Dynamic Response Impact of Vehicle Braking on Simply Supported Beam Bridges with Corrugated Steel Webs Based on Vehicle-Bridge Coupled Vibration Analysis

A novel approach for analyzing coupled vibrations between vehicles and bridges is presented,taking into account spatiotemporal effects and mechanical phenomena resulting fromvehicle braking.Efficient modeling and solution of bridge vibrations induced by vehicle deceleration are realized using this method.The method’s validity and reliability are substantiated through numerical examples.A simply supported beam bridge with a corrugated steel web is taken as an example and the effects of parameters such as the initial vehicle speed,braking acceleration,braking location,and road surface roughness on the mid-span displacement and impact factor of the bridge are analyzed.The results show that vehicle braking significantly amplifies mid-span displacement and impact factor responses in comparison to uniform vehicular motion across the bridge.Notably,the influence of wheelto-bridge friction forces is of particular significance and cannot be overlooked.When the vehicle initiates braking near the middle of the span,both the mid-span displacement and impact factor of the bridge exhibit substantial increases,further escalating with higher braking acceleration.Under favorable road surface conditions,the midspan displacement and the impact factor during vehicle braking may exceed the design values stipulated by codes.It is important to note that road surface roughness exerts a more pronounced effect on the impact factor of the bridge in comparison to the effects of vehicle braking.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge(WVB) system,there are various interactions among wind,vehicle and bridge.The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors,such as mean wind,fluctuating wind,buffeting,rail irregularities,light rail vehicle vibration and bridge stiffness.A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example.Firstly,a finite element model is built for the long cable-stayed bridge.The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements.Vehicles are modeled as mass-spring-damper systems.Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method.Then,aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests.Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method.Finally,dynamic responses of the WVB system are analyzed in a series of cases.The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent.The transverse forces of wheel axles mainly depend on the track irregularity.The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness.And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

Influence of vehicle-road coupled vibration on tire adhesion based on nonlinear foundation

The influence of pavement vibration on tire adhesion is of great significance to the structure design of vehicle and pavement.The adhesion between tire and road is the key to studying vehicle dynamics,and the precise description of tire adhesion affects the accuracy of dynamic vehicle responses.However,in most models,only road roughness is considered,and the pavement vibration caused by vehicle-road interaction is ignored.In this paper,a vehicle is simplified as a spring-mass-damper oscillator,and the vehicle-pavement system is modeled as a vehicle moving along an Euler-Bernoulli beam with finite length on a nonlinear foundation.The road roughness is considered as a sine wave,and the shear stress is ignored on the pavement.According to the contact form between tire and road,the LuGre tire model is established to calculate the tire adhesion force.The Galerkin method is used to simplify the partial differential equations of beam vibration into finite ordinary differential equations.A product-to-sum formula and a Dirac delt function are used to deal with the nonlinear term caused by the nonlinear foundation,which realizes the fast and accurate calculation of super-high dimensional nonlinear ordinary differential equations.In addition,the dynamic responses between the coupled system and the traditional uncoupled system are compared with each other.The obtained results provide an important theoretical basis for research on the influence of vehicle-road coupled vibration on tire adhesion.

Modal analysis of coupled vibration of belt drive systems

The modal method is applied to analyze coupled vibration of belt drive systems. A belt drive system is a hybrid system consisting of continuous belts modeled as strings as well as discrete pulleys and a tensioner arm. The characteristic equation of the system is derived from the governing equation. Numerical results demenstrate the effects of the transport speed and the initial tension on natural frequencies.

ZERO MODE NATURAL FREQUENCY AND NONLINEAR VIBRATION OF COUPLED LATERAL AND TORSION OF A LARGE TURBINE GENERATOR

Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF andvibrations resulted by it are studied. First, calculating method of the ZMNF excited byelectromagnetic in vibrational system of coupled mechanics and electrics are given from the view ofmagnetic energy. Laws that the ZMNF varies with active power and exciting current are obtained andare verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system isstudied by considering rest eccentricity, rotating eccentricity and swing eccentricity. UsingLargrange-Maxwell equation when three phases are asymmetric derives differential equation of thecoupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics ofresonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF willoccur in turbine generators by the action of electromagnetic. Because ZMNF varies withelectromagnetic parameters, resonance can occur when exciting frequency of the rotor speed is fixedwhereas exciting current change. And also find that a generator is in the state of large amplitudein rated exciting current.

