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.

Reinforcing effects of polypropylene on energy absorption and fracturing of cement-based tailings backfill under impact loading

Polypropylene(PP)fiber-reinforced cement-based tailings backfill(FRCTB)is a green compound material with superior crack resistance and has good prospects for application in underground mining.However,FRCTB exhibits susceptibility to dynamic events,such as impact ground pressure and blast vibrations.This paper investigates the energy and crack distribution behavior of FRCTB under dynamic impact,considering the height/diameter(H/D)effect.Split Hopkinson pressure bar,industrial computed tomography scan,and scanning electron microscopy(SEM)experiments were carried out on six types of FRCTB.Laboratory outcomes confirmed fiber aggregation at the bottom of specimens.When H/D was less than 0.8,the proportion of PP fibers distributed along theθangle direction of80°-90°increased.For the total energy,all samples presented similar energy absorption,reflectance,and transmittance.However,a rise in H/D may cause a rise in the energy absorption rate of FRCTB during the peak phase.A positive correlation existed between the average strain rate and absorbed energy per unit volume.The increase in H/D resulted in a decreased crack volume fraction of FRCTB.When the H/D was greater than or equal to 0.7,the maximum crack volume fraction of FRCTB was observed close to the incidence plane.Radial cracks were present only in the FRCTB with an H/D ratio of 0.5.Samples with H/D ratios of 0.5 and 0.6 showed similar distributions of weakly and heavily damaged areas.PP fibers can limit the emergence and expansion of cracks by influencing their path.SEM observations revealed considerable differences in the bonding strengths between fibers and the FRCTB.Fibers that adhered particularly well to the substrate were attracted together with the hydration products adhering to surfaces.These results show that FRCTB is promising as a sustainable and green backfill for determining the design properties of mining with backfill.

Macro Meso Response and Stress Wave Propagation Characteristics of MCT High-Voltage Switch Under Shock load

In order to study the dynamic and electrical coupling response characteristics of Metal Oxide Semiconductor Controlled Thyristor(MCT)high-voltage switch under the synergic action of mechanical load and high voltage,the separated Hopkinson pressure bar(SHPB)test system was used to simulate different impact load environments,and combined with the multi-layer high-voltage ceramic capacitor charging and discharging system,the instantaneous electrical signals of MCT high-voltage switch were collected.Combined with numerical simulation and theoretical analysis,the failure mode and stress wave propagation characteristics of MCT high voltage switch were determined.The mechanical and electrical coupling response characteristics and failure mechanism of MCT high voltage switch under dynamic load were revealed from macroscopic and microscopic levels.The results show that the damage modes of MCT high-voltage switches can be divided into non-functional damage,recoverable functional damage,non-recoverable damage and structural damage.Due to the gap between the metal gate and the oxide layer,the insulating oxide layer was charged.After placing for a period of time,the elastic deformation of the metal gate partially recovered and the accumulated charge disappeared,which induced the recoverable functional damage failure of the device.In addition,obvious cracks appeared on both sides of the monocrystalline silicon inside the MCT high-voltage switch,leading to unrecoverable damage of the device.

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.

Effect of roughness on the shear behavior of rock joints subjected to impact loading

The shear behavior is regarded as the dominant property of rock joints and is dramatically affected by the joint surface roughness.To date,the effect of surface roughness on the shear behavior of rock joints under static or cyclic loading conditions has been extensively studied,but such effect under impact loading conditions keeps unclear.To address this issue,a series of impact shear tests was performed using a novel-designed dynamic experimental system combined with the digital image correlation(DIC)technique.The dynamic shear strength,deformability and failure mode of the jointed specimens with various joint roughness coefficients(JRC)are comprehensively analyzed.Results show that the shear strength and shear displacement characteristics of the rock joint under the impact loading keep consistent with those under static loading conditions.However,the temporal variations of shear stress,slip displacement and normal displacement under the impact loading conditions show obviously different behaviors.An elastic rebound of the slip displacement occurs during the impact shearing and its value increases with increasing joint roughness.Two identifiable stages(i.e.compression and dilation)are observed in the normal displacement curves for the rougher rock joints,whereas the joints with small roughness only manifest normal compression displacement.Besides,as the roughness increases,the maximum compression tends to decrease,while the maximum dilation gradually increases.More-over,the microstructural analysis based on scanning electron microscope(SEM)suggests that the roughness significantly affects the characteristics of the shear fractured zone enclosing the joint surface.

