Ground-borne noise and vibration from underground rail systems

Ground-borne noise is one of the main causes of environmental impact from urban rail transit systems. The vibration resulting from track-train interaction is transmitted through the tunnel 3tructure and the surrounding ground to adjacent buildings. The resulting vibrations of the walls and floors of these buildings cause secondary radiation of noise. This paper presents a method for estimating A-weighted sound levels as well as noise and vibration spectra due to ground-transmitted vibration in buildings near subways.     

Numerical analysis of isolation of the vibration due to moving loads using pile rows

The isolation of the vibration due to moving loads using pile rows embedded in a poroelastic half-space is investigated in this study. Based on Biot's theory and integral transform method, the free field solution for a moving load applied on the surface of a poroelastic half-space and the fundamental solution for a harmonic circular patch load applied in the poroelastic half-space are derived first. Using Muki and Sternberg's method and the fundamental solution for the circular patch load as well as the obtained free field solution for the moving load, the second kind of Fredholm integral equations in the frequency domain describing the dynamic interaction between pile rows and the poroelastic half-space is developed. Numerical solution of the frequency domain integral equations and numerical inversion of the Fourier transform yield the time domain response of the pile–soil system. Comparison of our results with some known results shows that our results are in a good agreement with existing ones. Numerical results of this study show that velocity of moving loads has an important impact on the vibration isolation effect of pile rows. The same pile row has a better vibration isolation effect for the lower speed moving loads than for the higher speed ones. Also, the optimal length of piles for higher speed moving loads is shorter than that for lower speed moving loads. Moreover, stiff pile rows tend to produce a better vibration isolation effect than flexible pile rows do.     

Coupled flexural-torsional vibration of beams in the presence of static axial loads and end moments

The problem of coupled flexural-torsional vibration of a deep rectangular beam in the presence of a static axial load and an end moment is studied. Closed form analytical solutions are obtained for simply supported boundary conditions. Numerical results are obtained for the coupled frequencies and mode shapes (in terms of the location of axes of rotation of the cross-section) for different values of the load and the geometry parameters. The results show that the predominantly flexural frequencies of coupled flexural-torsional vibration can be obtained as uncoupled flexural frequencies of an equivalent beam-column by defining an effective axial load, and that by defining an equivalent moment parameter the presentation of the results for the predominantly flexural mode can be made in a form independent of the slenderness of the beam in the depth direction.     

Dynamic axle and wheel loads identification: laboratory studies

Two methods have been reported by Zhu and Law to identify moving loads on the top of a bridge deck. One is based on the exact solution (ESM) and the other is based on the finite element formulation (FEM). Simulation studies on the effect of different influencing factors have been reported previously. This paper comparatively studies the performances of these two methods with experimental measurements obtained from a bridge/vehicle system in the laboratory. The strains of the bridge deck are measured when a model car moves across the bridge deck along different paths. The moving loads on the bridge deck are identified from the measured strains using these two methods, and the responses are reconstructed from the identified loads for comparison with the measured responses to verify the performances of these methods. Studies on the identification accuracy due to the effect of the number of vibration mode used, the number of measuring points and eccentricities of travelling paths are performed. Results show that the ESM could identify the moving loads individually or as axle loads when they are travelling at an eccentricity with the sensors located close to the travelling path of the forces. And the accuracy of the FEM is dependent on the amount of measured information used in the identification.     

Resonance characteristics of high-speed trains passing simply supported bridges

This paper investigates the resonant characteristics of three-dimensional bridges when high-speed trains pass them. Multi-span bridges with high piers and simply supported beams were used in the dynamic finite element analysis. The dominated train frequencies proposed in this study can be clearly seen from the finite element result. To avoid resonance, the dominated train frequencies and the bridge natural frequencies should be as different as possible, especially for the first dominated train frequency and the first bridge natural frequency in each direction. If the two first frequencies are similar, the bridge resonance can be serious. This study also indicates that a suitable axial stiffness between two simple beams can reduce vibrations at a near-resonance condition. The axial stiffness of the continuous railway and the friction of the bearing plate should be enough to obtain this axial stiffness.     

Effectiveness of blowing for improving the high-speed trains aerodynamics

The promising method of drag reduction with the use of micro-blowing through the streamlined surface has been proposed for its use to the external surface of high-speed train. The advantages of high-speed train as an object of micro-blowing application are introduced. The corresponding RANS-based mathematical model is elaborated, and the computations of the external flow around a long train body are performed. Predictions of the turbulent boundary layer over penetrable surface with different modes of micro-blowing have been presented and analyzed. The developed modifications of mathematical model of turbulence have been used to take into account the micro-blowing influence in the inner region of turbulent boundary layer. The obtained results of parametric analysis of drag reduction depending on the area of permeable sections, intensity of micro-blowing, and high-speed train length have been analyzed. In particular, the dependence between drag reduction effect and length of train body with realized micro-blowing as well as its intensity is established. Realization of micro-blowing with blowing velocity just 0.25 % of train speed (V = 100 m/s) on the 70 % of the streamlined surface area for just one train carriage (L = 25 m) allows one to reduce the aerodynamic drag (including the most actual friction and head-tail pressure components) of the whole train (L = 200 m) by about 5.25 %, so in case of micro-blowing realization on all its 8 carriages, the train’s aerodynamic drag can be reduced approximately by 42 %.     

