Theoretical modeling and characteristic analysis of moving-train induced ground vibrations

An integrated train-track-subsoil dynamic interaction model of moving-train induced ground vibration is developed on the basis of vehicle dynamics, track dynamics and the Green's functions of subsoil. The model takes account of the vibrations of vehicle components, the quasi-static axle loads and the dynamic excitations between the wheels and track. The analyzed results from an example show that the ground vibration characteristics have a close relationship with train speed and soil properties; the dynamic responses excited by wheel-track irregularity have big influence on the high frequency components of ground vibration; with the increase of distance to the track, the ground acceleration has the tendency of decrease, and the relevance of acceleration curves and train excitation becomes less obvious; the intersections of moving load speed-lines and subsoil dispersion curves are some resonance frequencies that cause the amplification of ground vibrations; there exists a critical speed for moving train that is close to the minimum velocity of the Rayleigh's wave in the subsoil.     

Street-running LRT may not affect a neighbour's sleep

A comprehensive dynamic finite difference model and analysis was conducted simulating LRT running at the speed of 24 km/h on a city street. The analysis predicted ground borne vibration (GBV) to remain at or below the FTA criterion of a RMS velocity of 72 VdB (0.004 in/s) at the nearest residence. In the model, site-specific stratography and dynamic soil and rock properties were used that were determined from in situ testing. The dynamic input load from LRT vehicle running at 24 km/h was computed from actual measured data from Portland, Oregon's West Side LRT project, which used a low floor vehicle similar to the one proposed for the NJ Transit project.During initial trial runs of the LRT system, vibration and noise measurements were taken at three street locations while the vehicles were running at about the 20-24 km/h operating speed. The measurements confirmed the predictions and satisfied FTA criteria for noise and vibration for frequent events.This paper presents the analytical model, GBV predictions, site measurement data and comparison with FTA criterion.     

Isolation effect of a dynamic damper and a trench on ground vibration caused by a construction machine

In this study, a simple isolation method of ground vibration is proposed by using a dynamic damper and a trench, which is feasible for temporary use during a construction period. The ground is modeled as a two-dimensional plane model. Periodic impulsive excitation acts at one point on the ground surface, and the vibrations are measured at several evaluation points on the ground surface. A simple dynamic damper composed of a weight and a restoring element is set up at the ground surface or in the shallow trench, and the vibration isolation effect is examined. The simulation shows that the ground vibration can be isolated when the dynamic damper is set near the excitation point on the ground surface, and setting the dynamic damper in a shallow trench has almost the same isolation effect as that in a deep trench. The results indicate that the proposed isolation method is feasible for actual application.     

Calculation of ground vibration spectra from heavy military vehicles

The demand for reliable autonomous systems capable to detect and identify heavy military vehicles becomes an important issue for UN peacekeeping forces in the current delicate political climate. A promising method of detection and identification is the one using the information extracted from ground vibration spectra generated by heavy military vehicles, often termed as their seismic signatures. This paper presents the results of the theoretical investigation of ground vibration spectra generated by heavy military vehicles, such as tanks and armed personnel carriers. A simple quarter car model is considered to identify the resulting dynamic forces applied from a vehicle to the ground. Then the obtained analytical expressions for vehicle dynamic forces are used for calculations of generated ground vibrations, predominantly Rayleigh surface waves, using Green's function method. A comparison of the obtained theoretical results with the published experimental data shows that analytical techniques based on the simplified quarter car vehicle model are capable of producing ground vibration spectra of heavy military vehicles that reproduce basic properties of experimental spectra.     

Semi-analytical analysis of the isolation to moving-load induced ground vibrations by trenches on a poroelastic half-space

A semi-analytical model is proposed to investigate the screening efficiency of trenches to moving-load induced ground vibrations. The ground is modeled as a fully saturated poroelastic half-space governed by Biot's dynamic poroelastic theory. The trenches are obtained by placing three rectangular elastic layers with appropriate width upon the poroelastic half-space. By Helmholtz decomposition, the displacement fields of the elastic layers are decomposed into three scalar potentials. Analytical solutions are obtained based on Fourier transform and Fourier series in the transformed domain. The time-domain results are obtained by the fast Fourier transform (FFT). The different performances of trenches on a saturated poroelastic half-space and a single-phase elastic half-space to the moving load-induced ground vibration are identified. It is found that the discrepancy of the screening efficiencies between the two models becomes significant when the load speed approaches the Rayleigh wave speed of the ground surface. Also, some parametric studies for the screening efficiency of the trench on the poroelastic half-space are presented.     

