Velocity Law Research Articles

Experimental Research on Dynamic Response of Layered Medium under Impact Load

Stress waves propagating through multiple parallel fractures are attenuated due to the multiple wave reflections and transmissions at the fractures. The dynamic response of a layered medium under an impact load is systematically studied by a model test in this paper. The effects of the impact energy, number of joints, thickness of the medium and joint layer, material properties of the cementation layer, and other factors of the dynamic stress propagation and attenuation of layered media are analyzed. Studies have shown that Sadovsky’s empirical formula fits the attenuation law of vertical peak velocity well, and the obtained attenuation coefficient k and index b can be used for reflecting the dynamic response characteristics of layered media. The attenuation coefficient k is positively correlated with the impact height and negatively correlated with the plate thickness in a single-layer plate impact test. The thickness of the medium layer is the main factor affecting the vibration response of the layered medium in the impact test of the multi-layer slab. The medium thickness, the number of medium layers, and the number of joints have little influence. The different cementation materials and the change of cementation thickness will have a great influence on the dynamic response of layered media, when the cementation layer is filled with joint surfaces for the impact test of multi-layer plates.

Effects of Process Parameters on Density of GH5188 High-temperature Alloy after Selective Laser Melting

GH5188 high-temperature alloy specimens were fabricated by selective laser melting (SLM) and influencing laws of laser power, laser velocity and laser energy density on density of specimens were researched. The results shows that along with the laser energy density increases from 73.02 J/mm3 to 88.18 J/mm3, porosity in specimens decrease and relative density increases from 98.86% to 99.75%. However, as the laser energy density increase further, the density begins to decrease continuously. The main causes that effects relatively density including: the powder is not fused at low energy density, as well as the powder splash and gasification at higher energy density. Neither inadequate nor excessive laser energy density is conducive to improvement of density of specimens. As the increase of laser velocity and laser power, density of specimens increases firstly and then decreases. The variation trend of relative density is similar with that of laser energy density and there are reasonable ranges of laser velocity and laser power. However, influencing laws of laser velocity and laser power on density of specimens are different.

Dynamic Response and Safety Control of Newly Poured Secondary Lining Concrete under Large Section Tunnel Blasting-A Case Study of Longnan Tunnel of Ganshen High-speed Railway

The age of newly poured concrete is short, the cementation between aggregates is weak. At this time, the vibration will affect its performance. The secondary lining concrete newly poured in the tunnel is close to the work face and is susceptible to blasting vibration during construction. In order to study the safety threshold of blasting vibration velocity of newly poured secondary lining concrete in tunnels, the finite element model is established in ANSYS with the large-section Longnan tunnel project as an example. The attenuation law of vibration velocity in three directions of secondary lining under blasting load was analyzed by combining field blasting monitoring with numerical simulation, and the reliability of numerical simulation was verified. Through the numerical simulation results, the vibration velocity and von mises stress distribution of the newly poured secondary lining concrete of the tunnel are analyzed; combined with the dynamic tensile strength theory of concrete, the safety threshold of vibration velocity of newly poured secondary lining concrete of tunnel based on numerical calculation is established; through the indoor vibration test, taking the compressive strength and acoustic velocity of concrete as the indexes, the safety threshold of blasting vibration velocity of newly poured secondary lining concrete of tunnel based on shaking table test is obtained. Combined with the results of numerical simulation and vibration test, the safety threshold of blasting vibration velocity of newly poured secondary lining concrete in large-section tunnels is obtained, and the standard in this field is improved.

An Empirical Wall Law for the Mean Velocity in an Adverse Pressure Gradient for RANS Turbulence Modelling

An empirical wall law for the mean velocity in an adverse pressure gradient is presented, with the ultimate goal of aiming at the improvement of RANS turbulence models and wall functions. For this purpose a large database of turbulent boundary-layer flows in adverse pressure gradients from wind tunnel experiments is considered, and the mean velocity in the inner layer is analysed. The log law in the mean velocity is found to be a robust feature. The extent of the log-law region is reduced in ratio to the boundary layer thickness with increasing strength of the pressure gradient. An extended wall law emerges above the log law, extending up to the outer edge of the inner layer. An empirical correlation to describe the reduction of the log-law region is proposed, depending on the pressure-gradient parameter and on the Reynolds number in inner viscous scaling, whose functional form is motivated by similarity and scaling arguments. Finally, there is a discussion of the conjecture of the existence of a wall law for the mean velocity, which is governed mainly by local parameters and whose leading order effects are the pressure gradient and the Reynolds number, but whose details can be perturbed by higher-order local and history effects.

