Shock Wave Theory Research Articles

Study on Queue Length in the Whole Process of a Traffic Accident in an Extra-Long Tunnel

To investigate traffic accident patterns in undersea tunnels and quantify the relationship among various factors and traffic accidents in undersea tunnels, we analyzed the rules of evolution during the entire process of vehicle congestion queuing. Additionally, we built a maximum queue-length estimation model based on shock-wave theory and a whole-process queue-length estimation model based on real-time data input. The results demonstrate that the model is most precise when the data are not smoothed and the time interval is 30 s. The maximum accuracy of the model is not improved by data smoothing processing, but it is substantially improved when the time interval is between 5 and 15 s. Various movable window lengths have no discernible effect on the results. Maximum queue-length estimation model accuracy is 92.34%, while real-time whole-process queue-length estimation model accuracy is 83.50%. The accuracy of the proposed model is greater than that of the input–output model, indicating that the proposed model can support timely and reasonable control measures.

Predictive Cruise Control Under Cloud Control System for Urban Bus Considering Queue Dissipation Time

The driving conditions of urban consecutive signalized intersections are one of the main research scenarios for vehicle speed trajectory optimization, and typical for bus driving, where frequent acceleration and deceleration before and after the intersection can intensify the energy consumption of the bus. Prior research has predictive cruise controlled under Intelligent Transportation System, which is not feasible to directly communicate with controllers' units of Intelligent Connected Vehicles. Besides, the effect of queue dissipation is a topic that has received less attention in recent related work. Therefore, this paper proposes a vehicle-cloud hierarchical architecture based on Cloud Control System at first, under which a predictive cruise control for urban buses is deployed. Given the impact of intersection queue length and dissipation time on vehicle driving, a queue dissipation time estimation model based on shockwave theory is proposed to predict changes in intersection traffic state. The queue dissipation time equivalent to the extension of the red-light window is reflected in the constraints of the Receding Distance Horizon Dynamic Programming (RDHDP) algorithm for solving the optimal control problem. Eventually, comparison simulations, a segment of realistic trip between adjacent stops, are presented. The results show that the proposed method saves 44.94%-56.74% of energy consumption and at least 26.8s of waiting time compared to human drivers, and 22.72%-41.27% of energy consumption compared to vehicle with the Intelligent Vehicle Infrastructure Cooperative Systems.

Bi-level ramp merging coordination for dense mixed traffic conditions

Connected and Autonomous Vehicles (CAVs) hold great potential to improve traffic efficiency, emissions and safety in freeway on-ramp bottlenecks through coordination between mainstream and on-ramp vehicles. This study proposes a bi-level coordination strategy for freeway on-ramp merging of mixed traffic consisting of CAVs and human-driven vehicles (HDVs) to optimize the overall traffic efficiency and safety in congested traffic scenarios at the traffic flow level instead of platoon levels. The macro level employs an optimization model based on fundamental diagrams and shock wave theories to make optimal coordination decisions, including optimal minimum merging platoon size to trigger merging coordination and optimal coordination speed, based on macroscopic traffic state in mainline and ramp (i.e., traffic volume and penetration rates of CAVs). Furthermore, the micro level determines the real platoon size in each merging cycle as per random arrival patterns and designs the coordinated trajectories of the mainline facilitating vehicle and ramp platoon. A receding horizon scheme is implemented to accommodate human drivers’ stochastics as well. The developed bi-level strategy is tested in terms of improving efficiency and safety in a simulation-based case study under various traffic volumes and CAV penetration rates. The results show the proposed coordination addresses the uncertainties in mixed traffic as expected and substantially improves ramp merging operation in terms of merging efficiency and traffic robustness, and reducing collision risk and emissions, especially under high traffic volume conditions.

On the Theory of Shock Waves in Isotropic Hardening Plastic Media

Based on the thermomechanical model of plastic deformation of an elastically compressible isotropic hardening medium, the system of relations for describing plastic shock waves of finite amplitude is obtained, which satisfies the maximum entropy production principle at the front of strong discontinuity. A classification of admissible shock-wave transitions is performed within the framework of the model of isotropic hardening under the von Mises plasticity condition.

On the accuracy of one-way approximate models for nonlinear waves in soft solids.