Simulation of track-ground vibrations due to a high-speed train: the case of X-2000 at Ledsgard

This paper attempts to demonstrate an application of the author's simulation model for predicting the train-track and nearby ground-borne vibrations by the Swedish high-speed train X-2000 at Ledsgard. The validation of the computation results are tested against the available field measurement data at the site. In this way, the theoretical prediction of the model can be verified whilst also providing a clear-cut explanation of the observed data. The findings are stated as follows:The train-induced vibrations at the track differ significantly depending on train geometry and speed. At low speeds the response is quasi-static so that the track response due to train axle loads appears mostly downward at the point of their action. On the other hand, at high speeds the train-induced response becomes dynamic due to the inertia generated in the track-ground system, so that the track vibrations appear evenly in both upward and downward directions. As the results of the soft soil deposits at Ledsgard, the high train speed is almost in the trans-Rayleigh wave state so that a large amplified track response appeared due to the resonance between the track behavior and the Rayleigh wave propagation in the ground. This is explained by the frequency-wavenumber spectrum.To provide useful engineering information relating to vibration mitigation at the train track and nearby ground, a preliminary investigation was carried out by simulating the effect of constructing of a wave impeding barrier (WIB) at the site. The aforementioned frequency-wavenumber spectrum showed that the stiffening effects by the WIB installation into soft layers led a shift of response from a large dynamic one at high train speeds to a small, quasi-static one.     

单框架控制力矩陀螺转子动不平衡对遥感卫星成像的影响

分析了单框架控制力矩陀螺（SGCMG）转子在高速旋转时产生的动不平衡干扰力矩引起的星体颤振角和颤振角速度对TDI CCD相机成像的影响。通过坐标变换将转子坐标系下的干扰力矩转换至星体坐标系下的干扰力矩,将卫星姿态动力学方程计算出干扰力矩引起的星体颤振角位移和颤振角速度代入TDI CCD相机成像像移补偿模型;利用TDICCD相机像点与物点对应模型的仿真系统仿真了陀螺转子在不同转速下引起星体颤振角位移和角速度对相机成像的影响;最后,利用图像对比度和互相关相似性测度分析仿真成像质量。仿真显示：SGCMG转子在转速为3 000 r/min时,横向调制传递函数为0.997,图像互相关相似性测度为0.996 1;转速为6 000 r/min时,横向调制传递函数为0.928 3,图像互相关相似性测度为0.974 8。结果表明：SGCMG转子在高速旋转过程中引起的星体颤振角位移和角速度严重影响了TDI CCD相机的成像质量,应依据颤振的影响对SGCMG实施减震措施。     

Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles

An investigation into the dynamics of vehicle-occupant-structure-induced vibration of bridges traversed by moving vehicles is presented. The vehicle including the driver and passengers is modelled as a half-car planar model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory with arbitrary conventional boundary conditions. Due to the continuously moving location of the variable loads on the bridge, the governing differential equations become rather complicated. The numerical simulations presented here are for the case of vehicle travelling at a constant speed on a uniform bridge with simply supported end conditions. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of the dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span, while the maximum bending moment occurs at ±20% of the mid-span point. It is shown that one can find a critical speed at which the maximum values of the bridge dynamic deflection and the bending moment attain their global maxima.     

Sound propagation over layered poro-elastic ground using a finite-difference model

This article presents an axisymmetric pressure-velocity finite-difference formulation (PV-FD) based on Biot's poro-elastic theory for modeling sound propagation in a homogeneous atmosphere over layered poro-elastic ground. The formulation is coded in a computer program and a simulation of actual measurements from airblast tests is carried out. The article presents typical results of simulation comprising synthetic time histories of overpressure in the atmosphere and ground vibration as well as snapshots of the response of the atmosphere-ground system at selected times. Comparisons with the measurements during airblast tests performed in Haslemoen, Norway, as well as the simulations by a frequency-wave number FFP formulation are presented to confirm the soundness of the proposed model. In particular, the generation of Mach surfaces in the ground motion, which is the result of the sound speed being greater than the Rayleigh wave velocity in the ground, is demonstrated with the help of snapshot plots.     

