Ice-breaking methods have become increasingly significant with the ongoing development of the polar regions.Among many ice-breaking methods,ice-breaking that utilizes a moving load is unique compared with the common c...Ice-breaking methods have become increasingly significant with the ongoing development of the polar regions.Among many ice-breaking methods,ice-breaking that utilizes a moving load is unique compared with the common collision or impact methods.A moving load can generate flexural-gravity waves(FGWs),under the influence of which the ice sheet undergoes deformation and may even experience structural damage.Moving loads can be divided into above-ice loads and underwater loads.For the above-ice loads,we discuss the characteristics of the FGWs generated by a moving load acting on a complete ice sheet,an ice sheet with a crack,and an ice sheet with a lead of open water.For underwater loads,we discuss the influence on the ice-breaking characteristics of FGWs of the mode of motion,the geometrical features,and the trajectory of motion of the load.In addition to discussing the status of current research and the technical challenges of ice-breaking by moving loads,this paper also looks ahead to future research prospects and presents some preliminary ideas for consideration.展开更多
Safety evaluation of a bridge under Moving Abnormal Indivisible Loads(MAILs)directly relates to whether an oversized and/or overweight Large-Cargo Transportation(LCT)vehicle is permitted to pass the bridge.Safety eval...Safety evaluation of a bridge under Moving Abnormal Indivisible Loads(MAILs)directly relates to whether an oversized and/or overweight Large-Cargo Transportation(LCT)vehicle is permitted to pass the bridge.Safety evaluation can be updated by fusing bridge inspection data and load test data,but there are two fundamental difficulties in updating.The first difficulty is to develop an updating scheme to utilize the unstructured inspection data.The second difficulty is to develop a successive updating scheme using load test data based on the previous updating results of the inspection data.This paper proposed a framework,consisting of three modules,to tackle these two fundamental difficulties of updating.Module one is the updating of Finite Element Model(FEM)and resistance of the bridge based on fusing bridge inspection data and load test data.The first difficulty in utilizing the unstructured inspection data is tackled by introducing updating guidelines using the unstructured inspection data.The second difficulty in conducting a successively updating scheme using load test data based on previous updating results is tackled by Bayesian updating.Module two is the simulation of a bridge under a MAIL,updating the ProbabilityDensity Functions(PDFs)of Load Effects(LEs)of critical sections of critical components based on the updated FEM and the givenMAIL.Module three is the safety evaluation of the bridge based on the load-bearing capacity index and reliability index,updating indices based on the updated resistance and LE.Theillustrative examples consist of a simulated example and an engineering example,demonstrating the effectiveness of the proposed framework.The simulated example is the safety evaluation of a bridge under a MAIL,and the engineering example is the safety evaluation of the Anning River Bridge of the Yazhong-Jiangxi Ultra-High-Voltage Direct Current(UHVDC)MAIL project.The results show that it is crucial to fuse bridge inspection data and load test data for updating the safety evaluation of bridges under MAILs.展开更多
The dynamics of beams subjected to moving loads are of practical importance since the responses caused by these loads can be greater than those under equivalent static loads in some cases.In this work,a novel inertial...The dynamics of beams subjected to moving loads are of practical importance since the responses caused by these loads can be greater than those under equivalent static loads in some cases.In this work,a novel inertial nonlinear energy sink(NES)is applied for the first time to achieve vibration suppression in beams under moving loads.Based on the Timoshenko beam theory,the nonlinear motion equations of a beam with an inertial NES are derived using the energy method and Lagrange equations.The Newmark-βmethod combined with the Heaviside step function is adopted to calculate the responses of the beam under moving loads of constant amplitude and harmonic excitation.The accuracy of the modelling derivation and solution methodology are validated through comparisons with results from other studies.The results demonstrate that the velocity and excitation frequency of the moving load significantly affect the response of the beam as well as the performance of the inertial NES.To enhance its effectiveness under various moving load conditions,parametric optimization is numerically performed.The optimized inertial NES can achieve good performance by efficiently reducing the maximum deflection of the beam.The findings of this study contribute to advancing the understanding and application of NESs in mitigating structural vibrations caused by moving loads.展开更多
Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importan...Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importance in various engineering fields,including the design of precision robotics and advanced aerospace structures where components are subject to moving loads.In this paper,an inertial nonlinear energy sink(NES)is used for the first time to reduce the vibration response of graphene platelet(GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads.Based on the von Kármán nonlinear theory,the governing equations of the beam-NES system are derived using the Lagrange equation.The Newmark-Newton method,in conjunction with the Heaviside step function,is used to obtain the nonlinear responses of the beam under moving loads.The effects of the boundary spring stiffness,the GPL parameters,as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied.The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.展开更多
This work reviews models and methods for determining the dynamic response of pavements to moving vehicle loads in the framework of continuum-based three dimensional models and linear theories.This review emphasizes th...This work reviews models and methods for determining the dynamic response of pavements to moving vehicle loads in the framework of continuum-based three dimensional models and linear theories.This review emphasizes the most representative models and methods of analysis in the existing literature and illustrates all of them by numerical examples.Thus,13 such examples are presented here in some detail.Both flexible and rigid(concrete)pavement models involving simple and elaborate cases with respect to geometry and material behavior are considered.Thus,homogeneous or layered half-spaces with isotropic or cross-anisotropic and elastic,viscoelastic or poroelastic properties are considered.The vehicles are modeled as simple point or distributed loads or discrete spring-mass-dashpot system moving with constant or variable velocity.The dynamic response of the above pavement-vehicle systems is obtained by analytical/numerical or purely numerical methods of solution.Analytical/numerical methods have mainly to do with Fourier transforms or complex Fourier series with respect to both space and time.Purely numerical methods involve the finite element method(FEM)and the boundary element method(BEM)working in time or frequency domain.Critical discussions on the advantages and disadvantages of the various pavement-vehicle models and their methods of analysis are provided and the effects of the main parameters on the pavement response are determined through parametric studies and presented in the examples.Finally,conclusions are provided and suggestions for future research are made.展开更多
For the design and operation of a floating bridge, the understanding of its dynamic behavior under a moving load is of great importance. The purpose of this paper is to investigate the dynamic performances of a new ty...For the design and operation of a floating bridge, the understanding of its dynamic behavior under a moving load is of great importance. The purpose of this paper is to investigate the dynamic performances of a new type floating bridge, the pontoon-separated floating bridge, under the effect of a moving load. In the paper, a brief summary of the dynamic analysis of the floating bridge is first introduced. The motion equations for a pontoon-separated floating bridge, considering the nonlinear properties of connectors and vehicles＇ inertia effects, are proposed. The super-element method is applied to reduce the numerical analysis scale to solve the reduced equations. Based on the static analysis, the dynamic features of the new type floating bridge subjected to a moving load are investigated. It is found that the dynamie behavior of the pontoon-separated floating bridge is superior to that of the ribbon bridge by taking the nonlinearity of eonneetors into account.展开更多
In this study,ground vibrations due to dynamic loadings from trains moving in subway tunnels were investigated using a 2.5D finite element model of an underground tunnel and surrounding soil interactions.In our model,...In this study,ground vibrations due to dynamic loadings from trains moving in subway tunnels were investigated using a 2.5D finite element model of an underground tunnel and surrounding soil interactions.In our model,wave propagation in the infinitely extended ground is dealt with using a simple,yet efficient gradually damped artificial boundary.Based on the assumption of invariant geometry and material distribution in the tunnel's direction,the Fourier transform of the spatial dimension in this direction is applied to represent the waves in terms of the wave-number.Finite element discretization is employed in the cross-section perpendicular to the tunnel direction and the governing equations are solved for every discrete wave-number.The 3D ground responses are calculated from the wave-number expansion by employing the inverse Fourier transform.The accuracy of the proposed analysis method is verified by a semi-analytical solution of a rectangular load moving inside a soil stratum.A case study of subway train induced ground vibration is presented and the dependency of wave attenuation at the ground surface on the vibration frequency of the moving load is discussed.展开更多