Damage response of conventionally reinforced two-way spanning concrete slab under eccentric impacting drop weight loading

Reinforced concrete(RC)structures are generally designed to carry quasi-static gravity loads through almost indispensable components namely slab,however,it may be subjected to high intense loads induced from the impact of projectiles generated by the tornado,falling construction equipment,and also from accidental explosions during their construction and service lifespan.Impacts due to rock/boulder falls do occur on the structures located especially in hilly areas.Such loadings are not predictable but may cause severe damage to the slab/structure.It stimulates structural engineers and researchers to investigate and understand the dynamic response of RC structures under such impulsive loading.This research work first investigates the performance of 1000×1000×75 mm^(3)conventionally reinforced two-way spanning normal strength concrete slab with only tension reinforcement(0.88%)under the concentric impact load(1035 N)using the finite element method based computer code,ABAQUS/Explicit-v.6.15.The impact load is delivered to the centroid of the slab using a solid-steel cylindroconical impactor(drop weight)with a flat nose of diameter 40 mm,having a total mass of 105 kg released from a fixed height of 2500 mm.Two popular concrete constitutive models in ABAQUS namely;Holmquist-Johnson-Cook(HJC)and Concrete Damage Plasticity(CDP),with strain rate effects as per fib MODEL CODE 2010,are used to model the concrete material behavior to impact loading and to simulate the damage to the slab.The slab response using these two models is analyzed and compared with the impact test results.The strain rate effect on the reinforcing steel bars has been incorporated in the analysis using the Malvar and Crawford(1998)approach.A classical elastoplastic kinematic idealization is considered to model the steel impactor and support system.Results reveal that the HJC model gives a little overestimation of peak displacement,maximum acceleration,and damage of the slab while the predictions given by the CDP model are in reasonable agreement with the experimental test results/observations available in the open literature.Following the validation of the numerical model,analyses have been extended to further investigate the damage response of the slab under eccentric impact loadings.In addition to the concentric location(P1)of the impacting device,five locations on a quarter of the slab i.e.,two along the diagonal(P2&P3),the other two along the mid-span(P4&P5),and the last one(P6)between P3 and P5,covering the entire slab,are considered.Computational results have been discussed and compared,and the evaluation of the most damaging location(s)of the impact is investigated.It has been found that the most critical location of the impact is not the centroid of the slab but the eccentric one with the eccentricity of 1/6th of the span from the centroid along the mid-span section.

Dynamic response of UHMWPE plates under combined shock and fragment loading

Ultra-high molecular weight polyethylene(UHMWPE)fiber composite has been extensively used to construct lightweight protective structures against ballistic impacts,yet little is known about its performance when subjected to combined blast and fragment impacts.Built upon a recently developed laboratory-scale experimental technique to generate simulated combined loading through the impact of a fragment-foam composite projectile launched from a light gas gun,the dynamic responses of fullyclamped UHMWPE plates subjected to combined loading were characterized experimentally,with corresponding deformation and failure modes compared with those measured with simulated blast loading alone.Subsequently,to explore the underlying physical mechanisms,three-dimensional(3D)numerical simulations with the method of finite elements(FE)were systematically carried out.Numerical predictions compared favorably well with experimental measurements,thus validating the feasibility of the established FE model.Relative to the case of blast loading alone,combined blast and fragment loading led to larger maximum deflections of clamped UHMWPE plates.The position of the FSP in the foam sabot affected significantly the performance of a UHMWPE target,either enhancing or decreasing its ballistic resistance.When the blast loading and fragment impact arrived simultaneously at the target,its ballistic resistance was superior to that achieved when subjected to fragment impact alone,and benefited from the accelerated movement of the target due to simultaneous blast loading.

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.

