A novel approach to the dynamic response analysis of Euler-Bernoulli beams resting on a Winkler soil model and subjected to impact loads

This work presents a novel approach to the dynamic response analysis of a Euler-Bernoulli beam resting on a Winkler soil model and subjected to an impact loading.The approach considers that damping has much less importance in controlling the maximum response to impulsive loadings because the maximum response is reached in a very short time,before the damping forces can dissipate a significant portion of the energy input into the system.The development of two sine series solutions,relating to different types of impulsive loadings,one involving a single concentrated force and the other a distributed line load,are presented.This study revealed that when a simply supported Euler-Bernoulli beam,resting on a Winkler soil model,is subject to an impact load,the resulting vertical displacements,bending moments and shear forces produced along the span of the beam are considerably affected.In particular,the quantification of this effect is best observed,relative to the corresponding static solution,via an amplification factor.The computed impact amplification factors,for the sub-grade moduli used in this study,were in magnitude greater than 2,thus confirming the multiple-degree-of-freedom nature of the problem.

Mechanical behavior and failure mechanisms of rock bolts subjected to static-dynamic loads

This study explores the effects of dynamic and static loading on rock bolt performance a key factor in maintaining the structural safety of coal mine roadways susceptible to coal bursts.Employing a housemade load frame to simulate various failure scenarios,pretension-impact-pull tests on rock bolts were conducted to scrutinize their dynamic responses under varied static load conditions and their failure traits under combined loads.The experimental results denote that with increased impact energy,maximum and average impact loads on rock bolts escalate significantly under pretension,initiating plastic deformation beyond a certain threshold.Despite minor reductions in the yield load due to impactinduced damage,pretension aids in constraining post-impact deformation rate and fluctuation degree of rock bolts.Moreover,impact-induced plastic deformation causes internal microstructure dislocation,fortifying the stiffness of the rock bolt support system.The magnitude of this fortification is directly related to the plastic deformation induced by the impact.These findings provide crucial guidance for designing rock bolt support in coal mine roadway excavation,emphasizing the necessity to consider both static and dynamic loads for improved safety and efficiency.

Influence of railway wheel tread damage on wheel-rail impact loads and the durability of wheelsets

Dynamic wheel-rail contact forces induced by a severe form of wheel tread damage have been measured by a wheel impact load detector during full-scale field tests at different vehicle speeds.Based on laser scanning,the measured three-dimensional damage geometry is employed in simulations of dynamic vehicle-track interaction to calibrate and verify a simulation model.The relation between the magnitude of the impact load and various operational parameters,such as vehicle speed,lateral position of wheel-rail contact,track stiffness and position of impact within a sleeper bay,is investigated.The calibrated model is later employed in simulations featuring other forms of tread damage;their effects on impact load and subsequent fatigue impact on bearings,wheel webs and subsurface initiated rolling contact fatigue of the wheel tread are assessed.The results quantify the effects of wheel tread defects and are valuable in a shift towards condition-based maintenance of running gear,and for general assessment of the severity of different types of railway wheel tread damage.

CONVOLUTION OF THE IMPACT THREE-DIMENSIONAL ELASTO-DYNAMICS AND DYNAMIC STRESS INTENSITY FACTOR FOR AN ELLIPTIC CRACK

This paper presents a formulation for three-dimensional elasto-dynamics with an elliptic crack based on the Laplace and Fourier transforms and the convolution theorem. The dynamic stress intensity factor for the crack is determined by solving a Fredholm integral equation of the first kind. The results of this paper are very close to those given by the two-dimensional dual integral equation method.

Experimental study on dynamic mechanical property of cemented tailings backfill under SHPB impact loading

Cemented tailings backfill(CTB) have increasingly been used in recent years to improve the stability of mining stopes in deep underground mines. Deep mining processes are often associated with rock bursting and high-speed dynamic loading conditions. Therefore, it is important to investigate the characteristics and dynamic mechanical behavior of CTB. This paper presents the results of dynamic tests on CTB specimens with different cement and solid contents using a split Hopkinson pressure bar(SHPB). The results showed that some CTB specimens exhibited one to two lower stress peaks after reaching dynamic peak stress before they completely failed. The greater the cement-to-tailings ratio is, the more obvious the strain reaction. This property mainly manifested as follows. First,the dynamic peak stress increased with the increase of the cement-to-tailings ratio when the impact velocity was fixed. Second, the dynamic peak stress had a quadratic relationship with the average stress rate. Third, the cement-to-tailings ratio could enhance the increase rate of dynamic peak stress with strain rate. In addition, the dynamic strength enhancement factor K increased with the increase of strain rate, and its value was larger than that of the rock samples. The failure modes of CTB specimens under low-speed impact were tensile failure and X conjugate shear failure, where were nearly the same as those under static uniaxial and triaxial compression. The CTB specimens were crushed and broken under critical strain, a failure mode similar to that of low-strength concrete. The results of the experimental research can improve the understanding of the dynamic mechanical properties of CTB and guide the strength design of deep mining backfills.