Analyses of wave field from high-speed train on viaduct at shallow/deep soft grounds

In this paper, based on field measurements for the passage of the Shinkansen high speed trains on viaducts, the author reports the induced ground vibration features at distinctly different sites: one site is characterized by a deep soft soil and the other by a shallow soft soil both of which lie on stiff bottom. The conventional vibration assessment is normally addressed to the vibration levels based on acceleration maxima. However, in view of the vibration reception by nearby residents, firstly, a detailed investigation is attempted on the recorded time histories and on their Fourier spectra, locating the so-called low frequency vibration generation at the former site and such vibration impediment at the latter site. Then, theoretical consideration is to clarify the Shinkansen-train induced ground vibrations from a viaduct. The characterization based on the wave theory using the thin layer method reveals that, depending on the depth of surface layer, the ground-borne vibration is of significantly low frequency wave modes of dispersive propagation when it is deep or it makes the wave modes shifted towards higher frequency range when it is shallow. This finding makes an important element to better predict and assess vibration level and to develop barriers against it for mitigation.     

LOCAL-MODE RESONANCE AND ITS STRUCTURAL EFFECTS UNDER HORIZONTAL GROUND SHOCK EXCITATIONS

The dynamic response of building structures has been studied extensively for relatively low-frequency seismic actions, and it is established that the seismic response generally is governed by the global-mode vibration, i.e., the vibration in terms of the floor movement. Much less fundamental study has been done regarding the structural response to ground shock excitations with principal frequencies many times of the fundamental frequency of the structural system. Most of the existing code provisions on ground shock control have U001remained empirical. In this paper, it is demonstrated through numerical study and laboratory model testing that the structural response to high-frequency ground shocks have distinctive characteristics as compared to the seismic response, and most significant is the participation of the vibration at the local elemental level. Local-mode resonance could occur when the shock frequency is sufficiently high, and to a large extent it can be uncoupled from the global floor vibration. As a result, large force effects can develop at relatively small floor displacement, rendering the conventional displacement-based criteria inapplicable, while more focus on the stress-strain response is deemed necessary. The results pave a way for further development of more rational criteria for this category of the structural vibration problems.     

Vibration research of the AC dipole-girder system for CSNS/RCS

The China Spallation Neutron Source (CSNS) is a high intensity proton accelerator based facility. Its accelerator complex includes two main parts: an H^- linac and a rapid cycling synchrotron (RCS). The RCS accumulates the 80 MeV proton beam and accelerates it to 1.6 GeV, with a repetition rate of 25 Hz. The AC dipole of the CSNS/RCS is operated at a 25 Hz sinusoidal alternating current which causes severe vibration. The vibration will influence the long-term safety and reliable operation of the magnet. The dipole magnet of CSNS/RCS is an active vibration equipment, which is different from the ground vibration accelerator. It is very important to design and study the dynamic characteristics of the dipole-girder system. This paper takes the AC dipole and girder as a specific model system. A method for studying the dynamic characteristics of the system is put forward by combining theoretical calculation with experimental testing. The ANSYS simulation method plays a very important role in the girder structure design stage. With this method, the mechanical resonance phenomenon was avoided in the girder design time. At the same time the dipole vibratory force will influence the other equipment through the girder. Since it is necessary to isolate and decrease the dipole vibration, a new isolator was designed to isolate the vibratory force and decrease the vibration amplitude of the magnet.     