An Improved Dynamic Surface Sliding Mode Method for Autonomous Cooperative Formation Control of Underactuated USVS with Complex Marine Environment Disturbances

Abstract In this paper, a novel dynamic surface sliding mode control (DSSMC) method, combined with a lateral velocity tracking differentiator (LVTD), is proposed for the cooperative formation control of underactuated unmanned surface vehicles (USVs) exposed to complex marine environment disturbances. Firstly, in view of the kinematic and dynamic models of USVs and the design idea of a virtual control law in a backstepping approach, the trajectory tracking control problem of USVs’ cooperative formation is transformed into a stabilisation problem of the virtual control law of longitudinal and lateral velocities. Then, aiming at the problem of differential explosion caused by repeated derivation in the process of backstepping design, the first-order low-pass filter about the virtual longitudinal velocity and intermediate state quantity of position is constructed to replace differential calculations during the design of the control law, respectively. In order to reduce the steady-state error when stabilising the virtual lateral velocity control law, the integral term is introduced into the design of the sliding mode surface with a lateral velocity error, and then the second-order sliding mode surface with an integral is structured. In addition, due to the problem of controller oscillation and the role of the tracking differentiator (TD) in active disturbance rejection control (ADRC), the LVTD is designed to smooth the state quantity of lateral velocity. Subsequently, based on the dynamic model of USV under complex marine environment disturbances, the nonlinear disturbance observer is designed to observe the disturbances and compensate the control law. Finally, the whole cooperative formation system is proved to be uniformly and ultimately bounded, according to the Lyapunov stability theory, and the stability and validity of the method is also verified by the simulation results.

Mobile Sensor Networks for Finite-Time Distributed H∞ Consensus Filtering of 3D Nonlinear Distributed Parameter Systems with Randomly Occurring Sensor Saturation

This paper is concerned with designing a distributed bounded H∞ consensus filter to estimate an array of three-dimensional (3D) nonlinear distributed parameter systems subject to bounded perturbation. An optimization framework based on mobile sensing is proposed to improve the performance of distributed filters. The measurement output is obtained from a mobile sensor network, where a phenomenon of randomly occurring sensor saturation is taken into account to reflect the reality in a mobile networked environment. A sufficient condition is established by utilizing operator-dependent Lyapunov functional for the filtering error system to be finite-time bounded. Note that the velocity law of each mobile sensor is included in this condition. The effect from the exogenous perturbation to the estimation accuracy is guaranteed at a given level by means of H∞ consensus performance constraint. Finally, simulation examples are presented to demonstrate the applicability of the theoretical results.

The effect of deformation of special relativity by conformable derivative

In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

Study on the distribution law of airflow velocity in rectangular and semicircular roadway sections

AbstractReliable ventilation is the cornerstone of safe production in coal mines, and accurate monitoring of ventilation parameters is the fundamental guarantee of ventilation technology decision‐making. To improve the accuracy of airflow velocity monitoring in coal mine roadways, theoretical analysis, numerical simulation, and field tests were utilized to study the distribution law of airflow velocity in typical roadway sections. First, the calculation model of position of mean airflow velocity line in rectangular and semicircular arch roadway is established based on Boussinesq theory and Pelant turbulence theory. Then, to verify the correctness of the theoretical model, 25 groups of numerical simulation tests were conducted by using COMSOL‐Multiphysics 3.5a software. The errors between theoretical analysis and numerical simulation are all less than 4%. In addition, the numerical results also show that the contour line of airflow velocity in roadway section is consistent with the shape of roadway section, and the isoline of airflow velocity is basically parallel to the roadway wall. In addition, the closer to the roadway wall, the denser the airflow velocity isoline, indicating that the airflow velocity gradient near the wall is larger. And the thickness of the boundary layer decreases with the increase of airflow inlet velocity. Finally, field tests have been conducted in Chongqing Research Institute and Sima Coal Mine to further verify the correctness of the calculation model and numerical simulation results. The measured distribution law of airflow velocity is consistent with the numerical simulation. And the errors between theoretical analysis and field tests are all less than 4%.