Dynamic caustics test of blast load impact on neighboring different cross-section roadways

Using digital laser dynamic caustics experimental system and conducting simulation experiment researched the influence rule of blasting excavation of a new roadway on neighboring existed different cross-section roadways. The experimental results show that the influence of blast load on adjacent roadway has a good relationship with the cross-section of roadway. The expansion distance of precrack existed in circular, arch-wall, rectangular roadway is respectively 1.76, 1.61 and 0 cm under blast load.At the same time, the direct-blast side of rectangular roadway has more obvious damage compared with circular and arch-wall roadway. It explains that plane reflects more stress wave than arc, so that it exerts more tensile failure in the direct-blast side, which leads to less stress wave diffracting to the precrack in the back-blast side. When the precrack extends, higher value dynamic stress intensity factor in circular roadway works longer than that of arch-wall roadway. Indirectly, it explains that plane's weakening function on stress wave is significantly stronger than arc. Stress wave brings about self-evident influence on the upper and bottom endpoints of the rectangular roadway, and it respectively extends 1.03, 2.06 cm along the line link direction of the center of the blasthole and the upper and bottom endpoints on the right wall.

Evaluation of vertical impact factor coefficients for continuous and integral railway bridges under high-speed moving loads

In the railway bridge analysis and design method,dynamic train loads are regarded as static loads enhanced by an impact factor(IF).The IF coefficients for various railway bridges have been reported as a function of span length or frequency of the bridges in Eurocode(2003).However,these IF coefficient values neglect the effects of very high speeds(>200 km/h)and soil-structure interaction(SSI).In this work,a comprehensive study to assess the impact factor coefficients of mid-span vertical displacements for continuous and integral railway bridges subjected to high-speed moving loads is reported.Three different configurations,each for the three-dimensional(3D)continuous and integral bridge,are considered.Also,single-track(1-T)and two-track(2-T)“real train”loading cases for both these bridge types are considered.Subsequently,finite element analysis of the full-scale 3D bridge models,to identify their IF values,considering the effects of SSI for three different soil conditions,is conducted.The IF values obtained from the study for both bridge types are comparable and are greater than the values recommended by Eurocode(2003).The results reveal that with a loss of soil stiffness,the IF value reduces;thus,it confirms the importance of SSI analysis.

Mesoscopic modelling of UHPCC material under dynamic tensile loadings

This paper presents a new 3D mesoscopic model of ultra-high performance cement-based composite(UHPCC)to investigate its dynamic tensile behavior.In this model,the UHPCC is regarded as a two-phase material composed of cementitious matrix and randomly distributed fibers.The model is established using the commercial software LS-DYNA and involves generating the randomly distributed fiber elements with considerations of diameter,length,orientation and volume fraction,and then fully constraining them with the matrix.In particular,to capture the slipping effect between fibers and matrix that has a strong influence on the dynamic tensile behavior,the fibers are modelled by a fictitious material represented by the load-slip relation.The strain-rate effect of slipping force neglected in most of previous studies is considered by calibrating constitutive parameters of the fictitious material under different strain-rates based on the single fiber pullout tests.Finally,the 3D mesoscopic model is validated against three sets of tension-dominated experiments covered a wide range of loading intensity.Numerical predictions demonstrate that strain-rate effect of slipping force must be considered,and the neglect of it may lead to a great underestimation of the dynamic tensile strength of UHPCC material and would unavoidably underestimate the blast resistance of UHPCC components.

Dynamic reliability analysis of supercavity vehicle with stochastic parameters under impact loads

With dynamic reliability problems of stochastic parameters,supercavity vehicle is subject to impact loads.The supercavity vehicle is modeled by using eight-node super-parametric shell elements.The tail impact loads of supercavity vehicle structures are simplified into two stationary random processes with a certain phase difference,and the random excitations are transformed into sinusoidal ones in terms of the pseudo excitation method.The stress response of stochastic structure can be obtained through combining Newmark method with pseudo excitation perturbation method,and then all required digital features for dynamic reliability of supercavity vehicle have be calculated.The expressions of the mean value and the variance of dynamic reliability of supercavity vehicle with stochastic parameters are educed on the basis of the Poisson formula of calculating dynamic reliability.Finally,the influence of the randomness of structural parameters on the dynamic reliability is analyzed.And the feasibility and availability of this method were validated by comparing with the Monte Carlo method.

