Prediction Of Vibration Research Articles

Numerical modelling and analysis for nonlinear stiffness of subgrade soil subject to 3-D vehicle-track interaction

In this paper, a subgrade model with nonlinear stiffness is established and integrated into a previously constructed 3-D vehicle-track-subgrade (VTS) dynamic model, in which the prediction and assessment of the vehicle-induced railroad vibrations are achieved with high accuracy and versatility. The system excitations are originated from the initial and time-dependent geometric irregularity of the system, which includes several internal excitations, namely conventional rail irregularity and the soil deformation-induced track irregularity. In the numerical analysis, the nonlinear behavior of the subgrade soil is revealed by considering shear modulus and traffic loads. The numerical experiment indicates that subgrade soil has a greater dynamic stiffness reduction if the vehicle enters the soil region with initial deformations. Besides, it is shown that the soil vibrations will be significantly amplified once the vehicle running speed is larger than the Rayleigh wave velocity of the subgrade soil.

Aspects of vortex-induced in-line vibration at low Reynolds numbers: Simulation and prediction by a reduced-order model

The purpose of this study is to develop a reduced-order model (ROM) for the prediction of vortex-induced vibration of an elastically mounted circular cylinder constrained to oscillate purely in-line with a uniform free stream. The fluid force in the streamwise direction was modeled by an extended version of Morison’s equation that comprises an inviscid inertial component opposing the cylinder acceleration, a viscous drag component proportional to the square of the relative velocity of the free stream and the oscillating cylinder, and a wake drag component representing the excitation from vortex shedding. A van der Pol equation was employed to model the oscillating wake drag component. The coupling between the oscillating wake and the oscillating cylinder was accomplished by forcing the wake oscillator with a term proportional to either the acceleration or the velocity of the cylinder. The ROM parameters were tuned against data from numerical solutions of the full system of non-linear equations governing the fluid and cylinder motions for a cylinder with a mass ratio of 10 and a Reynolds number of 180. The results showed that acceleration forcing can predict well the amplitude response when the ROM is properly tuned, whereas velocity forcing leads to underestimation of the amplitude response. In addition, acceleration forcing can predict satisfactorily the magnitude of the total streamwise force and of the wake drag. However, the trend in the frequency response was not well predicted by acceleration forcing, which was predicted more satisfactorily by velocity forcing. Both acceleration and velocity forcing predicted satisfactorily the phase lag between the wake drag and the cylinder displacement. Predictions with the calibrated ROM at different mass ratios captured well the amplitude response as a function of the reduced velocity, including the narrowing of the range where relatively high amplitudes occur, as in the full numerical simulations. Linear stability analysis based on the ROM equations indicated that the interaction between the fluid and the vibrating cylinder has the characteristics of nonlinear resonance, where the selection of the common frequency of the system is sensitive to nonlinearities, which cannot be faithfully captured by the van der Pol wake oscillator.

Experimental Analysis and Machine Learning of Ground Vibrations Caused by an Elevated High-Speed Railway Based on Random Forest and Bayesian Optimization

With the aim of predicting the environmental vibrations induced by an elevated high-speed railway, a machine learning method was developed by combining a random forest algorithm and Bayesian optimization, using a dataset from on-site experiments. When it comes to achieving a rapid and effective prediction of environmental vibrations, there is little research on comparisons between and verifications of different algorithms, and none on the parameter tuning and optimization of machine learning algorithms. In this paper, a field experiment is firstly carried out to measure the ground vibrations caused by high-speed trains running on a bridge, and then the environmental vibration characteristics are analyzed in view of ground accelerations and weighted vibration levels. Subsequently, three machine learning algorithms using linear regression, support vector machine, and random forest are developed using an experimental database, and their prediction performance is discussed. Finally, two optimization models for the hyperparameter set of the random forest algorithm are further compared. The results show that the integrated random forest algorithm has a higher accuracy in predicting environmental vibrations than linear regression and the support vector machine; the Bayesian optimization has an excellent performance and a high efficiency in achieving efficient and in-depth optimization of parameters and can be combined with the RF machine learning algorithm to effectively predict the environmental vibrations induced by the high-speed railway.