Finite element modeling of a micro-drill and experiments on high speed ultrasonically assisted micro-drilling

Modal characteristics of a generic micro-drill and experiments on the micro-drilling with superimposing of longitudinal ultrasonic vibration are presented. Finite element (FE) analysis is used for identification of eigenfrequencies and modes of the drill. Dynamic influence of the drill shank is discussed and a hybrid model is proposed to account for it. The model is proven to be efficient for complicated drill models and advanced analysis. A high speed ultrasonically assisted micro-drilling (UAMD) system is established with air bearings and longitudinally vibrating workpiece. During the experiments the thrust force reduction is studied as well as effects of ultrasonic vibration frequency and rotational speed. A correlation study was conducted between the thrust force measurements and simulations from a nonlinear force model. It can be seen that the current one-dimensional model is not sufficient to describe the complete behavior of the drill. The FE model and force experimental results can be utilized for a full dynamic model of the UAMD system to study vibration and the cutting mechanism in the future.     

On rail vehicle vibrations induced by track unevenness: Analysis of the excitation mechanism

This paper deals with the analysis of the vibrations induced on the carbody of a rail vehicle by track unevenness. Attention is focused on the excitation mechanism of the carbody vibration modes, which has a strong influence on the vehicle's comfort. At first the problem is investigated through a simple three-degree-of-freedom analytical model, and the phenomenon of the critical velocities is analysed, pointing out how both rigid and flexible carbody vibration modes can be excited to a different extent, depending on the vehicle speed, and how they combine to produce the final carbody accelerations. Then the dynamic response of a real vehicle running on irregular track is simulated through a more detailed multibody model, suitable for quantitatively reproducing its dynamic behaviour in the 0-25 Hz frequency range. The 68 degrees-of-freedom of this model correspond to 35 rigid vibration modes of the vehicle components (carbody, bogie frames and wheelsets), plus the 33 carbody flexible modes which fall into the frequency-range of interest. In the last part of the paper, the obtained numerical results are compared to the experimental data collected during on-line tests, showing how the adopted numerical model accurately simulates the dynamic behaviour of the real vehicle at the different velocities, with very good agreement. The results presented in the paper demonstrate that the excitation of the flexible modes may have a decisive effect on carbody accelerations and that introducing carbody flexibility in the vehicle model turns out to be unavoidable for properly predicting a rail vehicle comfort performance.     

Effects of a multi-layered poro-elastic ground on attenuation of acoustic waves and ground vibration

Ground conditions affect the propagation of outdoor sound and vibration. This paper focuses on the interaction between air pressure and porous ground at low frequencies- where mechanisms other than the rigid porous effects used in locally reacting models may be important. A 2-D analytical model has been developed in this study for the calculation of acoustic and acousto-seismic admittances in a multi-layered poro-elastic ground. The model can be used as a prediction tool both for the ground effect on the sound and the generation of ground vibration by the sound. The modelled acoustic admittance is validated successfully against established rigid frame admittance models over a frequency range of 1 Hz-3 kHz. Moreover, the acousto-seismic impedance is verified against full scale airblast field test data measured during the Norwegian Trials full scale field test program. For certain ground types, the predicted acoustic admittance illustrates a different behaviour compared with predictions from the traditional rigid frame acoustic impedance models. This emphasises the importance of including a deformable frame in the model to obtain realistic results for these conditions.     

Free torsional vibration of nanotubes based on nonlocal stress theory

A new elastic nonlocal stress model and analytical solutions are developed for torsional dynamic behaviors of circular nanorods/nanotubes. Unlike the previous approaches which directly substitute the nonlocal stress into the equations of motion, this new model begins with the derivation of strain energy using the nonlocal stress and by considering the nonlinear history of straining. The variational principle is applied to derive an infinite-order differential nonlocal equation of motion and the corresponding higher-order boundary conditions which contain a nonlocal nanoscale parameter. Subsequently, free torsional vibration of nanorods/nanotubes and axially moving nanorods/nanotubes are investigated in detail. Unlike the previous conclusions of reduced vibration frequency, the solutions indicate that natural frequency for free torsional vibration increases with increasing nonlocal nanoscale. Furthermore, the critical speed for torsional vibration of axially moving nanorods/nanotubes is derived and it is concluded that this critical speed is significantly influenced by the nonlocal nanoscale.     