Investigation of block foundations resting on soil-rock and rock-rock media under coupled vibrations

In the present study,the dynamic response of block foundations of different equivalent radius to mass（R;/m） ratios under coupled vibrations is investigated for various homogeneous and layered systems.The frequency-dependent stiffness and damping of foundation resting on homogeneous soils and rocks are determined using the half-space theory.The dynamic response characteristics of foundation resting on the layered system considering rock-rock combination are evaluated using finite element program with transmitting boundaries.Frequencies versus amplitude responses of block foundation are obtained for both translational and rotational motion.A new methodology is proposed for determination of dynamic response of block foundations resting on soil-rock and weathered rock-rock system in the form of equations and graphs.The variations of dimensionless natural frequency and dimensionless resonant amplitude with shear wave velocity ratio are investigated for different thicknesses of top soil/weathered rock layer.The dynamic behaviors of block foundations are also analyzed for different rock-rock systems by considering sandstone,shale and limestone underlain by basalt.The variations of stiffness,damping and amplitudes of block foundations with frequency are shown in this study for various rock—rock combinations.In the analysis,two resonant peaks are observed at two different frequencies for both translational and rotational motion.It is observed that the dimensionless resonant amplitudes decrease and natural frequencies increase with increase in shear wave velocity ratio.Finally,the parametric study is performed for block foundations with dimensions of 4 m × 3 m × 2 m and 8m×5m×2m by using generalized graphs.The variations of natural frequency and peak displacement amplitude are also studied for different top layer thicknesses and eccentric moments.

TORSIONAL OSCILLATION CHARACTERISTICS OF ROTARY SHAFTS BASED ON TORSION AND BENDING COUPLED VIBRATION

The torsional oscillation characteristics on the bending and torsioh coupled vibration of rotary shaft system were investigated using the elasto-dynamic theory and other mathematic methods, such as difference approach, Fourier transform, and wavelet transform. It is concluded that mass eccentricity and other exciting modalities affect the bending and torsion coupled vibration of rotary shafts. Torsional vibration caused by bending vibration features linearity along with the change of amplitude of bending vibration. Meanwhile, energy spectrum concentrates on high frequency area with the wavelet analysis.

COUPLED VIBRATION OF STRUCTURAL THIN-WALLED CORES

This paper presents an analysis of the coupled vibration of asymmetric core structures in tall buildings. The governing equation of free vibration and its corresponding eigenvalue problem, which is a set of equations for laterally flexural vibrations in two different directions coupled by a warping-St. Venant torsional vibration, are derived. Based on the Calerkin method, a generalized approximate method is developed for the analysis of coupled vibration and thus proposed for determining the natural frequencies and mode shapes of the structure in triply-coupled vibration. The results of the proposed method for the example structure show good agreement with those of the FEM analysis. The proposed method has been shown to provide a simple and rapid, yet accurate, means for coupled vibration analysis of core structures.

Reinforcement Effect Evaluation on Dynamic Characteristics of an Arch Bridge Based on Vehicle-Bridge Coupled Vibration Analysis

To numerically evaluate the reinforcement effect on dynamic characteristics of a concrete-filled steel tube arch bridge with vibration problems,a 12-degree-of-freedom sprung-mass dynamic vehicle model and a 3D finite element bridge model were established.Then,the coupled equations of vehicle-bridge interaction were derived and a computer program was developed using the FORTRAN language.This program can accurately simulate vehicle-bridge coupled vibration considering the bumping effect and road surface irregularity during motion of the vehicle.The simulated results were compared with those of relevant literatures to verify the correctness of the self-developed program.Then,three reinforcement schemes for the bridge(Addition of longitudinal beams,Reinforcement of bridge decks,and Replacement of suspenders)were proposed and numerically simulated,and the vibration reduction effects of the three schemes were evaluated based on the numerical results to find effective ones.It is confirmed that the reinforcement scheme of Addition of longitudinal beams shows the most significant vibration reduction effect.It is recommended in the engineering practice that the combination of the reinforcement schemes of Addition of longitudinal beams and Replacement of bridge deck can be used to solve the excessive vibration problem.

Effect of Coupled Torsional and Transverse Vibrations of the Marine Propulsion Shaft System

In this study,the coupled torsional-transverse vibration of a propeller shaft system owing to the misalignment caused by the shaft rotation was investigated.The proposed numerical model is based on the modified version of the Jeffcott rotor model.The equation of motion describing the harmonic vibrations of the system was obtained using the Euler-Lagrange equations for the associated energy functional.Experiments considering different rotation speeds and axial loads acting on the propulsion shaft system were performed to verify the numerical model.The effects of system parameters such as shaft length and diameter,stiffness and damping coefficients,and cross-section eccentricity were also studied.The cross-section eccentricity increased the displacement response,yet coupled vibrations were not initially observed.With the increase in the eccentricity,the interaction between two vibration modes became apparent,and the agreement between numerical predictions and experimental measurements improved.Given the results,the modified version of the Jeffcott rotor model can represent the coupled torsional-transverse vibration of propulsion shaft systems.