Study on the Forced Torsional Vibration Response of Multiple Rotating Blades with Underplatform Dampers

Underplatform dampers (UPDs), a type of dry friction damper, are commonly used for vibration reduction of turbine blades. This study investigated the effect of UPDs on the forced torsional vibration response of turbine blades within a multi-blade system. Pre-stressed finite element modal analysis and the harmonic balance method were combined to calculate the forced torsional vibration responses of a system with and without UPDs. The experiments were then carried out on a rotating multi-blade system with and without UPDs, with a focus on the effect of mass stacking on damping performance. The results showed that the installation of underplatform dampers could increase the frequency corresponding to the maximum response of the blade torsional vibration and cause multiple peaks that varied in the vibration response based on the mass of the UPDs. With an appropriate normal force, the underplatform dampers could effectively reduce the blade torsional vibration by 68.9%. However, excessive normal force of UPDs could lead to multiple large vibration peaks, which should be avoided in engineering practice. Additionally, the numerical results for the forced torsional vibration response of the rotating multi-blade system with UPDs were relatively close to the experimental results, indicating that the calculation method could be effectively applied to the nonlinear prediction of forced vibrations of rotating blades with dampers.

Modelling of vortex-induced force and prediction of vortex-induced vibration of a bridge deck using method of multiple scales

With the increase of span length, long-span bridges become more flexible and susceptible to vortex-induced vibrations (VIV). Several models for vortex-induced force (VIF) and various methods for predicting VIV have been developed accordingly but without consensus. This paper uses the method of multiple scales, from a different angle of view, to analyze the general polynomial model for VIF and present a concise polynomial model for VIF and a simple method for predicting VIV of a bridge deck. The aeroelastic vibration of a deck section is simulated by the computational fluid dynamics (CFD) and the results are used to verify the concise polynomial model of VIF. The forced vibration of a deck section is also simulated by CFD to yield the simple method for predicting VIV together with the frequency response equation and the critical equation of VIV derived by the method of multiple scales. The results show that the even and cross terms of aerodynamic damping and stiffness in the general polynomial VIF model are small compared with the odd terms and can be thus omitted. The lock-in region and the amplitude of VIV of the deck section can be accurately predicted by the proposed simple method.

Site-Specific Amplitude-Distance Laws, Wave Velocities, Damping, and Transfer Functions of the Soil from Hammer Impacts and Application to Railway-Induced Ground Vibration: Similarities and Mid-Frequency Differences

PurposeThe purpose of this article is to check if and how hammer experiments can be applied to the prediction of railway vibration.MethodsThe propagation of ground vibrations is theoretically analysed with frequency-wavenumber and simplified methods. Experimental methods are presented which can characterise the site-specific ground vibrations by wave velocities, stiffness and damping. Measurements with hammer and train excitation have been performed at several sites.Results The one-third octave spectra show the stiffness-dependent amplitudes and the low- and high-frequency filter effects due to the layering and the damping of the soil. Specific train effects, an additional high-frequency filter, the sleeper passage frequency, and an amplified mid-frequency component can be clearly found. The attenuation with distance is analysed in detail where the theoretical exponential and the empirical frequency-dependent power law are considered. Hammer and train excitation show the same site-specific effects which are mainly due to the stronger or weaker damping of the soil. The train attenuation is generally weaker than the hammer attenuation. The attenuation exponent of the power law, which is strongly dependent on the site and the frequency, is reduced for the train vibration by 0.3–0.5 in agreement with the theory. Reasons are discussed for the overall power law and for the dominating mid-frequency component.ConclusionTherefore, it can be concluded that hammer experiments can well be used for the prediction of train vibrations.

