equation is investigated by the approach of dynamics.The existences of solitary wave including ω-shape solitary wave and periodic wave are proved via investigating the dynamical behaviors with phase space analyses.The sufficient conditions to guarantee the existences of the above solutions in different regions of the parametric space are given.All possible exact explicit parametric representations of the waves are also presented.Along with the details of the analyses,the analytical results are numerically simulated lastly.

Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

Quasi-static and dynamic tensile behaviors in electron beam welded Ti-6Al-4V alloy

The quasi-static and dynamic tensile behaviors in electron beam welded（EBW） Ti-6Al-4V alloy were investigated at strain rates of 10-3 and 103 s-1,respectively,by materials test system（MTS） and reconstructive Hopkinson bars apparatus.The microstructures of the base metal（BM） and the welded metal（WM） were observed with optical microscope.The fracture characteristics of the BM and WM were characterized with scanning electronic microscope.In Ti-6Al-4V alloy joint,the flow stress of WM is higher than that of BM,while the fracture strain of WM is less than that of BM at strain rates of 103 and 10-3 s-1,respectively.The fracture strain of WM has apparent improvement when the strain rate rises from 10-3 to 103 s-1,while the fracture strain of BM almost has no change.At the same time,the fracture mode of WM alters from brittle to ductile fracture,which causes improvement of the fracture strain of WM.

Dynamic behavior of tunneling triboelectric charges in two-dimensional materials

Although the research history of triboelectrification has been more than 2000 years, there are still many problems to be solved so far.The use of scanning probe microscopy provides an important way to quantitatively study the transfer, accumulation, and dissipation of triboelectric charges in the process of triboelectrification. Two-dimensional materials are considered to be key materials for new electronic devices in the post-Moore era due to their atomic-scale size advantages. If the electrostatic field generated by triboelectrification can be used to replace the traditional gate electrostatic field, it is expected to simplify the structure of two-dimensional electronic devices and reconfigure them at any time according to actual needs. Here, we investigate the triboelectrification process of various two-dimensional materials such as MoS_(2), WSe_(2),and ZnO. Different from traditional bulk materials, after two-dimensional materials are rubbed, the triboelectric charges generated may tunnel through the two-dimensional materials to the underlying substrate surface. Because the tunneling triboelectric charge is protected by the twodimensional material, its stable residence time on the substrate surface can reach more than 7 days, which is more than tens of minutes for the traditional triboelectric charge. In addition, the electrostatic field generated by the tunneling triboelectric charge can effectively regulate the carrier transport performance of two-dimensional materials, and the source–drain current of the field effect device regulated by the triboelectric floating gate is increased by nearly 60 times. The triboelectric charge tunneling phenomenon in two-dimensional materials is expected to be applied in the fields of new two-dimensional electronic devices and reconfigurable functional circuits.

Dynamic changes of behaviors, dentate gyrus neurogenesis and hippocampal miR-124 expression in rats with depression induced by chronic unpredictable mild stress

