Substructure Simulation of Inhomogeneous Track and Layered Ground Dynamic Interaction under Train Passage

The vibrations in track and ground induced by train passages are investigated by the substructure method with due consideration to dynamic interaction between an inhomogeneous track system comprising continuous rails and discrete sleepers, and the underlying viscoelastic layered half space ground. Initially, the total system is divided into two separately formulated substructures, i.e., the track and the ground. The rail is described by introducing the Green function for an infinite long Euler beam both for moving axle loads action from a train and for reactions from sleepers. The ground is formulated by the layer transfer matrix approach for wave propagation along the depth. Subsequently, these substructures are integrated to meet the displacement compatibility and force equilibrium via inertia of sleepers and stiffness of railpad springs. The dynamic equations are solved in the frequency–wave-number domain by applying the Fourier transform procedure. Based on the assumption of a constant train speed, the time domain response is evaluated from the inverse Fourier transform computation. The dispersive characteristics of the layered ground and the moving axle loads lead to significantly different response features, depending on the train speed. The response is classified as quasistatic for a low speed, whereas it is dynamic for a high-speed situation. An illustrative case study is presented for Swedish X-2000 train track properties and ground profile.     

Dynamic Behavior of Orthotropic Rectangular Plates under Moving Loads

The dynamic behavior of an orthotropic plate simply supported on a pair of parallel edges and under a system of moving loads is analyzed based on Lagrange equation and modal superposition. Thin plate theory is assumed for the plate model and no restriction is placed on the type of loading. Parameters of the plate affecting its dynamic behavior are discussed, and a new classification of the plates for computing the mode shapes and natural frequencies is proposed. The impact factors and the dynamic responses of a typical bridge deck are studied using the proposed method. Preliminary results indicate that the effect of eccentric loads on the impact factor depends on the proportion ratio between the flexural and torsional rigidities of the bridge deck, and the multilane loading case is less critical than a single-lane loading case.     

Dynamic Response of Plates on Elastic Foundation to Moving Loads

A procedure incorporating the finite strip method and a spring system has been developed and applied to treat the dynamic response of plate structure resting on an elastic foundation to moving loads. The response to a single moving concentrated load is first investigated and then the effects of velocity, elastic foundation stiffness, moving path, and distance between multiple moving loads are studied. The response under a moving harmonic load with constant velocity is finally treated and the effect of the load frequency is investigated. Results indicate that the foundation stiffness and the velocity and frequency of the moving load have significant effects on the dynamic response of the plate and on resonant velocities. Some of these findings might find use in practical applications.     

Dynamic Response of Footings Resting on a Sand Layer of Finite Thickness

Dynamic response of foundations depends on several factors, namely, size and shape of the foundations, depth of embedment, soil profile and properties, frequency of loading, and mode of vibration. An attempt was made in this Technical Note to investigate the dynamic behavior of foundations resting on a sand layer underlain by a rigid layer. Model block vibration tests were carried out in a pit of size 2.0?m×2.0?m×1.9?m using a concrete footing of size 0.4?m×0.4?m×0.1?m and a vertically acting rotating-mass type mechanical oscillator. Using locally available river sand, a sand layer of six different thicknesses was prepared, and, for each thickness, tests were carried out for two different static weights and three different dynamic loadings. It was observed that the resonant frequency decreases with an increase in layer thickness and it nearly equals that of the half-space when the thickness of the layer is more than three times the width of the footing. It was also observed that the radiation damping of the sand layer was affected by the presence of a rigid layer at bottom. Inclusion of rigid layer causes a 9.8% reduction with respect to homogeneous sand condition even for a sand layer of thickness four times the width of the footing.     

Response of Multilayer Foundation System beneath Railway Track under Cyclic Loading

For an efficient and economical design of a railway track system, it is necessary to understand the behavior of each track component with special reference to ballast and subgrade, which play a pivotal role in distributing the large, cyclic wheel loads longitudinally, laterally, and vertically away from the wheel contact area on the rail surface to the underlying soil strata. This paper presents an analytical model of a track-ballast-subgrade system with different formation soils such as dense uniform sand, stiff clay, loose sand, and soft clay modeled by using a mass-spring dashpot system with two degrees of freedom. This represents the varying energy distribution through ballast and subgrade in the vertical direction. Results are presented in the form of time-displacement response profiles for both the ballast and subgrade layers. In addition, the magnification factors for displacements with variation in subgrade soils for cyclic loading frequencies are reported. It is observed that the results obtained from the present analysis follow the experimentally observed trends already available in the literature.     