Train-Induced Vibration Prediction and Control of a Metro Depot and Over-Track Buildings

To predict and control the train-induced vibration in depot buildings, a case study of the depot of Tianjin Metro, Line 5, was conducted. The platform of the depot has been constructed and is in use, and the construction of over-track buildings has not been completed. Firstly, an in situ measurement was performed to obtain the train loads and validate the numerical model. Secondly, a finite element model of the track–soil–depot structure was established. The train was simplified as a series of two spring-mass models and the train load was simulated using the measured rail acceleration. The calculated results were validated by the measurement data. To predict the vibration responses of the over-track building to be built, a sub-system of the over-track building was added to the numerical model. Finally, the vibration control effect of vibration isolation bearings was discussed. The results indicate that vibrations exceeded guideline limits without mitigation measures in some rooms of the over-track building. The dominant frequency of the building floors is 31.5 Hz. Vibration isolation bearings effectively mitigated the vibrations, and the IL reached approximately 7–15 dB at about 31.5 Hz.

Fixed-point excitation prediction method for environmental vibration of urban rail transit

In urban rail transit construction, the empirical prediction equation is generally used to predict the environmental vibration along the line after its operation. It is used as the basis for whether to adopt a vibration-damping track or which vibration-damping track to use. Due to the superposition of complex factors such as geological conditions, differences in vehicles, and their running foundations on the prediction results, the track implementation should be considered at least with a design margin of 3 dB. However, there are still a large number of environmental vibration complaints. Therefore, an ecological vibration prediction method with higher prediction accuracy is proposed. The construction of the track-foundations, such as tunnel, bridge, and roadbed is completed. Before the track system is constructed, a fixed-point excitation load simulating the passage of trains is applied on the track-foundation, and the vibration-sensitive points around the line are directly measured by the actual measurement—environmental vibration prediction evaluation. The fixed-point vibration source function model for simulating train passing is deduced as the excitation load applied to the track-foundation; the fixed-point vibration source foundation finite element model and vehicle-track-foundation coupled dynamic model with the same track-foundation and foundation model have been established. The vibration response of the track-foundation and foundation surface when the train passes through is calculated separately. The results corresponding to different prediction methods of environmental vibration are compared and analyzed. The comparison between the theoretical prediction value of vibration response, the prediction value of the empirical equation, and the measured value shows that the vibration response waveform of the foundation surface is the same as that of the actual train passing under the action of the fixed-point vibration excitation source function. The vibration prediction error is much smaller than the empirical equation predicts the result. It shows that the prediction accuracy of the fixed-point excitation prediction method for environmental vibration is higher than that of the existing practical equation method. Because the fixed-point vibration source device is simple to implement and the ecological vibration field testing method is mature, it is beneficial to the field application of the fixed-point vibration excitation prediction method for urban rail transit environmental vibration.

Study on the influence of wheel inertia and longitudinal/lateral creep force on the corrugated wear on the metro curved track

Corrugated wear on the metro curved track was studied. Dynamic analysis was implemented to analyze the effects of the vehicle speed and the curve radius on the wheel-rail creep forces. A mixed Lagrangian/Eulerian description-based finite element model of a wheel/rail system was set up. The wheel inertia can be considered in this model. Moreover, the steady rolling of the wheel under different creepage for braking or traction can be simulated. The complex eigenvalue analysis is used to investigate the frequency-domain characteristics of the friction-induced vibration of the wheel/rail system under the steady-state curving of the wheel. The initiation of the corrugation under the friction-induced vibration of the wheel/rail system was studied. The effects of the creep forces in the longitudinal and lateral directions on the friction-induced vibration of the wheel/rail system were revealed. The results show the dominant cause of the corrugation on the low rail surface is the friction-induced vibration of the wheel/rail system at about 320 Hz. The friction-induced vibration on the side of the high rail is not easy to occur. Therefore, the corrugated wear hardly happens to the high rail. The corrugated wear caused by the friction-induced vibration is frequency-fixed. It is necessary to consider the wheel inertia in the study of the friction-induced vibration of the wheel/rail system. Without considering wheel inertia, missing prediction of the friction-induced vibration and overestimation of the occurrence probability and development speed of the corrugation may occur. The lateral creep force plays a leading role in the friction-induced vibration of the wheel/rail system, while the longitudinal creep force has little effect on the friction-induced vibration. The corrugated wear will become more serious as the curve radius becomes smaller.