Dynamic response characteristics of dry and watersaturated schist under impact loading

Many geological engineering hazards are closely related to the dynamic mechanical properties of rock materials.However,most existing studies on the dynamic mechanical properties of rock materials were conducted on the hard rocks such as sandstone,granite,limestone,and marble,whereas soft rocks,such as schist,are less studied.Therefore,in this study,a series of triaxial impact tests were conducted on dry and saturated schist by employing a modified triaxial split Hopkinson pressure bar system to reveal the coupling effects of water,strain rate,and triaxial confining pressure on the mechanical properties of schist.The results show that schist is a type of watersensitive rock and the stress-strain curve of saturated schist has apparent ductility.The effects of strain rate on dynamic strain,deformation modulus and peak stress were analyzed.The results also show that the dynamic peak stress is affected by the combined softening effect and viscous effect of water under impact loading.Finally,it was found that the failure mode of schist belongs to typical axial tensile failure under uniaxial impact tests,and shear failure is the main failure mode under triaxial impact tests.With the increase in confining pressure,the failure modes of schist change from tensile failure to shear failure.This research can provide useful parameters for geological engineering hazard prevention in mountain areas.

Experimental study on dynamic load magnification factor for ballastless track-subgrade of high-speed railway

The magnitude of dynamic load produced by high-speed trains depends on many factors,of which train speed is the most critical one.However,it is quite difficult to determine the effect of train speed on dynamic load using the theoretical methods due to the complexity of the interaction between vehicle and track-subgrade.Thus large-scale model test has gradually become an important approach for studying dynamic responses of ballastless track-subgrade of high-speed railway.In this study,a full-scale model of ballastless track-subgrade was constructed in accordance with the design and construction standards for Shanghai-Nanjing intercity high-speed railway line firstly.Then,the dynamic strain of slab and the dynamic earth pressure of subgrade were measured by conducting single wheel axle excitation test.In addition,the relationship between the dynamic load magnification factor（DLF） and the train speed was obtained.Finally,the DLF of track-subgrade under different train speeds was proposed,similar to that given by German Railway Standard.

Dynamic fracture behavior of rock under impact load using the caustics method

We studied the dynamic fracture mechanical behavior of rock under different impact rates. The fracture experiment was a three-point bending beam subjected to different impact loads monitored using the reflected caustics method. The mechanical parameters for fracture of the three-point bending beam specimen under impact load are analyzed. The mechanism of crack propagation is discussed. Experimental results show that the dynamic stress intensity factor increases before crack initiation. When the dynamic stress intensity factor reaches its maximum value the crack starts to develop. After crack initiation the dynamic stress intensity factor decreases rapidly and oscillates. As the impact rate increases the cracks initiate earlier, the maximum value of crack growth velocity becomes smaller and the values of dynamic stress intensity factor also vary less during crack propagation. The results provide a theoretical basis for the study of rock dynamic fracture.

EFFECT OF GEAR WIDTH AND HELIX ANGLE ON FACTOR OF DYNAMIC LOAD OF DOUBLE CIRCULAR ARC HELICAL GEARING

Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.

Dynamic response analysis of blocks-combined dam under impact load

In order to reduce the damage of ordinary gravity dam impacted by boulders in debris flow,a blocks-combined dam based practical project is proposed.The dynamic response of the proposed dam under impact load is investigated by using ABAQUS finite element software.Considering the impact velocity and impact height,the anti-impact performance of blocks-combined dam is discussed in terms of deformation,displacement,impact force,acceleration,and energy,and is compared with that of ordinary dam.Results show that the displacement,impact force and acceleration of dam increase with the increase of impact velocity and height.The impact energy of blocks-combined dam is mainly absorbed and consumed by the friction between the component interfaces,which is related to the location of impact point.Compared with the ordinary gravity dam,the blocks-combined dam has better impact resistance to boulders in debris flow.

Dynamic response of cylindrical cavity to anti-plane impact load by using analytical approach

The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.

Dynamic Impact Factor Induced by Idling Vehicle-Bridge Coupling Vibration

To analyze the impact effect induced by vehicle-bridge coupling vibration during traffic congesting, hundreds and thousands of congestion scenarios consisting of various vehicle platoons were collected and used to develop vehicle models as well as traffic congestion load models. Furthermore, the idling vehicle-bridge coupling model was established by the finite element method and the congestion models were applied to calculate dynamic impact factors. Compared with the value specified in Chinese codes, the calculated values were 1.15-2.67 times as large as the latter, which indicates the impact factors caused by idling vehicle-bridge coupling under congestion situations were much larger than those in normal traffic conditions. As a result, a calibration factor of 1.7 was recommended for bridge design or evaluation when considering vehicle-bridge coupling vibration under heavy traffic congestion. The proposed analytical model, analysis method, and results could also be beneficial references to further investigation in this field.