A closed-form out-of-plane dynamic displacement response of a curved track subjected to moving loads was proposed.The track structure was modeled as a planar curved Timoshenko beam periodically supported by the double...A closed-form out-of-plane dynamic displacement response of a curved track subjected to moving loads was proposed.The track structure was modeled as a planar curved Timoshenko beam periodically supported by the double-layer spring-damping elements.The general dynamic displacement response induced by the moving loads along the curve on the elastic semi-infinite space was firstly obtained in the frequency domain,according to the Duhamel integral and the dynamic reciprocity theorem.In the case of the periodic curved track structure subjected to moving loads,the dynamic displacement equation was simplified into a form of summation within the basic track cell instead of the integral.The transfer function for the curved track was expressed in the form of a transfer matrix.Single and series moving loads were involved in the calculation program.For the verification of the analytical model,the mid-span vertical deflection of a simply support curved beam subjected to moving load was recalculated and compared with the same case in the reference.The research results indicate that:under the same moving loads,the displacement response of the curved track decreases slightly with the increasing track radius,and the displacement response of the curved track with the radius greater than or equal to 600 m is almost equivalent to the displacement response of the straight track;the frequency spectrum of the curved track is more abundant than that of the straight track,which may result in more wheel-rail resonance and rail corrugation in the curved lines.展开更多
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 sp...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.展开更多
In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means t...In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.展开更多
In this study,the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated.The boundary conditions and properties of each beam vary,...In this study,the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated.The boundary conditions and properties of each beam vary,and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations.By examining a high-speed railway(HSR)with mixed boundary conditions,the rationality for the newly proposed method is verified,the difference in simulated multiple-beam models with different beam numbers is explored,and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined.Results suggest that the number of beams in the model should be as close to the actual beam number as possible.Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure.Neglecting the track-structure can overestimate the resonant speed of a high-speed railway,simply-supported beam bridge.The effective interval of foundation stiffness(EIFS)can provide a reference for future engineering designs.展开更多
The dynamic response of an infinite beam placed on a Pasternak foundation when the system was subjected to a moving load was investigated.We used the double Fourier transform and its inversion to solve the formulation...The dynamic response of an infinite beam placed on a Pasternak foundation when the system was subjected to a moving load was investigated.We used the double Fourier transform and its inversion to solve the formulations of the problem.A closed form analytic solution of the beam was obtained by the theorem of residues.We selected a numerical example to illustrate the dynamic response of the beam on Pasternak and Winkler foundations,respectively.We discuss the effect of the moving load velocity on the dynamic displacement response of the beam.The maximum deflection of the beam increases slightly with increased load velocity but increases significantly with reduced shear modulus of subgrade at a given velocity.The maximum deflection of a beam resting on a Pasternak foundation is much smaller than that of a beam on a Winkler foundation.展开更多
By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Base...By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half- space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of （sub-） hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of （sub-） soft beam and hard half-space but are similar to each other for the system of （sub-） hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity （the shear wave velocity of the beam for the system of soft beam and hard half-space）. The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave racliation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.展开更多
Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi-analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving ...Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi-analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier-Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.展开更多
The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate a...The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.展开更多
The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without ...The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without drainage consolidation was established using the finite element software ABAQUS.In this model,the traffic loads were simulated by two moving loads of rectangular pattern,and their amplitude,range,and moving speed were realized by a Fortran subroutine.The embankment fill was simulated by an equivalent linear viscoelastic model,which can reflect its viscoelasticity.The geogrid was simulated by the truss element,and the geocell was simulated by the membrane element.Infinite elements were utilized to weaken the boundary effect caused by the model geometry at the boundaries.Validation of the established numerical model was conducted by comparing the predicted deformations in the cross-section of the geosynthetic-reinforced embankment with those from the existing literature.On this basis,the dynamic stress and strain distribution in the pavement structure layer of the geosynthetic-reinforced embankment under a moving load was also analyzed.Finally,a parametric study was conducted to examine the influences of the different types of reinforcement,overload,and the moving load velocity on the geosynthetic-reinforced embankment.展开更多