An improved wavemaker velocity boundary condition for generating realistic waves in the numerical wave tank

Wavemaker velocity boundary condition method is one of the most common methods for wave generation in numerical wave tanks (NWTs). Traditional wavemaker velocity boundary condition (TWVBC) makes mass flux at the wavemaker boundary nonconservation, and produces a net mass transport flow in the NWT. In this paper, an improved wavemaker velocity boundary condition (IWVBC) is proposed by adding a reverse current at the wavemaker boundary. Through theoretical analysis, the phenomenon of mass nonconservation of regular and random waves is studied, and different modes of the net mass transport are found. Then, the IWVBC and TWVBC are applied to a computational fluid dynamics (CFD) model and the corresponding results are compared with reference data. The results show that the IWVBC can effectively maintain the mass conservation of the NWT and avoid the occurrence of net mass transport and the rise of mean water level. Furthermore, CFD results are basically consistent with the experimental law of wave profile, velocity and mass transport, which indicates that the IWVBC can reproduce realistic wave propagation characteristics in a NWT.

Analysis on the Vertical Additional Force of Shaft and Drainage Settlement Characteristics of Topsoil Containing Multiaquifers

The vertical additional force induced by the drainage consolidation settlement of the topsoil is one of the main factors for shaft wall fracture. To date, the number of aquifers of topsoil rises with the depth increasing of shaft, which would lead to a more serious additional force effect. Thus, studying the vertical additional force law of the shaft when drainage settlement occurs in its surrounding topsoil containing multiaquifers is of great significance to predicting the shaft stress and guarantying shaft safety. In this study, mechanical analysis of the topsoil with the shaft crossing multiaquifer was carried out, and the settlement of each aquifer and aquiclude was calculated by separating the single-slope drainage consolidation and the double-slope drainage consolidation. Then, the calculation model of vertical additional force was established due to the settlement caused by the reaction of the additional force on the topsoil containing multiaquifers, and the calculation model of shaft wall stress was also developed. Verification of this model was conducted by comparing the filed measurement data of the shaft wall strain and the theoretical data calculated by the stress model. Finally, the effect laws of drainage velocity, central aquifer thickness, location, and number on the additional force were obtained and analysed. This paper is expected to provide theoretical support for predicting the additional force and shaft wall stress during its service time.

Acoustic Emission Characteristics of Fracture and Damage in Coal Samples under Overstress Loading and Unloading Paths

Abstract As coal mining depth is over 1000 m, an overstressed effect is commonly observed around working face which shows a higher stress than the ultimate strength of the coal mass. Aiming at the problem of dynamic disasters induced by overstress loading and loading, a true triaxial AE monitoring unit was designed to systematically investigate the acoustic emission (AE) characteristics of fracture and damage. The AE results show that the ring counts of coal sample under true triaxial loading are influenced by three factors: loading level, individual differences, and loading rates. When under lower true triaxial loads, the coal sample damage represented by ring counts appears largely in loading phase, and the quantity is few. When true triaxial loads increase, the number of ring counts, especially in packing phase, increases significantly, which indicates that the damage process is transferred from loading phase to packing phase. The study on evolution laws of microcracks, wave velocity, and energy indicates that, during the initially true triaxial loads, the primary microcracks and the initial loading on primary dense areas contributes to a small amount of lower and higher velocity regions in the sample. Along with the increase of true triaxial loading, the closure of the primary microcracks and the fracture of the dense area result in a transfer and expansion of higher velocity regions and the formation of velocity anomaly regions. When approaching failure, the macrocracks throughout the sample present a large area of lower velocity band. The formation and closure of cracks, the fast transfer of high velocity region, and the velocity anomaly region indicate the unstable status of the sample. During the packing phase of true triaxial loads, the cracks are compacted, and the inner structures are thoroughly damaged in the sample, which eventually presents a continuous damage in a form of the shrink of the lower velocity region and the increase of integral velocity of the sample.

Experimental Investigation of Flow Control Technology for Grouting and Blocking of Flowing Water in Karst Conduits

Aiming at the grouting treatment in karst conduits with large flow and high velocity, we developed a simulation experiment system for conduit-type grouting blocking and investigated the blocking mechanism of flowing water grouting under the condition of flow control. Firstly, we studied the effect of flow control in conduit by controlling the opening of outlet valve and analyzed the variation law of velocity and pressure in conduits under different water heads, conduit diameters and valve opening quantitatively. Secondly, we conducted experiments of flowing water grouting under different flow control conditions, and revealed the influence law of flow control for flowing water grouting. The results show that: 1) with the increase of the intensity of flow control, the pressure in conduit increased gradually, and the velocity of flowing water decreased gradually. 2) When the volume ratio of water and cement was 1.2:1, the volume ratio of cement and sodium silicate was 2:1, the grouting volume was 540 L/h, and the flowing water velocity was 0.15 m/s, flowing water blocking under the condition of flow control achieved the optimal effect. 3) With flow control, the slurry deposition thickness increased more than 50% compared with no flow control; besides, the slurry retention rate increased, and the blocking effect significantly improved. The technology has been successfully applied in the grouting treatment project of China Resources Cement (Pingnan) Limestone Mine. And main water inflow points in the mine were blocked with an total amount of ∼210,200 m3/d water reduction. This study provided some theoretical guidance and reference experience for treatment engineering of water inflow in karst area.