CORRECTION FOR HOUSNER’S EQUATION OF BENDING VIBRATION OF A PIPE LINE CONTAINING FLOWING FLUID

This paper points out that Housner's equation of bending vibration of a pipe line containing flowing fluid is approximate and makes correction to it. An exact form of the vibration equation is given.

Travelling characteristics of road vehicles on single-level rail-cum-road bridge under the dynamic and aerodynamic impact of travelling trains

Aerodynamic and dynamic interference from trains is a key issue of concern for the safety of road vehicles travelling on single-level rail-cum road bridges.Based on the wind-road vehicle-train-bridge(WRTB)coupled vibration system developed herein,this study examines the dynamic characteristics when road vehicles meet trains in this situation.The influence of load combination,vehicle type and vehicle location is analyzed.A method to obtain the aerodynamic load of road vehicles encountering the train at an arbitrary wind speed is proposed.The results show that due to the windproof facilities and the large line distance between the railway and highway,the aerodynamic and dynamic influence of trains on road vehicles is slight,and the vibration of road vehicles depends on the road roughness.Among the road vehicles discussed,the bus is the easiest to rollover,and the truck-trailer is the easiest to sideslip.Compared with the aerodynamic impact of trains,the crosswind has a more significant influence on road vehicles.The first peak/valley value of aerodynamic loads determines the maximum dynamic response,and the quick method is optimized based on this conclusion.Test cases show that the optimized method can produce conservative results and can be used for relevant research or engineering applications.

Coupling vibration analysis of high-speed maglev train-viaduct systems with control loop failure

The risk of failure of the control loop can occur when a high-speed maglev train runs on viaduct.Meanwhile,the failure of the levitation magnets which balances the gravity of the maglev train could cause the train collision with track.To study the dynamic response of the train and the viaduct when the levitation magnet control loop failure occurs,a high-speed maglev train-viaduct coupling model,which includes a maglev controller fitted by measured force-gap data and considers the actual structure of train and viaduct,is established.Then the accuracy and effectiveness of the established approach are validated by comparing the computed dynamic responses and frequencies with the measurement results.After that,the dynamic responses of maglev train and viaduct are discussed under normal operation and control loop failures,and the most disadvantageous combination of control loop failures is obtained.The results show that when a single control loop fails,it only has a great influence on the failed electromagnet,and the maglev response of adjacent electromagnets has no obvious change and no collision occurs.But there is a risk of rail collisions when the dual control loop fails.

Adjacent mode resonance of a hydraulic pipe system consisting of parallel pipes coupled at middle points

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pipe subjected to the basement excitation at the left end is named as the active pipe,while the pipe without excitation is called the passive pipe.The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration coupling.The governing equation of the coupled system is deduced by the generalized Hamilton principle,and is discretized to the modal space.The modal correction is used during the discretization.The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket.The harmonic balance method(HBM)is used to study the responses in the adjacent natural frequency region.The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket,while the locations of them are not node points.The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes.The stiffness of the clip and bracket can release the vibration coupling.It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough.In this way,the vibration energy is reflected by the almost rigid bracket,and is hard to transfer to the passive pipe via a soft clip.The best choice is to set the clips at the pipe node points.The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.

Vibration Reduction Performance of Damping-Enhanced Water-Lubricated Bearing Using Fluid-Saturated Perforated Slabs

As the first link element for the transmission of shaft vibration to the pedestal and even to the hull,water-lubricated bearing plays a key role in suppressing vibration.Although the porous structure is considered as one of the main methods for improving the wideband vibration and noise reduction performance of materials in many industrial fields,the studies in the field of water-lubricated bearing remain insufficient.To enhance vibration reduction performance,a fluid-saturated perforated slab is designed in this study,and via the establishment of a fluid-solid coupled vibration model,the influence law and impact levels were analyzed and verified by simulation and experiments.The results obtained verified that the total vibration amplitude of damping-enhanced stern bearing in the vertical direction was smaller than that of the normal stern bearing,and the reduction amplitude of the characteristic frequency agreed with the optimal value at approximately 0.1 of the volume fraction of the liquid phase when the solid-fluid phase was rubber–water.Additionally,the increase in fluid fraction did not enhance the damping effect,instead,it unexpectedly reduced the natural frequency of the raw material significantly.This research indicates that the design of the fluid-saturated perforated slab is effective in reducing the transmission of the vibration amplitude from the shaft,and presents the best volume fraction of the liquid phase.