The expression of the equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads is obtained via the Fourier transformation method in the frequency wave nu...The expression of the equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads is obtained via the Fourier transformation method in the frequency wave number domain. Based on the obtained equivalent stiffness, the frequency wave number domain solution of the beam-half-space system is obtained by the compatibility condition between the beam and the half space. Critical velocity of harmonic moving loads along an infinite Euler-Bernoulli elastic beam is determined. The time domain solutions for the beam and the saturated poro-elastic half space are derived by means of the inverse Fourier transformation method. Also, the influences of the load speed, frequency and material parameters of the poro-elastic half space on the responses of the beam are investigated. Numerical results show that the frequency corresponding to the maximum deflection and bending moment increases with increasing load speed. Moreover, it can be seen that at higher frequencies, the dynamic response is independent of the load speed. The present results also show that for a beam overlying a saturated poro-elastic half space, there still exist critical velocities even when the load velocity is larger than the shear wave speed of the medium.展开更多
Vibration due to moving traffic loads is an important factor which induces frozen soil damage; this paper analyzed these vibration characteristics of frozen soil foundation under track loads. Firstly, seismic observat...Vibration due to moving traffic loads is an important factor which induces frozen soil damage; this paper analyzed these vibration characteristics of frozen soil foundation under track loads. Firstly, seismic observation array （SOA） technology was applied to monitor the three dimensional dynamic characteristics of frozen soil under movable track load in a per- mafrost region and seasonal frozen soil area. Secondly, a numerical simulation for the response of frozen soil under movable track load was performed based on finite element analysis （FEA）, The results show that dynamic characteristics of frozen soil in perpendicular and parallel direction of the track are obviously different. In the direction perpendicular to the track, the vertical acceleration amplitude had an abrupt increase in the 9-10 m from the track line. In the direction parallel to the track, the acceleration in vertical and horizontal direction had a quick attenuation compared to the other direction. Lastly, various parameters were analyzed for the purpose of controlling the dynamic response of frozen soil and the vibration attenuation in frozen soil layer.展开更多
The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space clue to a load moving with a constant velocity at a rough free surface. Expressions for normal and shear...The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space clue to a load moving with a constant velocity at a rough free surface. Expressions for normal and shear stresses are obtained in closed form. The substantial effects of influence parameters, viz., depth （from the free surface）, irregularity factor, maximum depth of irregularity, viscoelastic parameter, horizontal and vertical initial stresses, and frictional coefficient, on normal and shear stresses are investigated. Moreover, comparative study is carried out for three different cases of irregularity, viz., rectangular irregularity, parabolic irregulariW and no irregularity, which is manifested through graphs.展开更多
A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam br...A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.展开更多
基金Supported by the National Natural Science Foundation of China(Nos.52192693,52192690,52371270,U20A20327)the National Key Research and Development Program of China(Nos.2021YFC2803400).
文摘Ice-breaking methods have become increasingly significant with the ongoing development of the polar regions.Among many ice-breaking methods,ice-breaking that utilizes a moving load is unique compared with the common collision or impact methods.A moving load can generate flexural-gravity waves(FGWs),under the influence of which the ice sheet undergoes deformation and may even experience structural damage.Moving loads can be divided into above-ice loads and underwater loads.For the above-ice loads,we discuss the characteristics of the FGWs generated by a moving load acting on a complete ice sheet,an ice sheet with a crack,and an ice sheet with a lead of open water.For underwater loads,we discuss the influence on the ice-breaking characteristics of FGWs of the mode of motion,the geometrical features,and the trajectory of motion of the load.In addition to discussing the status of current research and the technical challenges of ice-breaking by moving loads,this paper also looks ahead to future research prospects and presents some preliminary ideas for consideration.
基金funded by the Science and Technology Development Fund(SKLIOTSC(UM)-2021-2023)the State Key Laboratory of Internet of Things for Smart City(University of Macao)(SKL-IoTSC(UM)-2024-2026/ORP/GA07/2023)Guangdong Provincial Key Laboratory of Modern Civil Engineering Technology(2021B1212040003).