The depression-like behavior phenotype,neurogenesis in the dentate gyrus and miR-124 expression in the hippocampus are the focus of current research on the pathogenesis of depression and antidepressant therapy.The present study aimed to clarify the dynamic changes of depression-like behavior,dentate gyrus neurogenesis and hippocampal miR-124 expression during depression induced by chronic stress to reveal pathological features at different stages of depression and to further provide insight into depression treatment.Chronic unpredictable mild stress depression models were established by exposing Sprague-Dawley rats to various mild stressors,including white noise,thermal swimming,stroboscopic illumination,soiled cages,pairing with three other stressed animals,cold swimming,tail pinch,restraint and water and food deprivation.Chronic unpredictable mild stress model rats underwent dynamic observation from 1 to 8 weeks and were compared with a control group(normal feeding without any stressors).To observe changes in the depression-like behavior phenotype during chronic unpredictable mild stress-induced depression,a sucrose preference test was used to evaluate the degree of anhedonia.An open-field test was used to evaluate locomotor activity and anxiety status.Compared with the control group,chronic unpredictable mild stress rats lost weight but did not have a depression-like behavioral phenotype at 1-4 weeks.Chronic unpredictable mild stress rats presented decreased sucrose preference and locomotor activity at 5-8 weeks.In addition,chronic unpredictable mild stress rats did not have significant anxiety-like behavior during 1-8 weeks of modeling.To observe neurogenesis dysfunctions and changes in neuronal number in the dentate gyrus during chronic unpredictable mild stress-induced depression,markers(DCX and DCX/BrdU)of neural proliferation and differentiation and the neuronal marker NeuN were assessed by immunofluorescence.Compared with the control group,neurogenesis and the neuronal number in the dentate gyrus did not change from 2 to 6 weeks;however,neural proliferation and differentiation in the dentate gyrus decreased,and the number of neurons decreased until the eighth week in the chronic unpredictable mild stress group.Real-time quantitative reverse transcription polymerase chain reaction assays and fluorescence in situ hybridization were used to measure the expression of hippocampal miR-124 during chronic unpredictable mild stress-induced depression.The results showed that the expression of hippocampal miR-124 was unchanged during the first 4 weeks but increased from 5 to 6 weeks and decreased from 7 to 8 weeks compared with the control group.These findings indicate that during chronic unpredictable mild stress-induced depression,the behavioral phenotype,miR-124 expression in the hippocampus,neurogenesis in the dentate gyrus and neuronal numbers showed dynamic changes,which suggested that various pathological changes occur at different stages of depression.All experimental procedures and protocols were approved by the Experimental Animal Ethics Committee of Guangzhou University of Chinese Medicine of China in March 2015.

QUALITATIVE ANALYSIS OF DYNAMICAL BEHAVIOR FOR AN IMPERFECT INCOMPRESSIBLE NEO-HOOKEAN SPHERICAL SHELL

The radial symmetric motion problem was examined for a spherical shell composed of a class of imperfect incompressible hyper-elastic materials, in which the materials may be viewed as the homogeneous incompressible isotropic neo-Hookean material with radial perturbations. A second-order nonlinear ordinary differential equation that describes the radial motion of the inner surface of the shell was obtained. And the first integral of the equation was then carded out. Via analyzing the dynamical properties of the solution of the differential equation, the effects of the prescribed imperfection parameter of the material and the ratio of the inner and the outer radii of the underformed shell on the motion of the inner surface of the shell were discussed, and the corresponding numerical examples were carded out simultaneously. In particular, for some given parameters, it was proved that, there exists a positive critical value, and the motion of the inner surface with respect to time will present a nonlinear periodic oscillation as the difference between the inner and the outer presses does not exceed the critical value. However, as the difference exceeds the critical value, the motion of the inner surface with respect to time will increase infinitely. That is to say, the shell will be destroyed ultimately.

Dynamic Behaviors of A Marine Riser Under Two Different Frequency Parametric Excitations

The marine risers are often subjected to parametric excitations from the fluctuation top tension. The top tension on the riser may fluctuate with multiple frequencies caused by irregular waves. In this paper, the influence between different frequency components in the top tension on the riser system is theoretically simulated and analyzed. With the Euler-Bernoulli beam theory, a dynamic model for the vibrations of the riser is established. The top tension is set as fluctuating with time and it has two different frequencies. The influences from the fluctuation amplitudes, circular frequencies and phase angles of these frequency components on the riser system are analyzed in detail. When these two frequencies are fluctuating in the stable regions, the riser system may become unstable because ω1+ω2≈2Ωn. The fluctuation amplitudes of these frequencies have little effect on the components of the vibration frequencies of the riser. For different phase angles, the stability and dynamic behaviors of the riser would be different.