Adaptive control with unknown mass estimation for a quadrotor-slung-load system

In aerial load transportation applications, knowing the mass of the load in advance is not always possible. The load dynamics depend on its mass and using a high-performance model-based controller with an inaccurate mass will introduce unmodeled disturbances to the system that will negatively affect the closed-loop performance. This paper addresses the design of a trajectory tracking controller for a quadrotor with a slung-load that has an unknown mass. The proposed solution is an adaptive controller with online estimation designed using the backstepping technique. Nonlinear control laws for thrust and angular velocity, and an adaption law for mass estimation are proposed, which guarantee the convergence of the trajectory tracking and the estimation errors to zero, and are robust to variations in load mass. Simulation and experimental results are presented to assess the validity and performance of the proposed controller.

Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces

An evolving surface finite element discretisation is analysed for the evolution of a closed two-dimensional surface governed by a system coupling a generalised forced mean curvature flow and a reaction–diffusion process on the surface, inspired by a gradient flow of a coupled energy. Two algorithms are proposed, both based on a system coupling the diffusion equation to evolution equations for geometric quantities in the velocity law for the surface. One of the numerical methods is proved to be convergent in the H^1 norm with optimal-order for finite elements of degree at least two. We present numerical experiments illustrating the convergence behaviour and demonstrating the qualitative properties of the flow: preservation of mean convexity, loss of convexity, weak maximum principles, and the occurrence of self-intersections.

Research on Uniaxial Compression Mechanics of Diorite under Flowing Acidic Solution Scouring

The bedrock used for underground construction has obvious traces of hydrodynamic scouring damage, and the mechanical properties of bedrock especially are severely damaged under a groundwater environment. On this basis, considering the excavated bedrock under various saturations, the uniaxial compression test of diorite is carried out. Meanwhile, scanning electron microscopy (SEM), electron energy spectroscopy (EDS) and X-ray diffraction (XRD) are used in the experiment. The variation law of the elastic p-wave velocity and microstructure and the response characteristics of the strength, deformation and mechanical parameters of rock under different flow rates and pH values are analyzed in detail. The results indicate that: (1) Saturations with a faster flow rate and lower pH value cause greater relative changes in the elastic longitudinal wave velocity of the samples. (2) The uniaxial compressive strength of the samples under various treatment conditions showed a decreasing trend. Compared with the dried samples, the uniaxial compressive strength of the samples under saturation with field flow rate v = 300 mm·s−1 and pH = 1 decreased by 46.08%, and the strength decreased by 35.67% under saturation with a field pH value = 6.56 and flow rate v = 900 mm·s−1. (3) The saturation with a stronger acidity, greater flow rate and longer action time causes the apparent dense structure of the diorite sample to be loose and accompanied by microcracks, which weakens its macromechanical properties. (4) Acid and hydrodynamic saturation produce water–rock chemical and physical effects on diorite, which weaken the connection force between mineral particles and the friction between fracture surfaces, reduce the elastic modulus, increase Poisson’s ratio and accelerate the failure of diorite.

Research on AUV Energy Saving 3D Path Planning with Mobility Constraints

This paper aims to focus on the path planning problem of AUV in the marine environment. As well as considering the path length and safe obstacle avoidance, ocean currents should not be ignored as the main factor affecting the navigation energy consumption of AUV. At the same time, the path should satisfy the mobility constraint of AUV; otherwise, the path is inaccessible to AUV. For the above problems, this paper presents a path planning algorithm based on an improved particle swarm (EPA-PSO); the fitness function is designed based on path length, energy consumption, and mobility constraints. The updated law of particle velocity and the initialization law of particles are improved, and the possible optimal solutions are stored in the feasible solution set; finally, the optimal solutions are obtained by comparison. The local jumping ability is given to the particle swarm so that the particles can jump out of the local optimal solution. The path planning simulation experiment is compared with the traditional PSO algorithm. The results show that the EPA-PSO algorithm proposed in this paper can be used in the AUV three-dimensional path planning process. It can effectively save energy and make the navigation path of AUV satisfy the requirements of maneuverability. The field experiment was completed in Shanghai, China, and the experiment proved that it was feasible to obtain a path satisfying the maneuverability constraints with optimal energy consumption for the problems studied in this paper.