The application of high-speed TV-holography to time-resolved vibration measurements

We describe an electronic speckle pattern interferometer (ESPI) system that has enabled non-harmonic vibrations to be measured with μs temporal resolution. The short exposure period and high framing rate of a high-speed camera at up to 40,500 frames per second allow low-power CW laser illumination and fibre-optic beam delivery to be used, rather than the high peak power pulsed lasers normally used in ESPI for transient measurement. The technique has been demonstrated in the laboratory and tested in preliminary industrial trials. The ability to measure vibration with high spatial and temporal resolution, which is not provided by techniques such as scanning laser vibrometry, has many applications in manufacturing design, and in an illustrative application described here revealed previously unmeasured “rocking” vibrations of a car door. It has been possible to make the measurement on the door as part of a complete vehicle standing on its own tyres, wheels and suspension, and where the excitation was generated by the running of the vehicle's own engine.     

Plasticity due to superimposed macrosonic and static strains

The aim of this investigation was to study the effect of superposition of a high power ultrasonic and a ‘static’ strain on the microstructure of commercial aluminium containing 1% Si and 0.6% Mg (the static strain resulting from a constant strain-rate tensile test). A special specimen design for resonance (20 kHz) is described and the results of macroscopic measurements on the specimen are given. The internal structure was studied by transmission electron microscopy and the results obtained are supported by scanning electron microscopy of the resulting fracture surfaces. The observed internal structure is explained on the basis of the developed structure due only to the ultrasonic stress fields.     

Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads

Different types of actuating and sensing mechanisms are used in new micro and nanoscale devices. Therefore, a new challenge is modeling electromechanical systems that use these mechanisms. In this paper, free vibration of a magnetoelectroelastic (MEE) microbeam is investigated in order to obtain its natural frequencies and buckling loads. The beam is simply supported at both ends. External electric and magnetic potentials are applied to the beam. By using the Hamilton's principle, the governing equations and boundary conditions are derived based on the Euler–Bernoulli beam theory. The equations are solved, analytically to obtain the natural frequencies of the MEE microbeam. Furthermore, the effects of external electric and magnetic potentials on the buckling of the beam are analyzed and the critical values of the potentials are obtained. Finally, a numerical study is conducted. It is found that the natural frequency can be tuned directly by changing the magnetic and electric potentials. Additionally, a closed form solution for the normalized natural frequency is derived, and buckling loads are calculated in a numerical example.     

On the sources of wayside noise generated by high-speed trains

A linear array of 14 microphones was used to measure radiated noise generated by a four-carriage electric train travelling at speeds between 160 and 250 km/h. Most of the results given in this paper pertain to apparent source locations of wheel/rail interaction noise, although preliminary data collected in a concurrent study of railway aerodynamic noise are briefly mentioned. An analysis of the measurements suggests that apparent sources of wheel/rail interaction noise are located (i) in the rail or substructure at low frequencies, (ii) on the wheel rim just below the axle at intermediate or peak frequencies, and (iii) on the lower part of the wheel and possibly in the rail at high frequencies.     

Plane hydroelastic beam vibrations due to uniformly moving one axle vehicle

The hydroelastic vibrations of a beam with rectangular cross-section is analyzed under the effect of an uniformly moving single axle vehicle using modal analysis and two-dimensional potential flow theory of the fluid neglecting the effect of surface waves aside the beam. For the special case of homogeneous beam resting on the surface of a water filled prismatic basin, the normal modes are determined considering surface waves in beam direction under the condition of compensating the volume of the enclosed fluid. The way to determine the vertical acceleration of the single axle vehicle is shown, which governs the response of the system. As analysis results the course of wheel load, the surface waves along the beam and the flow velocity distribution of the fluid is demonstrated for a continuous floating bridge under the passage of a rolling mass moving with uniform speed.     

Experimental analysis of a high-speed railway bridge under Thalys trains

In this paper dynamic experiments on the Antoing Bridge located on the high-speed railway line between Paris and Brussels are reported. The experiments were co-operatively carried out by the Northern Jiaotong University from China, the Catholic University of Leuven, the Free University of Brussels and the Belgium Railway Company NMBS-SNCB from Belgium. The bridge is composed of multi-span simply supported PC girders with spans of 50 m and U-shaped sections. The loads are the high-speed Thalys trains with articulated vehicles. The speeds of the Thalys trains were between 265 and 310 km/h. In the experiments, the dynamic responses of the bridge such as the deflections, the accelerations and the strains that were measured by a laser velocity displacement transducer accelerometers and strain gauges, respectively. Many useful results have been obtained from the analysis of the recorded data. The tests and the measured results can be a reference for the study and the design of high-speed railway bridges.     