文摘Safety evaluation of a bridge under Moving Abnormal Indivisible Loads(MAILs)directly relates to whether an oversized and/or overweight Large-Cargo Transportation(LCT)vehicle is permitted to pass the bridge.Safety evaluation can be updated by fusing bridge inspection data and load test data,but there are two fundamental difficulties in updating.The first difficulty is to develop an updating scheme to utilize the unstructured inspection data.The second difficulty is to develop a successive updating scheme using load test data based on the previous updating results of the inspection data.This paper proposed a framework,consisting of three modules,to tackle these two fundamental difficulties of updating.Module one is the updating of Finite Element Model(FEM)and resistance of the bridge based on fusing bridge inspection data and load test data.The first difficulty in utilizing the unstructured inspection data is tackled by introducing updating guidelines using the unstructured inspection data.The second difficulty in conducting a successively updating scheme using load test data based on previous updating results is tackled by Bayesian updating.Module two is the simulation of a bridge under a MAIL,updating the ProbabilityDensity Functions(PDFs)of Load Effects(LEs)of critical sections of critical components based on the updated FEM and the givenMAIL.Module three is the safety evaluation of the bridge based on the load-bearing capacity index and reliability index,updating indices based on the updated resistance and LE.Theillustrative examples consist of a simulated example and an engineering example,demonstrating the effectiveness of the proposed framework.The simulated example is the safety evaluation of a bridge under a MAIL,and the engineering example is the safety evaluation of the Anning River Bridge of the Yazhong-Jiangxi Ultra-High-Voltage Direct Current(UHVDC)MAIL project.The results show that it is crucial to fuse bridge inspection data and load test data for updating the safety evaluation of bridges under MAILs.
基金supported by the National Natural Science Foundation of China(Grant Nos.12102015 and 12472003)the General Program of Science and Technology Development Project of the Beijing Municipal Education Commission(Grant No.KM202110005030)the Key Research Project of Zhejiang Market Supervision Administration(Grant No.ZD2024013).
文摘The dynamics of beams subjected to moving loads are of practical importance since the responses caused by these loads can be greater than those under equivalent static loads in some cases.In this work,a novel inertial nonlinear energy sink(NES)is applied for the first time to achieve vibration suppression in beams under moving loads.Based on the Timoshenko beam theory,the nonlinear motion equations of a beam with an inertial NES are derived using the energy method and Lagrange equations.The Newmark-βmethod combined with the Heaviside step function is adopted to calculate the responses of the beam under moving loads of constant amplitude and harmonic excitation.The accuracy of the modelling derivation and solution methodology are validated through comparisons with results from other studies.The results demonstrate that the velocity and excitation frequency of the moving load significantly affect the response of the beam as well as the performance of the inertial NES.To enhance its effectiveness under various moving load conditions,parametric optimization is numerically performed.The optimized inertial NES can achieve good performance by efficiently reducing the maximum deflection of the beam.The findings of this study contribute to advancing the understanding and application of NESs in mitigating structural vibrations caused by moving loads.
基金Project supported by the National Natural Science Foundation of China(No.12472003)the Key Research Project of Zhejiang Market Supervision Administration(No.ZD2024013)the Technical Project of Research Institute of Highway Ministry of Transport of China(No.0225KF12SC1002)。
文摘Moving-load induced vibrations can,in certain instances,exceed those caused by equivalent static loads,especially at the critical velocity of moving loads.Suppressing these vibrations is of critical practical importance in various engineering fields,including the design of precision robotics and advanced aerospace structures where components are subject to moving loads.In this paper,an inertial nonlinear energy sink(NES)is used for the first time to reduce the vibration response of graphene platelet(GPL)-reinforced nanocomposite beams with elastic boundaries under moving loads.Based on the von Kármán nonlinear theory,the governing equations of the beam-NES system are derived using the Lagrange equation.The Newmark-Newton method,in conjunction with the Heaviside step function,is used to obtain the nonlinear responses of the beam under moving loads.The effects of the boundary spring stiffness,the GPL parameters,as well as the velocity and frequency of the moving loads on the beam response and the performance of the NES are thoroughly studied.The results of this work provide insights into applying NESs to suppress the nonlinear vibrations induced by moving loads in composite structures with elastic boundaries.
文摘This work reviews models and methods for determining the dynamic response of pavements to moving vehicle loads in the framework of continuum-based three dimensional models and linear theories.This review emphasizes the most representative models and methods of analysis in the existing literature and illustrates all of them by numerical examples.Thus,13 such examples are presented here in some detail.Both flexible and rigid(concrete)pavement models involving simple and elaborate cases with respect to geometry and material behavior are considered.Thus,homogeneous or layered half-spaces with isotropic or cross-anisotropic and elastic,viscoelastic or poroelastic properties are considered.The vehicles are modeled as simple point or distributed loads or discrete spring-mass-dashpot system moving with constant or variable velocity.The dynamic response of the above pavement-vehicle systems is obtained by analytical/numerical or purely numerical methods of solution.Analytical/numerical methods have mainly to do with Fourier transforms or complex Fourier series with respect to both space and time.Purely numerical methods involve the finite element method(FEM)and the boundary element method(BEM)working in time or frequency domain.Critical discussions on the advantages and disadvantages of the various pavement-vehicle models and their methods of analysis are provided and the effects of the main parameters on the pavement response are determined through parametric studies and presented in the examples.Finally,conclusions are provided and suggestions for future research are made.