Simple strain-rate viscoelasticity models of isotropic soft solid are introduced. The constitutive equations account for finite strain, incompressibility, material frame-indifference, nonlinear elasticity, and viscous dissipation. A nonlinear viscous wave equation for the shear strain is obtained exactly and corresponding one-way Burgers-type equations are derived by making standard approximations. Analysis of the travelling wave solutions shows that these partial differential equations produce distinct solutions, and deviations are exacerbated when wave amplitudes are not arbitrarily small. In the elastic limit, the one-way approximate wave equation can be linked to simple wave theory and shock wave theory, thus, allowing direct error measurements.

Investigation of Formation Process and Intensity of Coal and Gas Outburst Shockwave

The shock wave of a coal and gas outburst is a high-pressure and high-speed impact airflow formed rapidly after the outburst. The propagation destroys the ventilation facilities and causes the destruction of the ventilation system. The theoretical research on the outburst shock wave is of great significance. In order to deeply understand the formation mechanism of the outburst shock wave, this paper draws on the shock wave theory to theoretically analyze the microscopic formation process of the outburst shock wave. The main difference between the formation process of a coal and gas outburst shock wave and the formation process of a general shock wave is that the outburst shock wave has a solid–gas flow zone in the high-pressure zone. The calculation formulas of pressure, density, temperature and other parameters before and after the outburst shock wave are derived. After the outburst shock wave passes through, the pressure, temperature and density of the roadway air will change suddenly. The relationship expression between outburst gas pressure and outburst shock wave intensity is derived, which can reflect the role of pulverized coal in the formation process of a shock wave. In order to facilitate the understanding and calculation, the concept of equivalent sound velocity of coal-gas flow is proposed, and the direct calculation of the impact strength of a coal and gas outburst is attempted. This paper is helpful to improve the understanding of the essence of a coal and gas outburst shock wave. It is also of great significance to outburst disaster relief.

Dynamic crushing characteristics of bio-inspired minimal surface primitive structures

It has been proven that the triply periodic minimal surface structures (TPMS), a specific type of bio-inspired structures classified as cellular structures with continuous non-self-intersecting surfaces, have excellent energy absorption capability. However, the dynamic crushing characteristics of the TPMS have not been well comprehended. The dynamic response of minimal surface primitive structures under different crushing speeds is numerically investigated in this study. The dynamic crushing stresses of the primitive structure at the loading location and stationary side are measured to investigate the dynamic effect due to the shock wave propagation. Furthermore, the influences of other parameters, i.e., the crushing speed, relative density, and strain rate effect on the crushing stress are also discussed. The obtained results indicate that the plateau stress at the loading location is highly sensitive to the crushing speed while the opposite trend is observed for the plateau stress at the stationary side. It is also found that the primitive structures tend to deform following four distinct mode shapes, i.e., “X” mode, “K” mode, “I1” and “I2” mode, which are dependent on the crushing speed and relative density. Moreover, the energy absorption efficiency is used to define the densification strain, which shows no clear relationship with the relative density. Finally, the empirical models based on the shock wave theory and previous empirical model of honeycomb structures are developed to predict the plateau stress at the loading location and stationary side with/without strain rate effect. The predictions of the proposed analytical models agree well with the numerical results.

Analysis of dynamic processes in the impact system of drilling machines

Modern drilling machines designed for the destruction of rocks have a diverse structure, various performance characteristics and in most cases a well-defined limited scope of application. The most common for the destruction of rocks of high strength are impact drilling machines. One of the most effective ways to increase the productivity of such machines is to find rational geometric parameters of colliding elements. The article proposes and substantiates a methodology for studying shock systems based on the application of the shock wave theory. According to the calculation results, the parameters and design solutions of the elements of drilling machines are given, the use of which will allow to increase productivity and reduce energy consumption for the destruction of rock.

High Time-Resolution Queue Profile Estimation at Signalized Intersections Based on Extended Kalman Filtering

The dynamic spatiotemporal characteristics of queues at urban intersections are crucial to traffic operation tasks such as signal performance measure and signal optimization. This paper addresses the high time-resolution estimation of queue profile at urban signalized intersection using Extended Kalman Filtering (EKF) with data of connected vehicles (CVs). The main features of this work are as follows: (i) a machine learning method was applied to construct a dynamic shockwave propagation model based on shockwave theory and historical data of CVs; (ii) a heuristic approach was proposed to measure the shockwave speed for use in EKF; (iii) an urban queue estimator was designed to combine the dynamic shockwave propagation model and real-time shockwave information via EKF to deliver second-by-second queue profile estimates. The queue estimator does not require any priori information about vehicle arrival patterns and the market penetration rate (MPR) of CVs. The performance and robustness of the queue estimator were evaluated using both simulation and real-world CV data. The results show that the method can provide satisfactory queue estimation results at various MPR levels of CVs, with the estimation error of 2.5 vehicles at the MPR of 5%, and of 0.5 vehicle at the MPR of 40%.