Determination of Dynamic Track Modulus from Measurement of Track Velocity during Train Passage

The measurement of track stiffness, or track modulus, is an important parameter for assessing the condition of a railway track. This paper describes a method by which the dynamic track modulus can be determined from the dynamic displacements of the track during normal train service, measured using geophones. Two techniques are described for calculating the track modulus—the inferred displacement basin test (DBT) method and a modified beam on an elastic foundation (BOEF) method. Results indicate that the viscoelastic response of the soil will influence the value of track modulus determined using the DBT method. The BOEF method was therefore used to calculate the apparent increase in axle load due to train speed. Hanging or partly supported sleepers were associated with a relatively small increase in dynamic axle loads with train speed.     

Control of Suspension Bridge Nonlinear Vibrations due to Moving Loads

The flexibility and low damping of the long-span suspended cables in the suspension bridges make them prone to vibrations due to wind and moving loads, which affect the dynamic response of the suspended cables and the bridge deck. This paper shows the design of two control schemes to control the nonlinear vibrations in the suspended cable and the bridge deck due to a vertical load moving on the bridge deck with a constant speed. The first control scheme is an optimal state feedback controller. The second control scheme is a robust state feedback controller, whose design is based on the design of optimal controllers. The proposed controllers, whose design is based on Lyapunov theory, guarantee the asymptotic stability of the system. A vertical cable between the bridge deck and the suspended cable is used to install a hydraulic actuator able to generate the active control force on the bridge deck. The MATLAB software is used to simulate the performance of the system with the designed controllers. The simulation results indicate that the proposed controllers are capable of significantly reducing the nonlinear oscillations of the system. In addition, the performance of the system with the proposed controllers is compared to the performance of the system controlled with a velocity feedback controller. It is found that the system with the proposed controllers can provide better performance than the system with the velocity feedback controller.     

Concentrations of Pressure Between an Elastically Supported Beam and a Moving Timoshenko-Beam

The present paper is concerned with the motion of an elastically supported beam that carries an elastic beam moving at constant speed. This problem provides a limiting case to the assumptions usually considered in the study of trains moving on rail tracks. In the literature, the train is commonly treated as a moving line-load with space-wise constant intensity, or as a system of moving rigid bodies supported by single springs and dampers. In extension, we study an elastically supported infinite beam, which is mounted by an elastic beam moving at a constant speed. Both beams are considered to have distributed stiffness and mass. The moving beam represents the train, while the elastically supported infinite beam models the railway track. The two beams are connected by an interface modeled as an additional continuous elastic foundation. Here, we follow a strategy by Stephen P. Timoshenko, who showed that a beam on discrete elastic supports could be modeled as a beam on a continuous elastic Winkler (one-parameter) foundation without suffering a substantial loss in accuracy. The celebrated Timoshenko theory of shear deformable beams with rotatory inertia is used to formulate the equations of motion of the two beams under consideration. The resulting system of ordinary differential equations and boundary conditions is solved by means of the powerful methods of symbolic computation. We present a nondimensional study on the influence of the train stiffness and the interface stiffness upon the pressure distribution between train and railway track. Considerable pressure concentrations are found to take place at the ends of the moving train.     

Dynamic Response of Suspension Bridge to High Wind and Running Train

A framework is presented for predicting the dynamic response of long suspension bridges to high winds and running trains. A three-dimensional finite-element model is used to represent a suspension bridge. Wind forces acting on the bridge, including both buffeting and self-excited forces, are generated in the time domain using a fast spectral representation method and measured aerodynamic coefficients and flutter derivatives. Each 4-axle vehicle in a train is modeled by a 27-degrees-of-freedom dynamic system. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. By applying a mode superposition technique to the bridge only and taking the measured track irregularities as known quantities, the number of degrees of freedom of the bridge-train system is significantly reduced and the coupled equations of motion are efficiently solved. The proposed formulation is then applied to a real wind-excited long suspension bridge carrying a railway inside the bridge deck of a closed cross section. The results show that the formulation presented in this paper can predict the dynamic response of the coupled bridge-train systems under fluctuating winds. The extent of interaction between the bridge and train depends on wind speed and train speed.     