基金This project was supported by the Commission of Science Technology and Industry for National Defense .
文摘For the design and operation of a floating bridge, the understanding of its dynamic behavior under a moving load is of great importance. The purpose of this paper is to investigate the dynamic performances of a new type floating bridge, the pontoon-separated floating bridge, under the effect of a moving load. In the paper, a brief summary of the dynamic analysis of the floating bridge is first introduced. The motion equations for a pontoon-separated floating bridge, considering the nonlinear properties of connectors and vehicles＇ inertia effects, are proposed. The super-element method is applied to reduce the numerical analysis scale to solve the reduced equations. Based on the static analysis, the dynamic features of the new type floating bridge subjected to a moving load are investigated. It is found that the dynamie behavior of the pontoon-separated floating bridge is superior to that of the ribbon bridge by taking the nonlinearity of eonneetors into account.
基金Project supported by the National Natural Science Foundation of China (Nos. 51178418 and 51222803)the National Key Technology R&D (863) Program of China (No. 2009BAG12A01-B12-3)
文摘In this study,ground vibrations due to dynamic loadings from trains moving in subway tunnels were investigated using a 2.5D finite element model of an underground tunnel and surrounding soil interactions.In our model,wave propagation in the infinitely extended ground is dealt with using a simple,yet efficient gradually damped artificial boundary.Based on the assumption of invariant geometry and material distribution in the tunnel's direction,the Fourier transform of the spatial dimension in this direction is applied to represent the waves in terms of the wave-number.Finite element discretization is employed in the cross-section perpendicular to the tunnel direction and the governing equations are solved for every discrete wave-number.The 3D ground responses are calculated from the wave-number expansion by employing the inverse Fourier transform.The accuracy of the proposed analysis method is verified by a semi-analytical solution of a rectangular load moving inside a soil stratum.A case study of subway train induced ground vibration is presented and the dependency of wave attenuation at the ground surface on the vibration frequency of the moving load is discussed.
基金Project supported by the National Natural Science Foundation of China(Nos.51008017 and 51378001)the Research Fund for Beijing Postdoctoral Work,and the Innovation Fund for PhD of Beijing Jiaotong University(No.2011YJS261),China
文摘A closed-form out-of-plane dynamic displacement response of a curved track subjected to moving loads was proposed.The track structure was modeled as a planar curved Timoshenko beam periodically supported by the double-layer spring-damping elements.The general dynamic displacement response induced by the moving loads along the curve on the elastic semi-infinite space was firstly obtained in the frequency domain,according to the Duhamel integral and the dynamic reciprocity theorem.In the case of the periodic curved track structure subjected to moving loads,the dynamic displacement equation was simplified into a form of summation within the basic track cell instead of the integral.The transfer function for the curved track was expressed in the form of a transfer matrix.Single and series moving loads were involved in the calculation program.For the verification of the analytical model,the mid-span vertical deflection of a simply support curved beam subjected to moving load was recalculated and compared with the same case in the reference.The research results indicate that:under the same moving loads,the displacement response of the curved track decreases slightly with the increasing track radius,and the displacement response of the curved track with the radius greater than or equal to 600 m is almost equivalent to the displacement response of the straight track;the frequency spectrum of the curved track is more abundant than that of the straight track,which may result in more wheel-rail resonance and rail corrugation in the curved lines.
文摘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.