Dynamic Failure Model of Thin Coal and Rock Mass under Uniform Impact Load

During the excavation of deep coal and rock mass, the radial stress of the free face changes from three-dimensional compression state to two-dimensional stress, bearing the combined action of dynamic disturbance and static load at the same time. With that, many mines suffer from dynamic disasters, such as coal and gas outburst, rock burst and rock caving during deep mining excavation, which is often accompanied by plate crack, spalling and other disasters, seriously affecting the stability of stope and roadway. Taking thin rectangular coal and rock mass as the research object, the dual equation of the free vibration was derived and the exact solution model of the free vibration was established with the use of Hamilton dual system. Based on the action characteristics of the uniform impact load, the effective mode of the forced vibration was obtained by using the Duhamel integral principle and the orthogonality of the mode function. Based on the third strength theory and the numerical simulation results, the dynamic damage process and development trend of coal and rock mass were analyzed under uniform impact load. It was concluded that the starting position of dynamic damage can be judged by the first order main mode, and the development direction and trend of the damage can be judged by the fifth and sixth order main modes. It was concluded that the vibration mode functions of coal and rock mass with four side fixed (C-C-C-C), the two sides fixed and simply supported on the other (S-C-S-C) are mainly composed of three modes that are the first order (dominant frequency), the fifth order and the sixth order, from which the dynamic damage mechanism is preliminarily studied.

THE DYNAMIC COMPUTATION OF CLOSED CYLINDRICAL SHELL UNDER IMPACT LOAD

This article discusses the dynamic computation of the closed cylindrical shell under impact load. In the text we analyse the changes of the momenta and the energy on each stage in the impact process, take into account the effect of the mass of impact object and the system of the closed cylindrical shell by impact, and transform the distributed mass of the whole cylindrical shell into an only concentrated 'equivalent mass' by the method of reduced mass. Consequently we derive the dynamic factor of the closed cylindrical shell due to impact load.The method proposed in this paper is of practical worth and is more convenient in calculations.

Long-term mechanical behavior and characteristics of cemented tailings backfill through impact loading

Cemented tailings backfill(CTB)structures are important components of underground mine stopes.It is important to investigate the characteristics and dynamic behavior of CTB materials because they are susceptible to disturbance by dynamic loading,such as excavation and blasting.In this study,the authors present the results of a series of Split-Hopkinson pressure bar(SHPB)single and cyclic impact loading tests on CTB specimens to investigate the long-term dynamic mechanical properties of CTB.The stress-strain relationship,dynamic strength,and dynamic failure characteristics of CTB specimens are analyzed and discussed to provide valuable conclusions that will improve our knowledge of CTB long-term mechanical behavior and characteristics.For instance,the dynamic peak stress under cyclic impact loading is approximately twice that under single impact loading,and the CTB specimens are less prone to fracture when cyclically loaded.These findings and conclusions can provide a new set of references for the stability analysis of CTB materials and help guide mine designers in reducing the amount of binding agents and the associated mining cost.

Test and numerical investigations on static and dynamic characteristics of extra-wide concrete self-anchored suspension bridge under vehicle loads

The present work is aimed at studying the mechanic properties of the extra-wide concrete self-anchored suspension bridge under static and dynamic vehicle loads. Based on the field test using 12 heavy trucks and finite element simulations, the static deformations of different components, stress increments and distributions of the girder, as well as the vibration characteristics and damping ratio of the Hunan Road Bridge were analyzed, which is the widest self-anchored suspension bridge in China at present. The dynamic responses were calculated using the Newmark-β integration method assisted by the simulation models of bridge and vehicles, the influences on the dynamic impact coefficient(DIC) brought by the vehicle parameters, girder width, eccentricity travel and deck flatness were also researched. The spatial effect of the girder is obvious due to the extra width, which performs as the stress increments distribute unevenly along the transverse direction, and the girder deflections and stress increments of the upper plate change as a "V" and "M" shape respectively under the symmetrical vehicle loads affected by the shear lag effect, cross slope and local effect of the wheels, the maximum of stress increments are located in the junctions with the inner webs. The obvious girder torsional deformation and the apparent unevenness of the hanger forces between the two cable planes under the eccentric vehicle loads, together with the mode shapes such as the girder transverse bending and torsion which appear relatively earlier, all reflect the weakened torsional rigidity of the extra-wide girder. The transverse displacements of towers are more obvious than the longitudinal ones. As for the influences on the DIC, the static effect of the heavier vehicles plays a major role when pass through with a higher speed and the changes of vehicle suspension stiffness generate greater impacts than the suspension damp. The values of DIC in the vehicle-running side during the eccentric travel, affected by the restricts from the static effects of the eccentric moving trucks, are significantly smaller than the vehicle-free side, the increase in the road roughness is the most sensitive one among the above influential factors. The results could provide references for the design, static and dynamic response analysis of the similar extra-wide suspension bridges.