Integrated macro-micro modelling for individual vehicle trajectory reconstruction using fixed and mobile sensor data

Vehicle trajectories can provide a clear picture of the traffic flow that plays a pivotal role in traffic management and control. Two types of traffic sensors, i.e., fixed and mobile sensors, are widely adopted to collect road traffic information. However, fully-sampled vehicle trajectories are far from obtainable through those sensors due to their fixed-location measurements or low penetration rates. To overcome these issues, this study proposes an integrated macro–micro framework to reconstruct individual vehicle trajectories on freeways under a multi-source data environment, in which fixed-location sensor data that collect positions and velocities of vehicles in a certain place and a small fraction of probe vehicle (PV) data that yield continuous trajectories are available. The framework consists of three modules. First, at the macro level, we apply shockwave theory and fundamental diagram to expand the partially detected information to the whole space–time diagram, and then establish a velocity baseline for evaluation of the trajectory fusion thereafter. Second, at the micro level, we develop two trajectory estimation algorithms based on extended car-following models to generate individual trajectories between any two consecutive PVs, in which two candidate trajectories will be generated for each non-probe vehicle. Third, we tailor a trajectory fusion algorithm to integrate the macro- and micro-level models, and apply dynamic programming to solve the optimal trajectories as per the established velocity baseline. The proposed framework is finally tested with NGSIM and HighD datasets. The results show that our integrated method attains a notable improvement in accuracies and smoothness of reconstructed trajectories compared to the non-integrated and the classical Variational Theory-based methods respectively.

Research on the Influence of Impedance-Layer Changes on the Protective Properties of Wave-Impedance Materials under Hypervelocity Impact

The hypervelocity impact of space debris causes damage or destruction to spacecraft. The continuous damage caused by space debris creates greater requirements for protective materials. Wave-impedance gradient-protection material is a new type of space-debris-protection material with high kinetic-energy dissipation. However, the relationship between the distribution characteristics of the impedance layer and the protective performance is still unclear. This study provides guidance for the design of high-performance wave-impedance gradient materials by establishing the quantitative relationship between impedance-layer distribution characteristics and protective performance. Based on the one-dimensional shock-wave theory, this paper analyzes the propagation process of shock waves in wave-impedance gradient materials, establishes a transmission model of shock waves with changes in impedance layers, and quantitatively studies the influence of the change in wave impedance on the impact pressure, internal-energy conversion, and projectile- breaking characteristics by means of a numerical simulation. The results show that, when the surface and back of the wave-impedance gradient material are titanium alloy and nylon, respectively, the total transmission coefficient increases from 0.206 to a maximum of 0.339 with the continuous change in the gradient. The reduction amplitude of the shock wave with time under the three working conditions is Ti-Al-Mg-Ny > Ti-Al-Ny > Ti-Ny. The relationship of the transformed internal energy is Ti Al-Mg-Ny > Ti-Al-Ny > Ti-Ny, and the projectile breaking area is Ti-Al-Mg-Ny > Ti-Al-Ny > Ti-Ny. The analysis shows that the continuous change in wave impedance is beneficial to reduce the attenuation of the amplitude of the shock wave in the hypervelocity projectile, to keep the stress amplitude of the shock wave at a higher level, and to improve the internal-energy conversion and impact-breaking degree of the projectile, thereby enhancing the protection performance of the wave-impedance gradient material.

Dynamic Response and Energy Absorption Characteristics of a Three-Dimensional Re-Entrant Honeycomb

In this paper, we design a new three-dimensional honeycomb with a negative Poisson’s ratio. A honeycomb cell was first designed by out-of-plane stretching a re-entrant honeycomb and the honeycomb is built by spatially combining the cells. The in-plane response and energy absorption characteristics of the honeycomb are studied through the finite element method (FEM). Some important characteristics are studied and listed as follows: (1) The effects of cell angle and impact velocity on the dynamic response are tested. The results show that the honeycomb exhibits an obvious negative Poisson’s ratio and unique platform stress enhancement effect under the conditions of low and medium velocity. An obvious necking phenomenon appears when the cell angle parameter is 75°. (2) Based on the one-dimensional shock wave theory, the empirical formula of the platform stress is proposed to predict the dynamic bearing capacity of the honeycomb. (3) The energy absorption in different conditions are investigated. Results show that as the impact velocity increases, the energy absorption efficiency gradually decreases. In addition, with the increase of cell angle, the energy absorption efficiency is gradually improved. The above study shows that the honeycomb has good potential in using in vehicle industry as an energy absorption material. It also provides a new strategy for multi-objective optimization of mechanical structure design.

