Elastic Support Model Research Articles

Analysis of parameters on the wheel–rail P2 force of subways

An experiment of falling wheels was performed in this study along with full-field tests, for a type of subway train on four subway lines. The results confirmed that 40–80 Hz vibration signals on the ground and train are caused by the wheel–rail P2 force. Vehicle–track-coupled dynamics models were created where the single-layer elastic support model, double-layer elastic support model and floating slab track model were considered. The results were validated by available experimental data and three types of theoretical models: Jenkins, Winkler and double-beam model. This shows that the amplitude of the P2 force increases with larger suspended rail joint angle, higher train speed, heavy unsuspended mass and stronger fastener stiffness. Besides, both fastener damping and the vertical stiffness of primary suspension enabled control of the amplitude of the P2 force in a limited interval. Supporting stiffness of track and unsprung mass played a key role in the frequency of the P2 force. However, the vertical stiffness of the primary suspension had a reduced effect on the frequency of P2 force as compared with the supporting stiffness. Thus, for an effective change to the supporting stiffness, the fastener stiffness could be changed accordingly.

Analysis of the Influence of Differential Consolidation Settlement of Foundation on Redistribution of Internal Forces in Superstructure of Buildings

In order to explore the influence of differential settlement of foundation on the internal force and deformation of super-frame structure, the stress and deformation of the traditional fixed support model and the elastic support model under the local effect of the differential settlement of the two columns are compared. The model without considering the settlement of the structure (Model 1), the traditional fixed support model (Model 2), and the vertical elastic support model (Model 3) are respectively constructed for analysis. The left end of the frame column and A/1-2 beam are taken as an example, the axial force of the frame column in Model 3 significantly decreases from -817.8kN to -415.3kN compared with Model 1, with a reduction of 49%; the shear force at the left end of the lower A/1-2 beam increases from 42.3kN to 43.5kN with an increase of 3%; and the bending moment increases from -27.2kN⋅m to 152.7kN⋅m. Those indicate the shear force and bending moment of the beam directly connected with the subsidence column under the action of the elastic support model are smaller than that under the action of the fixed support model. It is hoped that these change rules can provide reference for the design and reinforcement of similar projects in the future.

A 3D model for coupling dynamics analysis of high-speed train/track system

A 3D dynamic model of a high-speed train coupled with a flexible ballast track is developed and is presented in this study. In this model, each vehicle is modeled as a 42 degrees of freedom multi-body system, which takes into consideration the nonlinear dynamic characteristics of the suspensions. A detailed inter-vehicle connection model including nonlinear couplers and inter-vehicle dampers, and the linear tight-lock vestibule diaphragm is established to simulate the effect of the end connections of neighboring vehicles on dynamic behavior. The track is modeled as a traditional three-layer discrete elastic support model. The rails are assumed to be Timoshenko beams supported by discrete sleepers. Each sleeper is treated as an Euler beam and the ballast bed is replaced by equivalent rigid ballast bodies. The reliability of the present model is then validated through a detailed numerical simulation comparison with the commercial software SIMPACK, with the effect of the track flexibility on the train/track interaction being analyzed simultaneously. The proposed model is finally applied to investigate the difference between dynamic performances obtained using the entire-train/track model (TTM) and the single-vehicle/track model (VTM). Several key dynamic performances, including vibration frequency response, ride comfort, and curving performance, calculated by the two types of dynamic models are compared and discussed. The numerical results show that there is a significant difference between the dynamic behaviors obtained by VTM and TTM, and that inter-vehicle connections have an important influence on the dynamic behavior of high-speed vehicles.

Research for Non-Destructive Detection of Vertical Prestressed Tensile Force in Box Girder

Fine rolled twisted bars as the vertical prestressed reinforcement has been widely used in the prestressed concrete box girder, but it is hard to effectively control the loss of prestressed force in the practical engineering. Too much loss of prestressed force will lead to diagonal cracks in box girder webs. According to the dynamic theory, take the exposed segment of fine rolled twisted bars as the beam model, take the anchorage segment as a rigid arm and two elastic supports, this article establishes the plane elastic support model of vertical prestressed fine rolled twisted bar. The nonlinear relationship between vertical prestressed tensile force P and the plane stiffness of elastic supports K is established by an indoor experiment, and at the same time the anchoring section stiffness coefficient method is used to verify the effectiveness of this method and conduct an engineering application. This paper provides a theoretical basis for the test of vertical prestressed tensile force in box girder.

Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

A new method is proposed to identify the power spectral density (PSD) of vertical track irregularities. A vertical coupled vehicle–track dynamic model is established. In this model, a vehicle is simplified as a multi-rigid-body model with 10 degrees of freedom, and a track is treated as a three-layer discrete elastic support model in which the rail, which is supported discretely by the sleepers, is described by Bernoulli–Euler beam theory. The vehicle and track models are coupled by a linearized Hertzian spring. The axle box acceleration is selected as the measurement data, and the stationary PSD of the axle box acceleration is simply transformed into its displacement PSD. The PSD of the vertical track irregularities is identified using a combination of the inverse pseudo-excitation method and the symplectic mathematical method. The accuracy of the proposed method is investigated for the different measurement noise levels, vehicle speeds, primary suspension parameters and PSD classes. The numerical results indicate that the proposed method can accurately identify the PSD of the vertical track irregularities.