Constitutive model for concrete subjected to impact loading

To better design and analyze concrete structures, the mechanical properties of concrete subjected to impact loadings are investigated. Concrete is considered to be a two-phase composite made up of micro-cracks and solid parts which consist of coarse aggregate particles and a cement mortar matrix. The cement mortar matrix is assumed to be elastic, homogeneous and isotropic. Based on the Moil-Tanaka concept of average stress and the Eshelby equivalent inclusion theory, a dynamic constitutive model is developed to simulate the impact responses of concrete. The impact compression experiments of concrete and cement mortar are also carried out. Experimental results show that concrete and cement mortar are rate-dependent. Under the same impact velocity, the load-carrying capacity of concrete is higher than that of cement mortar. Whereas, the maximum strain of concrete is lower than that of cement mortar. Regardless of whether it is concrete or cement mortar, with the increase in the impact velocity, the fragment size of specimens after experiment decreases.

Study on Electromagnetic Force and Vibration of Turbogenerator End Windings under Impact Load(Ⅱ): Analysis of Vibration of End Windings under Impact Load

On the basis of the study of transient eddy current field in the end region of turbogenerator and electromagnetic force of end region winding, this paper analyzes the electromagnetic vibration of the turbogenerator roundly. A 320 MW turbogenerator is taken as an example to specify the electromagnetic force of end region winding and therefore the vibration in the case that the generator is affected by impact load. Some conclusions are drawn on the basis of the specification. Vibration of windings under imaginary faults is simulated, so that the vibration law of the end winding of turbogenerator can be studied further. On the basis of this, the countermeasure against winding vibration can be advanced.

Study on Electromagnetic Force and Vibration of Turbogenerator End Windings under Impact Load(Ⅰ): Analysis of Electromagnetic Force of End Windings under Impact Load

In this paper, the boundary value problem (BVP) of 3 D transient eddy current field in the end region in the case that the generator is affected by impact load is specified. Besides, ways to implement discrete methods in both time domain and space domain during the solution of the problem are investigated. The Crank Nicolson scheme is utilized to attain the iterative format of time differential, after taking factors that can ensure both computation precision and stability into consideration. In this paper, the magnetic distribution in the end region of a turbogenerator in the case that the generator is affected by impact load is specified. As a result, it provides foundation for further study of electromagnetic force and electromagnetic vibration in the end region of the turbogenerator.

Parameter calibration of the tensile-shear interactive damage constitutive model for sandstone failure

The tensile-shear interactive damage(TSID)model is a novel and powerful constitutive model for rock-like materials.This study proposes a methodology to calibrate the TSID model parameters to simulate sandstone.The basic parameters of sandstone are determined through a series of static and dynamic tests,including uniaxial compression,Brazilian disc,triaxial compression under varying confining pressures,hydrostatic compression,and dynamic compression and tensile tests with a split Hopkinson pressure bar.Based on the sandstone test results from this study and previous research,a step-by-step procedure for parameter calibration is outlined,which accounts for the categories of the strength surface,equation of state(EOS),strain rate effect,and damage.The calibrated parameters are verified through numerical tests that correspond to the experimental loading conditions.Consistency between numerical results and experimental data indicates the precision and reliability of the calibrated parameters.The methodology presented in this study is scientifically sound,straightforward,and essential for improving the TSID model.Furthermore,it has the potential to contribute to other rock constitutive models,particularly new user-defined models.

Calculating changes in fractal dimension of surface cracks to quantify how the dynamic loading rate affects rock failure in deep mining

The split-Hopkinson pressure bar(SHPB)and digital image correlation(DIC)techniques are combined to analyze the dynamic compressive failure process of coal samples,and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates.The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load.During the dynamic compression process,the evolution of the coal sample cracks presents distinct stages.In the crack propagation stage,the fractal dimension increases rapidly with the progress of loading,and in the crack widening stage,the fractal dimension increases slowly with the progress of loading.The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate;the initial cracks appear earlier.At the same loading time point,when the loading rate is greater,the fractal dimension of the cracks observed in the coal sample is greater.

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.