A general model of the axle vibration in piezoelectric motors

In the present work a general model of the vibrational behavior of the axle of a piezoelectric motor is proposed. In this motor, a cylinder-shaped permanent magnet, which act as a rotor, is pressed in contact with an end of a steel axle by means of the magnetic forces. The other end of the axle is fitted at the center of a rotating traveling wave generator. A piezoelectric membrane, vibrating in a flexural anti-symmetrical mode, or a thick disk, vibrating in a radial anti-symmetrical mode, can be exploited as traveling wave generators. In the first case a bending moment, in the second case a transverse force is applied to the axle. In both cases, if the driving frequency coincides with a resonance frequency of the axle, the axle acts as a resonant displacement amplifier; a continuous slipping takes place between the axle and the rotor, and a torque is transmitted to the rotor. The proposed model is able to describe the axle vibrational behavior when it is excited by a bending moment, by a transverse force, and also when these two excitations are simultaneously applied. The axle is modeled as a four-port system and all its transfer functions, as well as the transversal displacement along the axle at each frequency can be easily computed. Computed results have been compared with experimental measurements carried out on two motor prototypes that exploit as traveling wave generators a membrane and a disk, respectively. A good agreement was obtained by properly taking into account the loading effect of the generator on the axle.     

Heat propagation due to torsional vibration of shafts

Torsional vibration of rotating shafts can yield substantial temperatures in the shaft due to heat generated from material damping. It has been recently observed that such a situation in electric generators can lead to insulation failures and machine outages. In the study reported here forced torsional vibration is assumed, and both lumped mass and continuous systems are considered. The hysteretic model for material damping is used to yield the heat generation in the elastic deformation range and an elastoplastic material is assumed in the plastic range. The heat conduction equation is solved for a cylindrical shaft with surface cooling. Closed form solutions and expressions for the maximum temperatures and the maximum surface temperatures are obtained and tabulated for design purposes. It is shown that substantial temperatures can develop in shafts undergoing torsional vibration.     

Suspended bridges subjected to moving loads and support motions due to earthquake

The paper deals with the vibration of suspended bridges subjected to the simultaneous action of moving loads and vertical support motions due to earthquake. The basic partial integro-differential equation is applied to the vertical vibration of a suspended beam. The dynamic actions of traffic loads are modelled as a row of equidistant moving forces, while the earthquake is considered by vertical motions of supports. The governing equation is solved first analytically to receive an ordinary differential equation and next numerically. Moreover, the designed world's largest suspended bridge—Messina Bridge—is investigated (central span of length 3.3 km). The paper studies the effect of various lags of the earthquake arrival because the earthquake may appear at any time when the train moves along a large-span bridge. The modified Kobe earthquake records have been applied to calculations. The results indicate that the interaction of both the moving and seismic forces may substantially amplify the response of long-span suspended bridges in the vicinity of the supports and increase with the rising speed of trains.     

A matrix model of the axle vibration of a piezoelectric motor

In this work, a matrix model of the axle vibration of a piezoelectric motor is proposed. The stator of this motor is composed of a thin piezoelectric membrane and a steel axle fitted at the center of the membrane. The rotor consists of a cylinder-shaped permanent magnet, pressed in contact with the other end of the axle by means of the magnetic forces. A travelling wave is excited in the membrane by using four electrodes and four, properly delayed, driving signals. The rotating flexural displacement of the membrane produces a wide precessional motion of the axle. In this way, a continuous slipping takes place between the axle and the rotor, and therefore, a torque is transmitted to the rotor. In this paper, the precessional motion of the axle is modeled as the composition of two transverse vibrations belonging to two perpendicular planes passing through the axle. The axle, vibrating in its transverse mode, is modeled as a two-port system: the input is the bending moment supplied by the membrane, and the output is the transverse force at the terminal end of the axle. With this model, we have computed the trasmission transfer function as a function of frequency, and the transversal displacement along the axle at its resonance frequency. The computed results are in reasonable agreement with experimental interferometric measurements carried out on a prototype.     

Axisymmetric dynamic behaviour of thick plate subjected to impulsive loads

Analysis is carried out for the case where a thick circular plate is subjected to impulsive load. The horizontal displacement u is assumed to be in the form of u = zu₁ + zⁿu_n, where n is an odd integer. The fundamental equations governing the displacement are introduced, with use of equilibrium conditions. The relationships between frequencies and R/h (radius/thickness) are obtained and they are compared with those given by Mindlin theory. For the case where the fundamental equation is introduced by the variational calculus, it is necessary to notice whether restrained conditions are satisfied or not.     

From chiral vibration to static chirality in (135)Nd

Electromagnetic transition probabilities have been measured for the intraband and interband transitions in the two sequences in the nucleus (135)Nd that were previously identified as a composite chiral pair of rotational bands. The chiral character of the bands is affirmed and it is shown that their behavior is associated with a transition from a vibrational into a static chiral regime.