THE DYNAMICAL BEHAVIOR OF FULLY DISCRETE SPECTRAL METHOD FOR NONLINEAR SCHRODINGER EQUATION WITH WEAKLY DAMPED

Nonlinear Schrodinger equation (NSE) arises in many physical problems. It is a very important equation. A lot of works studied the wellposed, the existence of solution of NSE etc. And there are many works studied the numerical methods for it. Recently, since the development of infinite dimensional dynamic system the dynamical behavior of NSE has been investigated. The paper [1] studied the long time wellposedness, the existence of universal attractor and the estimate of Lyapunov exponent for NSE with weakly damped. At the same time it was need to study the large time new computational methods and to discuss its convergence error estimate, the existence of approximate attractors etc. In this pape we study the NSE with weakly damped (1.1). We assume,where 0【λ【2 is a constant. If we wish to construct the higher accuracy computational scheme, it will be difficult that staigh from the equation (1.1). Therefore we start with (1. 4) and use fully discrete Fourier spectral method with time difference to

Numerical investigation of dynamical behavior of tethered rigid spheres in supersonic flow

The dynamical behavior of two tethered rigid spheres in a supersonic flow is numerically investigated. The tethered lengths and radius ratios of the two spheres are different. The two spheres, which are centroid axially aligned initially, are held stationary first, then released, and subsequently let fly freely in a supersonic flow. The mean qualities of the system and the qualities of the bigger sphere are considered and compared with the situations without the tether. In the separation process, six types of motion caused by the spheres, tether, and fluid interaction are found. The results show that the mean x-velocity of the system changes in a different manner for different radius ratios, and the x-velocity of the bigger sphere is uniformly reduced but through different mechanisms.

Physical and dynamic mechanical behaviors of marble after heat treatment in quasi-vacuum and air-filled environments

The dynamic mechanical properties of rock specimens after thermal treatment in the air-filled environment(AE:i.e.,at the free surface)have been extensively investigated,yet they are rarely estimated in the quasi-vacuum environment(VE:i.e.,far from free surface),which is of special importance in engineering practice.Several precise laboratory tests(i.e.,split Hopkinson pressure bar test)on marble samples in both AE and VE were performed to investigate physical and dynamic mechanical behaviors of marble after heat treatment(25℃ to 900℃)in AE and VE.The tests results demonstrate that related properties of marble could be divided into three different stages by corresponding critical temperatures of 300℃ and 600℃,at which heat damage factors are 0.29(0.30)and 0.88(0.92)in VE(AE),respectively.The thermal damage developes more fully in AE than in VE.The thermal environment plays an important role,especially in Stage 3.Specifically,a conspicuous difference(greater than 20%)between AE and VE occurs in corresponding dynamic strength and the anti-deformation capacities of tested marble specimen.The influence of heat damage of rock is very important and valuable in engineering practice,particularly when the temperature is very high(greater than 600℃).

Nonlinear dynamic behaviors of ball bearing rotor system

Nonlinear forces and moments caused by ball bearing were calculated based on relationship of displacement and deflection and quasi-dynamic model of bearing.Five-DOF dynamic equations of rotor supported by ball bearings were estimated.The Newmark-β method and Newton-Laphson method were used to solve the equations.The dynamic characteristics of rotor system were studied through the time response,the phase portrait,the Poincar?maps and the bifurcation diagrams.The results show that the system goes through the quasi-periodic bifurcation route to chaos as rotate speed increases and there are several quasi-periodic regions and chaos regions.The amplitude decreases and the dynamic behaviors change as the axial load of ball bearing increases;the initial contact angle of ball bearing affects dynamic behaviors of the system obviously.The system can avoid non-periodic vibration by choosing structural parameters and operating parameters reasonably.

Dynamic Friction Behaviors of Pneumatic Cylinders

This paper deals with experimental investigation and modeling of dynamic friction behaviors in the sliding regime of pneumatic cylinders. Using three pneumatic cylinders, friction characteristics are investigated and modeled under various conditions of velocity variation and pressures. It is shown that a hysteretic behavior can be seen at low velocities in the friction force-velocity relation and the friction force varies nearly linearly with the velocity at high velocities. The hysteretic loop is expanded to higher velocities when the frequency of the velocity variation is increased, and its size is increased with increasing driving pressure and is decreased with increasing resistance pressure. It is shown that such behaviors can be relatively accurately simulated by the new modified LuGre model in which a few static parameters are varied with the frequency of velocity variation.