Dynamic impedances and free-field vibration analysis of pile groups in saturated ground

A three-dimensional (3D) numerical model basing on the thin layer element method and the flexible volume method was established for the computation of dynamic impedances and free-field vibrations of rigidly-capped pile groups embedded in saturated ground. The piles were considered as beams and the saturated ground was represented by Biot?s three-dimensional elastodynamic theory. By recourse to the thin layer element method, Green function of the three dimensional saturated ground was obtained and then verified. The dynamic interaction of the piles and the saturated ground was solved by using the flexible volume method, in which the piles were discretized into three dimensional Euler−Bernoulli beam elements and the dynamic stiffness matrix of saturated ground was formed at the pile−soil interaction nodes by using the Green function. Impedances of the 2×2 pile group and free-field displacement and pore pressure responses caused by harmonic vertical, lateral and rocking forces (moments) applied at the cap center were presented, respectively, for different soil permeability and excitation frequencies. It is found that the soil permeability and the excitation frequency have significant influence on the impedances and the free-field vibration responses.     

Regenerative vibration avoidance due to tool tangential dynamics in interrupted turning operations

Linear stability models are often used to predict regenerative vibrations in turning representing continuous operations, simple cutting geometries with constant coefficients and/or dominant modes acting in the feed direction. However, turning of components with interrupted features, such as turbine cases, may lead to large tool overhangs with vibration motions in the cutting speed direction and tool cut-off periods that result in the latter approaches being insufficient. This paper proposes a stability model for chatter in interrupted turning when the dominant vibration is orthogonal to the chip section plane. The method requires the calculation of a dynamic displacement factor that depends on the tool vibration frequency. The simulations of the model are supported by experimental tests for different contact fractions.     

Linear parameter varying control design for rotating systems supported by journal bearings

Linear parameter varying (LPV) control is a model-based control technique that takes into account time-varying parameters of the plant. In the case of rotating systems supported by lubricated bearings, the dynamic characteristics of the bearings change in time as a function of the rotating speed. Hence, LPV control can tackle the problem of run-up and run-down operational conditions when dynamic characteristics of the rotating system change significantly in time due to the bearings and high vibration levels occur. In this work, the LPV control design for a flexible shaft supported by plain journal bearings is presented. The model used in the LPV control design is updated from unbalance response experimental results and dynamic coefficients for the entire range of rotating speeds are obtained by numerical optimization. Experimental implementation of the designed LPV control resulted in strong reduction of vibration amplitudes when crossing the critical speed, without affecting system behavior in sub- or super-critical speeds.     

The effect of critically moving loads on the vibrations of soft soils and isolated railway tracks

The dynamic response of the railway track is strongly influenced by the underlying soil. For a soft soil and very high train speeds or for a very soft soil and regular train speeds, the train speed can be close to the speed of elastic waves in the soil. This paper presents a detailed study of the so-called “moving-load effect”, i.e. an amplification of the dynamic response due to the load movement, for the tracks on soft soil. The analysis is carried out by evaluating the related integrals in the wavenumber domain. The influence of the load speed is quantified for a large set of parameters, showing that the effect on the soil vibration is reduced with increase of the frequency, track width and inverse wave velocity. Therefore, the moving-load effect associated with vibratory train loads is negligible whereas the amplification associated with the moving dead weight of the train can be significant. The strong moving-load effect on a perfectly homogeneous soil, however, can be strongly diminished by a layered or randomly varying soil situation. This theoretical result is affirmed by measurements at a test site in Germany where the trains run on a very soft soil at a near-critical speed. The results for soft soils are compared with experimental and theoretical results for a stiff soil. It is found that the influence of the stiffness of the soil is much stronger than the moving-load effect. This holds for the soil vibration as well as for the track vibration which both show a minor dependence on the load speed but a considerable dependence on the soil stiffness in theory and experiment.Railway tracks can include soft isolation elements such as rail pads, sleeper shoes and ballast mats. For these types of isolation elements and normal soil conditions, the influence of the load speed is usually negligible. There is only one isolation measure for which the moving load may be effective: a track which is constructed as a heavy mass-spring system. The resonance of this track system is shifted to lower frequencies and amplitudes for increasing train speed. A critical train speed can be reached if the mass-spring system has a marginal bending stiffness along the track.