A predictive model for strain hardening and inertia effect of aluminum tubes filled with aluminum foam

Studies on strain hardening and inertia effect of foam-filled tube (FFT) remain limited. Therefore, this work has conducted mesoscopic finite element analyses on FFTs. The 7075-T651 aluminum alloy is chosen for tube material and the 1100-H14 aluminum is employed for the base material of closed-cell foam. The deformation mechanism of the interaction between tube and foam, and the inertia effect on compressive response of FFTs, are both revealed. Results show that due to the interaction, FFT has a higher compressive stress compared with the sum of empty tube and individual foam under the same mass. As more material is involved, the load-bearing capacity, strain hardening, and interaction stress of FFTs all increase with the relative density of infilled foam. A predictive model is established to predict the compressive stress and strain hardening of FFTs. The load-bearing capacity of tube, the plastic hardening of foam, and the interaction effect between tube and foam are all considered in this model. Moreover, due to the inertia effect, the stress at the impact end is significantly higher than that at the support end under high-velocity impact. The one-dimensional shock wave theory is added to the model, enabling the prediction under high-velocity impact.

Influence Mechanism of Foamed Concrete Coating Thickness on the Blast Resistance of RC Walls.

How to effectively reduce the damage of frequent accidental explosions and explosion attacks to existing walls is an important concern of the blast resistance field. In the present study, the influence of the foamed concrete (density 820 kg/m3, water-cement ratio 0.4) coating thickness on the blast resistance of a 120 mm RC (reinforced concrete) wall was studied through blast experiments, numerical simulations, and shock wave theory. Results show that the influences of foamed concrete on the blast resistance of RC walls are jointly decided by the stress drop caused by impedance effect and exponential attenuation and the stress rise caused by high-speed impact compression. The coating thickness mainly affects the foam concrete’s fragmentation degree and stress attenuation. A lower critical coating thickness exists in foamed concrete-coated RC walls. The blast resistance of the RC wall will decrease when the coating thickness is less than that value. The lower critical coating thickness is related to the intensity of blast load and the energy absorption capacity of foamed concrete, and it can be predicted by monitoring the explosive stress and energy incident to the RC wall.

An Eco-Driving Approach With Flow Uncertainty Tolerance for Connected Vehicles Against Waiting Queue Dynamics on Arterial Roads

Eco-driving incorporating multiple signalized intersections simultaneously has been proven to substantially benefit connected vehicles (CVs) in energy performance. However, ignoring the dynamic variation of waiting queues before downstream intersections may prevent CVs from following the obtained speed profile on security grounds. In this article, the dynamic variation of the waiting queue is modeled and predicted based on shockwave theory and data-driven-based traffic flow prediction. To formulate the waiting queues as additional time-varying constraints for optimization problems, an extended traffic signal model is constructed based on the prediction. Furthermore, a hierarchical optimization framework is proposed, under which the hybrid optimization problem is decomposed into a discrete problem and a continuous one. Monte Carlo simulation demonstrates that if the proposed eco-driving approach is implemented, failure to follow the reference speed profile decreases by 79.4%. Also, the fuel consumption can be saved by over 4% compared with approaches ignoring the waiting queue.

Experimental study on pressure evolution of detonation waves penetrating into water

Propagation of detonation waves crossing the gas–liquid interface is a basic phenomenon worth studying for underwater detonation engines. In this work, the pressure evolution of detonation waves penetrating into water is theoretically and experimentally investigated. The one-dimensional shock wave theory is adopted to solve the pressure–velocity relations of the reflected and transmitted shock wave in different mediums. Experiments under different filling pressure are performed based on a two-phase shock tube system. Theoretical results show that the range of pressure rise ratios between the detonation and transmitted wave is 2.40–2.50. Its trend is determined by the total atoms number of fuel under low filling pressure, but dominated by the ratio of C/H atoms under high filling pressure. Experimental results demonstrate that pressure rise ratios are in good agreement with the theoretical values. There are similar attenuation laws (decay to 50% in 0.3 ms) for subsequent pressure development after those two waves. Under the interface effect, the transmitted wave is stretched and the pressure zone becomes wider. The difference of acoustic impedance between two phases leads to wave property changes at the interface and exit. These changes result in the reciprocating cavitation zones and reformed shock waves in the water, greatly influencing the water pressure.