基金supported by the National Key Technology R&D Program (Grant 2011BAJ02B01-02)the National Natural Science Foundation of China (Grant 11602065)
文摘In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
基金Supported by:National Natural Science Foundations of China under Grant Nos.U1934207 and 51778630the Hunan Innovative Provincial Construction Project under Grant No.2019RS3009+1 种基金the Innovation-driven Plan in Central South University under Grant No.2020zzts159the Fundamental Research Funds for the Central Universities of Central South University under Grant No.2018zzts189。
文摘In this study,the dynamic response of an elastically connected multi-beam structure subjected to a moving load with elastic boundary conditions is investigated.The boundary conditions and properties of each beam vary,and the difficulty of solving the motion equation is reduced by using a Fourier series plus three special transformations.By examining a high-speed railway(HSR)with mixed boundary conditions,the rationality for the newly proposed method is verified,the difference in simulated multiple-beam models with different beam numbers is explored,and the influence of material parameters and load speed on the dynamic response of multiple-beam structures is examined.Results suggest that the number of beams in the model should be as close to the actual beam number as possible.Models with an appropriate beam number can be used to describe in detail the dynamic response of the structure.Neglecting the track-structure can overestimate the resonant speed of a high-speed railway,simply-supported beam bridge.The effective interval of foundation stiffness(EIFS)can provide a reference for future engineering designs.
文摘The dynamic response of an infinite beam placed on a Pasternak foundation when the system was subjected to a moving load was investigated.We used the double Fourier transform and its inversion to solve the formulations of the problem.A closed form analytic solution of the beam was obtained by the theorem of residues.We selected a numerical example to illustrate the dynamic response of the beam on Pasternak and Winkler foundations,respectively.We discuss the effect of the moving load velocity on the dynamic displacement response of the beam.The maximum deflection of the beam increases slightly with increased load velocity but increases significantly with reduced shear modulus of subgrade at a given velocity.The maximum deflection of a beam resting on a Pasternak foundation is much smaller than that of a beam on a Winkler foundation.
基金Project supported by the National Natural Science Foundation of China (No.50538010) the Doctoral Education of the State Education Ministry of China (No.20040335083) Encouragement Fund for Young Teachers in University of Ministry of Education.
文摘By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half- space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of （sub-） hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of （sub-） soft beam and hard half-space but are similar to each other for the system of （sub-） hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity （the shear wave velocity of the beam for the system of soft beam and hard half-space）. The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave racliation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.
基金The project is partially supported by the National Natural Science Foundation of China (50538010)
文摘Based on the thin layer method originally proposed in frequency domain, an explicit time domain semi-analytical solution has been developed for simulating three-dimensional layered ground responses to harmonic moving loads. The Fourier-Laplace transforms were applied to derive the transformed solution that satisfied the boundary conditions of horizontal infinities. The eigenvalue decomposition was performed with respect to Laplace parameter to express the ground motion corresponding to the eigenmodes. The formulation for each eigenmode incorporating the moving load expression was transformed back into time domain analytically, and the global system responses were given by means of the general mode superposition method. The proposed explicit time domain solution is suitable for studying various types of moving load acting on or inside the ground. In this paper a moving harmonic load with rectangular distribution was adopted to demonstrate the ground response simulation. Two illustrative examples for moving load with speeds below or above the ground Rayleigh wave velocity were presented to test the computational accuracy and efficiency of the proposed approach. A parametric study was also performed to investigate the influences of soil properties on the ground responses.
文摘The present paper is concerned with the investigation of disturbances in＇a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion, when a moving source is acting along one of the co-ordinate axis on the boundary of the medium. Eigen value approach is applied to study the disturbance in Laplace-Fourier transform domain for a two dimensional problem. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using a numerical technique for the inversion of Laplace transform based on Fourier expansion techniques. These expressions are calculated numerically for a copper like material and depicted graphically. As special cases, the results in generalized thermoelastic and elastic media are obtained. Effect of presence of diffusion is analyzed theoretically and numerically.
基金This research was funded through the National Natural Science Foundation of China(Grant Nos.52108299 and 52178312)the China Postdoctoral Science Foundation(Grant No.2021M693740)the Basal Research Fund Support by Chongqing University.
文摘The performance of geosynthetic-reinforced embankments under traffic moving loads is always a hotspot in the geotechnical engineering field.A three-dimensional(3D)model of a geosynthetic-reinforced embankment without drainage consolidation was established using the finite element software ABAQUS.In this model,the traffic loads were simulated by two moving loads of rectangular pattern,and their amplitude,range,and moving speed were realized by a Fortran subroutine.The embankment fill was simulated by an equivalent linear viscoelastic model,which can reflect its viscoelasticity.The geogrid was simulated by the truss element,and the geocell was simulated by the membrane element.Infinite elements were utilized to weaken the boundary effect caused by the model geometry at the boundaries.Validation of the established numerical model was conducted by comparing the predicted deformations in the cross-section of the geosynthetic-reinforced embankment with those from the existing literature.On this basis,the dynamic stress and strain distribution in the pavement structure layer of the geosynthetic-reinforced embankment under a moving load was also analyzed.Finally,a parametric study was conducted to examine the influences of the different types of reinforcement,overload,and the moving load velocity on the geosynthetic-reinforced embankment.