Studying Characteristics of Train-Induced Ground Vibrations Adjacent to an Elevated Railway by Field Experiments

This paper investigates the characteristics of the ground vibration induced by moving trains on elevated railways using a number of field measurements at various train speeds. The experimental results indicate that the vibration at the dominant frequencies is quite large in both the vertical and horizontal directions, where the dominant frequencies and their influence factors can be evaluated using two simple theoretical equations deducted from the trainload in the frequency domain. Furthermore, the vibration at the dominant frequencies increases almost proportionally to the train speed, except at the resonance condition, which can be found both in field experiments and using the equation of the influence factor.     

高温排风机转子的动力特性与转子结构优化

对风机转子在积泥(液)和高温工况下的动力性能进行了讨论;并根据铜冶炼行业高温烟气的特点,指出了现国内用于铜冶炼行业中高温烟气排放的大型工业风机的转子结构上存在的缺陷,并进行有效整改。     

Dynamic Characteristics of Chilean Bridges with Seismic Protection

A new highway system is being constructed in Chile including many bridges. Due to the high seismic risk in the country, high damping rubber bearings, friction bearings, and passive energy dissipation devices have been considered in the design of the majority of the new moderate and large span bridges. Their design follows American Association of State Highway guidelines and technical specifications from the Chilean Ministry of Public Works. Experimental and analytical studies have been performed in three of these structures: (1) a 383 m long continuous beam bridge supported on high damping rubber bearings; (2) a 268 m long continuous beam bridge supported on friction bearing with additional viscous dampers; and (3) a five-span simply supported beam bridge resting on neoprene bearings. Predominant periods and damping characteristics for small amplitude vibrations have been determined from output-only nonparametric analyses. Comparison with standard analytical structural models indicates that the models normally used for analysis yield comparable predominant periods and mode shapes but the damping values typically recommended are larger than the ones observed from ambient vibrations, even when additional energy dissipation elements are present.     

Controlling Characteristics of Passive Mega-Subcontrolled Frame Subjected to Random Wind Loads

The passive mega-subcontrolled structure proposed recently is a new form of structure associated with the design and construction of supertall buildings. However, a shortcoming still exists in its structural configuration. In this paper, a new configuration of the passive mega-subcontrolled frame is proposed. A more realistic analytical model of this structure subjected to random wind loads is presented, in which the substructures are treated as a multi-degree-of-freedom (MDOF) system and a nonwhite stochastic process in time and space is used. The dynamic equations and the response spectrum expressions, as well as the mean square response expressions, are derived on the basis of complex modal-analysis theory. A practical steel passive mega-subcontrolled frame is investigated; it is designed with reference to the conventional mega-subframe used in the Tokyo City Hall. The influence of the relative mass ratio and the relative stiffness ratio on the controlling effectiveness is investigated; and a proposed relative stiffness region, which is very useful in practical engineering design, is first presented. The corresponding computing results demonstrate that the structural configuration proposed here has extraordinary effectiveness in controlling displacement responses and acceleration responses, and the shortcoming that existed in the previously presented configuration can be overcome effectively.     

Fatigue Damage of Steel Bridges Due to Dynamic Vehicle Loads

This paper focuses on the fatigue damage caused in steel bridge girders by the dynamic tire forces that occur during the crossing of heavy transport vehicles. This work quantifies the difference in fatigue life of a short-span and a medium-span bridge due to successive passages of either a steel-sprung or an air-sprung vehicle. The bridges are modeled as beams to obtain their modal properties, and air-sprung and nonlinear steel-sprung vehicle models are used. Bridge responses are predicted using a convolution method by combining bridge modal properties with vehicle wheel forces. A linear elastic fracture mechanics model is employed to predict crack growth. For the short-span bridge, the steel-sprung vehicle caused fatigue failure up to 6.5 times faster than the air-sprung vehicle. For the medium-span bridge, the steel-sprung vehicle caused fatigue failure up to 277 times faster than the air-sprung vehicle.     

Identification of a Distribution of Stiffness Reduction in Reinforced Concrete Slab Bridges Subjected to Moving Loads

The method for identifying arbitrary stiffness reduction in damaged reinforced concrete slab bridges under moving loads is proposed and dynamic signals measured at several points are used as response data to reflect the properties of the moving loads sensitivity. In particular, the change in stiffness in each element before and after damage, based on the system identification method, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in this work is more feasible than the conventional element-based damage detection method from the computational efficiency because the procedure of finite-element analysis coupled with microgenetic algorithm using six unknown parameters irrespective of the number of elements are considered. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical calculations show that the proposed technique is a feasible and practical method that can prove the exact location of a damaged region as well as inspect the complex distribution of deteriorated stiffness, although there is a modeling error between actual bridge results and numerical model results as well as a measurement error like uncertain noise in the response data.     