Nonlinear Dynamic Analysis of Coupled Gear-Rotor-Bearing System with the Effect of Internal and External Excitations

Extensive studies on nonlinear dynamics of gear systems with internal excitation or external excitation respectively have been carried out. However, the nonlinear characteristics of gear systems under combined internal and external excitations are scarcely investigated. An eight-degree-of-freedom（8-DOF） nonlinear spur gear-rotor-bearing model, which contains backlash, transmission error, eccentricity, gravity and input/output torque, is established, and the coupled lateral-torsional vibration characteristics are studied. Based on the equations of motion, the coupled spur gear-rotor-bearing system（SGRBS） is investigated using the Runge-Kutta numerical method, and the effects of rotational speed, error fluctuation and load fluctuation on the dynamic responses are explored. The results show that a diverse range of nonlinear dynamic characteristics such as periodic motion, quasi-periodic motion, chaotic behaviors and impacts exhibited in the system are strongly attributed to the interaction between internal and external excitations. Significantly, the changing rotational speed could effectively control the vibration of the system. Vibration level increases with the increasing error fluctuation. Whereas the load fluctuation has an influence on the nonlinear dynamic characteristics and the increasing excitation force amplitude makes the vibration amplitude increase, the chaotic motion may be restricted. The proposed model and numerical results can be used for diagnosis of faults and vibration control of practical SGRBS.

VIBRATION ANALYSIS OF TURBINE BASED ON FLUID-STRUCTURE COUPLING

The vibration of a Francis turbine is analyzed with the additional quality matrix method based on fluid-structure coupling （FSC）. Firstly, the vibration frequency and mode of blade and runner in air and water are calculated. Secondly, the influences to runner frequency domain by large flow, small flow and design flow working conditions are compared. Finally the influences to runner modes by centrifugal forces under three rotating speeds of 400 r/rain, 500 r/min and 600 r/rain are compared. The centrifugal force and small flow working condition have greatly influence on the vibration of small runner. With the increase of centrifugal force, the vibration frequency of the runner is sharply increased. Some order frequencies are even close to the runner natural frequency in the air. Because the low frequency vibration will severely damage the stability of the turbine, low frequency vibration of units should be avoided as soon as possible.

Analysis on vibration characteristics of large-size rectangular piezoelectric composite plate based on quasi-periodic phononic crystal structure

Based on the theory of composite materials and phononic crystals(PCs),a large-size rectangular piezoelectric composite plate with the quasi-periodic PC structure composed of PZT-4 and epoxy is proposed in this paper.This PC structure can suppress the transverse vibration of the piezoelectric composite plate so that the thickness mode is purer and the thickness vibration amplitude is more uniform.Firstly,the vibration of the model is analyzed theoretically,the electromechanical equivalent circuit diagram of three-dimensional coupled vibration is established,and the resonance frequency equation is derived.The effects of the length,width,and thickness of the piezoelectric composite plate at the resonant frequency are obtained by the analytical method and the finite element method,the effective electromechanical coupling coefficient is also analyzed.The results show that the resonant frequency can be changed regularly and the electromechanical conversion can be improved by adjusting the size of the rectangular piezoelectric plate.The effect of the volume fraction of the scatterer on the resonant frequency in the thickness direction is studied by the finite element method.The band gap in X and Y directions of large-size rectangular piezoelectric plate with quasi-periodic PC structures are calculated.The results show that the theoretical results are in good agreement with the simulation results.When the resonance frequency is in the band gap,the decoupling phenomenon occurs,and then the vibration mode in the thickness direction is purer.

DYNAMIC ANALYSIS OF A SPATIAL COUPLED TIMOSHENKO ROTATING SHAFT WITH LARGE DISPLACEMENTS

The dynamic simulation is presented for an axial moving flexible rotating shafts, which have large rigid motions and small elastic deformation. The effects of the axial inertia, shear deformation, rotating inertia, gyroscopic moment, and dynamic unbalance are considered based on the Timoshenko rotating shaft theory. The equations of motion and boundary conditions are derived by Hamilton principle, and the solution is obtained by using the perturbation approach and assuming mode method. This study confirms that the influence of the axial rigid motion, shear deformation, slenderness ratio and rotating speed on the dynamic behavior of Timoshenko rotating shaft is evident, especially to a high-angular velocity rotor.