基金the National Natural Science Foundatio of China (No. 50679041)the Foundation of Jiangx Educational Committee (No. GJJ09367)
文摘The expression of the equivalent stiffness of the saturated poro-elastic half space interacting with an infinite beam to harmonic moving loads is obtained via the Fourier transformation method in the frequency wave number domain. Based on the obtained equivalent stiffness, the frequency wave number domain solution of the beam-half-space system is obtained by the compatibility condition between the beam and the half space. Critical velocity of harmonic moving loads along an infinite Euler-Bernoulli elastic beam is determined. The time domain solutions for the beam and the saturated poro-elastic half space are derived by means of the inverse Fourier transformation method. Also, the influences of the load speed, frequency and material parameters of the poro-elastic half space on the responses of the beam are investigated. Numerical results show that the frequency corresponding to the maximum deflection and bending moment increases with increasing load speed. Moreover, it can be seen that at higher frequencies, the dynamic response is independent of the load speed. The present results also show that for a beam overlying a saturated poro-elastic half space, there still exist critical velocities even when the load velocity is larger than the shear wave speed of the medium.
基金supported by the National High Technology Research and Development Program of China (863, 2008AA11Z104)
文摘Vibration due to moving traffic loads is an important factor which induces frozen soil damage; this paper analyzed these vibration characteristics of frozen soil foundation under track loads. Firstly, seismic observation array （SOA） technology was applied to monitor the three dimensional dynamic characteristics of frozen soil under movable track load in a per- mafrost region and seasonal frozen soil area. Secondly, a numerical simulation for the response of frozen soil under movable track load was performed based on finite element analysis （FEA）, The results show that dynamic characteristics of frozen soil in perpendicular and parallel direction of the track are obviously different. In the direction perpendicular to the track, the vertical acceleration amplitude had an abrupt increase in the 9-10 m from the track line. In the direction parallel to the track, the acceleration in vertical and horizontal direction had a quick attenuation compared to the other direction. Lastly, various parameters were analyzed for the purpose of controlling the dynamic response of frozen soil and the vibration attenuation in frozen soil layer.
基金the National Board of Higher Mathematics (NBHM) for their financial support to this research work through Project no. NBHM/R.P.78/ 2015/Fresh/2017/24.1.2017 entitled “Mathematical modeling of elastic wave propagation in highly anisotropic and heterogeneous media”
文摘The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space clue to a load moving with a constant velocity at a rough free surface. Expressions for normal and shear stresses are obtained in closed form. The substantial effects of influence parameters, viz., depth （from the free surface）, irregularity factor, maximum depth of irregularity, viscoelastic parameter, horizontal and vertical initial stresses, and frictional coefficient, on normal and shear stresses are investigated. Moreover, comparative study is carried out for three different cases of irregularity, viz., rectangular irregularity, parabolic irregulariW and no irregularity, which is manifested through graphs.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11002093,11172183,and 11202142)the Science and Technology Fund of the Science and Technology Department of Hebei Province,China(Grant No.11215643)
文摘A novel model is proposed which comprises of a beam bridge subjected to an axial load and an infinite series of moving loads. The moving loads, whose distance between the neighbouring ones is the length of the beam bridge, coupled with the axial force can lead the vibration of the beam bridge to codimension-two bifurcation. Of particular concern is a parameter regime where non-persistence set regions undergo a transition to persistence regions. The boundary of each stripe represents a bifurcation which can drive the system off a kind of dynamics and jump to another one, causing damage due to the resulting amplitude jumps. The Galerkin method, averaging method, invertible linear transformation, and near identity nonlinear transformations are used to obtain the universal unfolding for the codimension-two bifurcation of the mid-span deflection. The efficiency of the theoretical analysis obtained in this paper is verified via numerical simulations.