Responses of jointed rock masses subjected to impact loading

Impact-induced damage to jointed rock masses has important consequences in various mining and civil engineering applications. This paper reports a numerical investigation to address the responses of jointed rock masses subjected to impact loading. It also focuses on the static and dynamic properties of an intact rock derived from a series of laboratory tests on meta-sandstone samples from a quarry in Nova Scotia, Canada. A distinct element code(PFC2D) was used to generate a bonded particle model(BPM) to simulate both the static and dynamic properties of the intact rock. The calibrated BPM was then used to construct large-scale jointed rock mass samples by incorporating discrete joint networks of multiple joint intensities into the intact rock matrix represented by the BPM. Finally, the impact-induced damage inflicted by a rigid projectile particle on the jointed rock mass samples was determined through the use of the numerical model. The simulation results show that joints play an important role in the impactinduced rock mass damage where higher joint intensity results in more damage to the rock mass. This is mainly attributed to variations of stress wave propagation in jointed rock masses as compared to intact rock devoid of joints.

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 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-poim 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.

Analytical and numerical studies on the nonlinear dynamic response of orthotropic membranes under impact load

Orthotropic membrane components and structures are widely used in building structures, instruments and meters, electronic engineering, space and aeronautics, etc., because of their light weights. However, the same lightweight combined with low stiffness make membranes prone to vibration under dynamic loads, and in some cases the vibration may lead to structural failure. Herein, the undamped nonlinear vibration response of pretension rectangular orthotropic membrane structures subjected to impact loading is studied by analytical and numerical methods. The analytical solution is obtained by solving the governing equations by the Bubnov-Galerkin method and the Lindstedt-Poincare perturbation method. Numerical analysis has also been carried out based on the same theoretical model. The analytical and numerical results have been compared and analyzed, and the influence of various model parameters on membrane vibration discussed. The results obtained herein provide some theoretical basis for the vibration control and dynamic design of orthotropic membrane components and structures.

Methods for Progressive Collapse Analysis of Building Structures Under Blast and Impact Loads

Progressive collapse of building structures under blast and impact loads has attracted great attention all over the world. Progressive collapse analysis is essential for an economic and safe design of building structures against progressive collapse to blast and impact loads. Because of the catastrophic nature of progressive collapse and the potentially high cost of constructing or retrofitting buildings to resist it, it is imperative that the progressive collapse analysis methods be reliable. For engineers, their methodology to carry out progressive collapse evaluation need not only be accurate and concise, but also be easily used and works fast. Thus, many researchers have been spending lots of effort in developing reliable, efficient and straightforward progressive collapse analysis methods recently. In the present paper, current progressive collapse analysis methods available in the literature are reviewed. Their suitability, applicability and reliability are discussed. Our recent proposed new method for progressive collapse analysis of reinforced concrete frames under blast loads is also introduced.

Crack dynamic propagation properties and arrest mechanism under impact loading

Crack dynamic propagation and arrest behaviors have received extensive attention over the years.However,there still remain many questions,e.g.under what conditions will a running crack come to arrest?In this paper,drop weight impact(DWI)tests were conducted to investigate crack arrest mechanism using single cleavage triangle(SCT)rock specimens.Green sandstone was selected to prepare the SCT specimens.Dynamic stress intensity factors(DSIFs)were calculated by ABAQUS code,and the critical DSIFs were determined by crack propagation speeds and fracture time measured by crack propagation gauges(CPGs).The test results show that the critical DSIF at propagation decreases with crack propagation speed.Numerical simulation for SCT specimens under different loading waves was performed using AUTODYN code.The reflected compressive wave from the incident and transmitted plates can induce crack arrests during propagation,and the number of arrest times increases with the wave length.In order to eliminate the effect of the incident and transmitted plates,models consisting of only one SCT specimen without incident and transmitted plates were established,and the same trapezoid-shaped loading wave was applied to the SCT specimen.The results show that for the SCT specimen with transmitted boundary(analogous to an infinite plate),the trapezoid-shaped loading wave cannot induce crack arrest anymore.The numerical results can well describe the occurrence of crack arrest in the experiments.