Dynamic Crushing Analysis of Hexagonal-Kagome Combined Honeycomb with Negative Poisson’s Ratio

To enhance the mechanical performances of traditional honeycombs, a novel combined honeycomb (HKH) was proposed based on the regular hexagonal honeycomb (RHH) and Kagome honeycomb (KH). A systematic investigation of the in-plane dynamic crushing behaviors of the honeycombs was conducted via the finite element method, and the crashworthiness characteristics of the three honeycombs were examined. Using one-dimensional shock wave theory and least squares fitting, a fitting formula of the plateau stress was obtained, and the deformation mechanism of the HKH was determined based on the elastic buckling of the cell wall. The results showed that the HKH exhibited a higher plateau stress than the RHH for any velocity impact, while the negative Poisson’s ratio effect was more significant than that of the KH for low-velocity impacts (the peak Poisson’s ratios of the HKH and KH were −0.312 and −0.286, respectively). Furthermore, the effects of the impact velocity and relative density on the energy absorption and auxetic performances were explored. In this study, a novel design was proposed by combining various cell elements to obtain better crashworthiness, providing a new concept to promote the development of lightweight materials.

A new queue shock wave theory based on platoon dispersion modeling

Statistical platoon dispersion models are developed mainly for traffic flow macro-simulation. While the queueing theory outputs the same delay results as those applied in shock wave theory, the dynamic process of queue forming and dissipating can be simulated only by the latter. Traditional shock wave theory treats traffic flow as a compressible fluid; hence, shock waves form whenever the state of speed–density changes. Similarly, shock waves form because of signal lights when simulating traffic flow with platoon dispersion models. This paper theoretically analyzes the queueing process based on a newly proposed platoon dispersion model, with the assumption that speed follows truncated normal distribution. Besides solving the queueing equations approximately with mathematical methods, an analytical table method is proposed to find the boundary solutions. Application methods are also presented for both static and dynamic scenarios. This theory can be applied to optimize signal timing for queue management, particularly for congestion control.

Discrete Boltzmann modeling of plasma shock wave

Plasma shock waves widely exist and play an important role in high-energy-density environment, especially in the inertial confinement fusion. Due to the large gradient of macroscopic physical quantities and the coupled thermal, electrical, magnetic, and optical phenomena, there exist not only hydrodynamic non-equilibrium (HNE) effects but also strong thermodynamic non-equilibrium (TNE) effects around the wavefront. In this work, a two-dimensional single-fluid discrete Boltzmann model is proposed to investigate the physical structure of ion shock. The electron is assumed inertialess and always in thermodynamic equilibrium. The Rankine–Hugoniot relations for single-fluid theory of plasma shock wave is derived. It is found that the physical structure of shock wave in plasma is significantly different from that in normal fluid and somewhat similar to that of detonation wave from the sense that a peak appears in the front. The non-equilibrium effects around the shock front become stronger with increasing Mach number. The charge of electricity deviates oppositely from neutrality in upstream and downstream of the shock wave. The large inertia of the ions causes them to lag behind, so the wavefront charge is negative and the waverear charge is positive. The variations of HNE and TNE with Mach number are numerically investigated. The characteristics of TNE can be used to distinguish plasma shock wave from detonation wave.

Dynamic deformation of Al under shock loading

The microstructure evolution of single crystal Al under shock loading is investigated using both numerical simulations and shock wave theory. Using momentum mirror method with loading velocity in the range of 0.8 ∼ 1.2 km/s, the results show the generation of a split two-wave structure, in which the (fcc → bcc) transition wave and preceding elastic precursor are connected by the plastic zone. The Hugoniot state of the body-centered phase does not deviate from the theoretical Hugoniot curve considering both the lattice vibration and thermal activation of electrons. The metastable bcc phase would change into fcc phase again once the uniaxial stress is released during the unloading stage. For shock loading tests with piston velocity larger than 1.5 km/s, the shock Hugoniot would enter into melting state. While the impact velocity is larger than 4.0 km/s, solitary wave can propagate stably at the shock front. Further analysis of wave velocity show that the competition between the transition wave propagation and dislocation mobility determines the full development of plastic zone. This new finding suggests that the dynamic response of solids might be tuned by engineering the distribution of microstructures to control the dislocation multiplication.