Study on Derailment Mechanism and Safety Operation Area of High-Speed Trains Under Earthquake

In order to investigate the derailment mechanism and safety operation area of high-speed trains under earthquake, a coupled vehicle-track dynamic model considering earthquake effect is developed, in which the vehicle is modeled as a 35 degrees of freedom (DOF) multibody system with nonlinear suspension characteristic and the slab track is modeled as a discrete elastic support model. The rails of the track are assumed to be Timoshenko beams supported by discrete rail fasteners, and the slabs are modeled with solid finite elements. The system motion equations are solved by means of an explicit integration method in time domain. The present work analyzes in detail the effect of earthquake characteristics on the dynamical behaviors of a vehicle-track coupling system and the transient derailment criteria. The considered derailment criteria include the ratio of the wheel/rail lateral force to the vertical force, the wheel loading reduction, the wheel/rail contact point traces on the wheel tread, and the wheel rise with respect to the rail top, respectively. The present work also finds the safety operation area, the derailment area, and the warning area of high-speed trains under earthquake, and their boundaries. These areas consist of three key parameters influencing the dynamical behavior of high-speed train and track under earthquake. The three key influencing parameters are, respectively, the vehicle speed and the lateral and vertical peak ground acceleration (PGA) of an earthquake. The results obtained indicate that the lateral earthquake motion has a greater influence on the vehicle dynamic behavior and its running safety compared to the vertical earthquake motion. The risk of derailment increases quickly with the increasing of lateral earthquake motion amplitude. The lateral earthquake motion is dominant in the vehicle running safety influenced by an earthquake. While the vertical earthquake motion promotes jumping of the wheels easily, not easy is flange climb derailment. And the effect of the vehicle speed is not significant under earthquake.

Study on the Frame Structure under Nonuniform Settlement

In this paper, the effect of the non-uniformity settlement of ground foundation on the upper frame structure is studied. It takes a four-story space frame structure with two spans as an example. The different pedestals are installed at the joint of column footing, which respectively form the fixed supported model and the elastic supported model. Basin shaped settlement is applied in each model. The result shows that the beams are principally suffered with the bending moment and the columns principally suffered with axial force, shear force and bending moment, and that the elastic support model has certain economy.

Effect of tangent track buckle on vehicle derailment

In order to investigate the effect of a tangent track buckle on the dynamic derailment of a railway vehicle, a coupled vehicle/track dynamics model is developed, in which the vehicle is modeled as a 35 D.O.F. multibody system and the track is modeled as a 3-layer discrete elastic support model. Rails are assumed to be Timoshenko beams supported by discrete sleepers, and the effects of vertical and lateral motions and rolling of the rail on the wheel/rail creepages are taken into account. The sleepers are treated as Euler beams on elastic foundation for the vertical vibration, while as lumped masses in the lateral direction. A moving sleeper support model is developed to simulate the effect of the periodical discrete sleepers on the vehicle/track interaction. The vehicle and the track are coupled by wheel/rail contacts whereas the normal forces and the creep forces are calculated using the Hertzian contact theory and the nonlinear creep theory by Shen et al., respectively. The equations of motion of the coupled vehicle/track system are solved by means of an explicit integration method. A tangent track buckle is simulated with a cosine function, which describes the misalignment of the track with different lengths due to its buckling. In the analysis the effects of the buckle wavelength and amplitude and of the vehicle speed on the dynamic behavior of the coupled vehicle/track system are considered. The present paper analyzes in detail the conventional derailment coefficients which include the ratio of the wheel/rail lateral force to the vertical force, the wheel load reduction, and the new criteria indicating the wheel/rail contact point traces and the wheel rise with respect to the rail. These criteria are simultaneously used to evaluate the risk of derailment of the whole vehicle. The numerical results obtained indicate that the track misalignment caused by the buckle and the vehicle speed have a great influence on the whole vehicle running safety when the vehicle passes through the buckled tangent track.

Visual simulation of the grinding process

Grinding is one of the machining methods for finishing that is performed by using a large number of abrasive grains with irregular shapes and random distribution. While this feature enables accurate and high-quality machining, it complicates analysis of the grinding process. To solve this problem, a great number of computer simulations have been carried out using the Monte Carlo method. Most of them, however, statically calculate geometric interaction between a grain and a workpiece, and have not provided enough achievements for practical applications. In this study, taking this background into account, a simulation program has been developed based on the elastic support model of a grain in which the elasticity of grain support changes according to its location. The program focuses on the generation process of a workpiece surface, and simulates the interaction between grains and a workpiece, which includes the elastic and plastic deformation as well as the removal of workpiece material. Examples of the simulation shown in this study verify the fact that the simulation program facilitates analysis of the microscopic grinding phenomena, and can be used as a practical tool for predicting the grinding results and for optimizing grinding parameters.

Analysis of vibration power flow from a vibrating machinery to a floating elastic panel

A fully rigid–elastic-coupled dynamic model was developed for a vibration isolation system consisting of a rigid vibrating machinery, multiple resilient mounts and a floating elastic panel. This model was applied to investigate the vibration power transmission behavior of an X–Y motion stage-based system used in semiconductor wire-bonding equipment. The natural frequencies and modal characteristics of the system and its subsystems were numerically evaluated. The total power flow from the X–Y motion stage (the vibrating machinery) to the equipment table (the floating elastic panel) through multiple resilient mounts and the contribution of each force component at mounting junctions to the total power flow were analysed in the concerned frequency range for different types of excitations. The total power flow predicted by the developed model was also compared with that calculated using a conventional elastic support model. It was shown that the developed model provides a more accurate prediction of the total power flow in the frequency range of interest.