Investigation of acoustic characterization of ultrasonic air coupling testing of NEPE propellant under strain control

To explore the acoustic characterization of composite solid propellant materials, the wave equation of the viscoelastic body was derived based on the linear viscoelastic constitutive model, and the theoretical relationship between ultrasonic sound velocity and attenuation coefficient, which are closely related to mechanical properties, such as elastic modulus, viscosity coefficient, and complex modulus, was obtained. Ultrasonic air-coupled testing experiments of the NEPE (Nitrate Ester Plasticized Polyether) propellant under different tensile strain states were carried out to obtain the variation law of ultrasonic transmission wave peak amplitude, sound velocity, and attenuation coefficient with strain variables in combination with the variation in propellant porosity under tensile strain. Furthermore, the acoustic parameters with strain and porosity were fitted by the regression equation, and the effect of mesoscopic damage on macroscopic mechanical properties was analyzed. The results show that with the increase in NEPE propellant tensile strain, the porosity increases exponentially. With the increase in porosity, the sound velocity decreases by first polynomials, the wave amplitude decreases by second polynomials, and the attenuation coefficient increases by third polynomials.

Quantitative dislocation multiplication law for Ge single crystals based on discrete dislocation dynamics simulations

This is the first report of a quantitative dislocation multiplication law for Ge single crystals based on discrete dislocation dynamics simulations. The multiplication was studied as a function of dislocation density and effective shear stress in periodic boundary conditions close to melting point of Ge, utilizing a specifically developed diamond cubic dislocation mobility module in agreement with experiments in literature. We report an average dislocation velocity law of a dislocation ensemble linearly proportional to the resolved shear stress – analogous to the single dislocation velocity law – with a reduced average dislocation mobility. Exponential dislocation multiplication was observed with a multiplication parameter δ linear proportional to the effective shear stress for various stress states and simulation volumes. The coefficient of the dislocation multiplication law was determined to be 4.0 ⋅10−3 [mN−1].

Numerical Simulation of Fluid Flow in Carbonate Rocks Based on Digital Rock Technology

Strong heterogeneity, low matrix permeability, and complex oil–water interaction make the fluid flow in carbonate rocks extremely complicated. In this study, we quantitatively characterize and simulate single-phase and multiphase flows with multiscale pore–vug–fracture structures involved in the carbonate reservoir developments. The main studies and conclusions include: (i) The CT technology is utilized to characterize the pores, fractures, and vugs of carbonate cores at multiple scales. It is found that even if the CT resolution reaches 0.5 μm, the pores of the core are still unconnected as a network, indicating that the carbonate matrix is particularly tight. The existence of fractures can increase the effective permeability, and even poorly connected fractures can significantly increase the permeability because it reduces the flow distance through the less permeable matrix. (ii) A numerical model of low-porosity strongly heterogeneous carbonate rocks was constructed based on digital image processing. Simulations of single-phase fluid flow under reservoir conditions were conducted, and the effects of surrounding pressure, pore pressure, and core size on the single-phase flow were investigated. Due to the strong heterogeneity of carbonate rocks, the pores, vugs, and fractures cause local preferential flow and disturbance within the core, which significantly affects the fluid flow path and the pressure distribution in the core. The overall permeability is a composite representation of the permeability of numerous microelements in the specimen. Permeability increases with an increasing pore pressure, and it decreases with increasing circumferential pressure. (iii) The gas–water two-phase flow model of a low-porosity strongly heterogeneous carbonate rock was established based on digital image processing. The variation law of the two-phase outlet flow velocity with the inlet gas pressure and the movement law of the two-phase interface of carbonate rock samples were obtained. Under certain surrounding pressure, the outlet gas velocity is larger than the outlet water velocity; with the increase of the inlet gas pressure, the pore space occupied by the gas phase in the rock becomes larger. With the increase of the surrounding pressure, the velocities of both outlet gas and water decrease. As the sample size decreases, the velocities of both outlet gas and water increase.

Influence of sample thickness and cross-sectional area on flexoelectric effect under one-dimensional impact

The shock wave generates the strain gradient and consequent electric polarization in samples due to the flexoelectric effect during the impact process. At present, some scholars have studied the influence law of different impact velocities, but the influence of different thickness and cross-sectional area of samples on flexoelectric effect is still blank. In this letter, we have studied the voltage variation of barium titanate samples with different thickness and cross-sectional area under a certain impact velocity. The results show that the maximum voltage value caused by flexoelectric effect increases as the thickness increases, which is basically in positive proportion; it decreases with the increase of diameter, which is in inverse proportion. This research will lay a theoretical foundation for the fabrication of flexoelectricity sensor.