Dynamic Response of a Highway Bridge Subjected to Moving Vehicles

Several full-scale load tests were performed on a selected Florida highway bridge. The bridge was dynamically excited by two fully loaded trucks, and the strain, acceleration, and displacement at selected points were recorded for the investigation of the bridge’s dynamic response. Experimental data were compared with simplified vehicle and bridge finite-element models. The vehicle was represented as a three-dimensional mass–spring–damper system with 11?degrees of freedom, and the bridge was modeled as a combination of plate and beam elements that characterize the slab and girders, respectively. The equations of motion were formulated with physical components for the vehicle and modal components for the bridge. The coupled equations were solved using a central difference method. It was found that the numerical analysis matched well with the experimental data and was used to successfully explain critical dynamic phenomena observed during the testing. Impact factors for this tested bridge were thoroughly investigated by using these models.     

Design and Dynamic Analysis of an Adjustable Inertia Absorber for Semiactive Structural Vibration Attenuation

A new class of adaptive tuned vibration absorber, a variable effective inertia absorber, is presented to impart optimum vibration absorption. The tuning scheme has two facets: spectral analysis of the excitation and a concurrent in situ tuning of the absorber. The spectral analysis reveals the frequency content of the excitation. The online tuning uses the frequency content of the excitation to reposition a moving mass and change the damping coefficient of a variable rate damper for optimal (broadband) or tonal vibration suppression. The nonlinear differential equations of motion are linearized and then utilized to develop the online tonal and the broadband tuning of the variable effective inertia absorber. A case study is presented to demonstrate the novelty of the concept. The results show that the retuned absorber delivers considerable vibration suppression improvement over the detuned one.     

Domain Decomposition Method for Calculating the Failure Probability of Linear Dynamic Systems Subjected to Gaussian Stochastic Loads

In this paper the problem of calculating the probability of failure of linear dynamic systems subjected to random vibrations is considered. This is a very important and challenging problem in structural reliability. The failure domain in this case can be described as a union of linear failure domains whose boundaries are hyperplanes. Each linear limit state function can be completely described by its own design point, which can be analytically determined, allowing for an exact analytical calculation of the corresponding failure probability. The difficulty in calculating the overall failure probability arises from the overlapping of the different linear failure domains, the degree of which is unknown and needs to be determined. A novel robust reliability methodology, referred to as the domain decomposition method (DDM), is proposed to calculate the probability that the response of a linear system exceeds specified target thresholds. It exploits the special structure of the failure domain, given by the union of a large number of linear failure regions, to obtain an extremely efficient and highly accurate estimate of the failure probability. The number of dynamic analyses to be performed in order to determine the failure probability is as low as the number of independent random excitations driving the system. Furthermore, calculating the reliability of the same structure under different performance objectives does not require any additional dynamic analyses. Two numerical examples are given demonstrating the proposed method, both of which show that the method offers dramatic improvement over standard Monte Carlo simulations, while a comparison with the ISEE algorithm shows that the DDM is at least as efficient as the ISEE.     

Vibration Serviceability of a Building Floor Structure. I: Dynamic Testing and Computer Modeling

Buildings with large column-free floors or long-cantilevered structures can be susceptible to annoying vibrations due to everyday occupants’ activities such as walking. Computer modeling and analytical representation of building structural properties to predict the floor response subjected to excitations due to human activities are important issues that require further studies. Vibration testing and analysis of built structures can assist in more accurate estimation of structure dynamic properties. This paper presents the results of the modal testing conducted on an office building floor and analysis of the collected vibration measurements. It compares these results with the structural response using computer analyses. It also presents a sensitivity study to assess the importance of various structural parameters on the floor dynamic response. From the results presented, it is concluded that for the structure used in this study the raised flooring and nonstructural elements acted mainly as added mass and did not contribute to the floor damping. Conclusions are also made on the importance of various structural parameters on floor response and the analysis of the modal test results.     

轧机机架的动态特性仿真与结构优化

应用有限元分析方法,对某铝带二辊轧机机架装配系统进行了动态特性仿真,得出了固有频率和振型的变化规律.针对轧机机架的薄弱环节,通过参数化方法进行灵敏度分析和结构优化设计,使系统的动态特性得到提高,该结论为高性能轧机的设计优化,提供了一定的参考.