A new dynamic model for gear systems incorporating the sliding friction and time-varying pressure angle

The dynamic characteristics of gear systems are affected by the sliding friction and time-varying pressure angle. In the previous studies, the sliding friction is usually neglected for simplification, while the pressure angle is always considered as a constant. Therefore, the coupling effect between the sliding friction and pressure angle is not considered. In view of this, a new six degrees-of-freedom model for spur gear systems is proposed. The sliding friction and time-varying pressure angle are emphasized in this model. The differential equations of motion are derived using Lagrange’s equation. The Runge–Kutta numerical integration algorithm is applied to gain dynamic response. The proposed model is somewhat more realistic compared to previous models. Furthermore, parametric studies are carried out to reveal the effects of friction coefficient and equivalent shaft-bearing stiffness (directly related to translational motion and time-varying pressure angle). The coupling effect between the sliding friction and pressure angle is verified not only by the mathematical model but also by the dynamic response. The results reveal that both friction coefficient and equivalent shaft-bearing stiffness affect the contact ratio and pressure angle and lead to distinctive dynamic responses. This research can provide a foundation for further study and be used as a reference for gear system design and vibration prediction.

Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

In modeling of micro/nanodevices, numerous approaches have been developed that take into account material length scale parameters to capture size effects. In this work, the variational formulation of the microstructure-dependent Timoshenko beam model is developed considering Hamilton’s principle and modified couple stress theory (MCST) which involves the material length scale parameter. The Moore–Gibson–Thompson (MGT) thermoelastic model is employed to present the governing equations of motion and boundary conditions. The numerical outcomes illustrated by classical and non-classical approaches reveal the behavior of both the deflection and thermal moment of the beam. In addition, the dissipation in the deflection and the thermal moment is visually depicted in standardized curves. Several peaks in graphical plots are then detected as a function of the dimensionless time, which bring to light some interesting features of MGT model in the prediction of thermoelastic vibration of the microstructure model of Timoshenko beam.

Prediction of Blast-Induced Ground Vibration Using Gene Expression Programming (GEP), Artificial Neural Networks (ANNs), and Linear Multivariate Regression (LMR)

Prediction of Blast-Induced Ground Vibration Using Gene Expression Programming (GEP), Artificial Neural Networks (ANNs), and Linear Multivariate Regression (LMR)

Vibration Prediction and Evaluation System of the Pumping Station Based on ARIMA–ANFIS–WOA Hybrid Model and D-S Evidence Theory

Research on the vibration response prediction and safety early warning is of great significance to the operation and management of pumping station engineering. In the current research, a hybrid prediction method was proposed to predict vibration responses of the pumping station based on a single model of autoregressive integrated moving average (ARIMA), a combined model of the adaptive network-based fuzzy inference system (ANFIS) and whale optimization algorithm (WOA). The performance of the developed models was studied based on the effective stress vibration data of the blades in a shaft tubular pumping station. Then, the D-S evidence theory was adopted to perform safety early warning of the operation state by integrating the displacement, velocity, acceleration and stress indicators of the vibration responses of the pumping station. The research results show that the proposed prediction model ARIMA–ANFIS–WOA exhibited better accuracy in obtaining both linear and nonlinear characteristics of vibration data than the single prediction model and hybrid model with different optimization algorithms. The D-S evidence fusion results quantitatively demonstrate the safe operation state of the pumping station. This research could provide a scientific basis for the real-time analysis and processing of data in pumping station operation and maintenance systems.

Machine learning-based deep data mining and prediction of vortex-induced vibration of circular cylinders

By means of numerical, experimental and field measurements, an unprecedented amount of data regarding vortex-induced vibration (VIV) of circular cylinders has become accessible recently. In this study, machine learning (ML) models are developed to predict the transverse VIV amplitude Y* and amplitude-velocity relations. First of all, an ML database is established by aggregating reliable, published data. Then, three ML techniques are developed, including support vector regression with particle swarm optimization (PSO + SVR), extreme learning machine (ELM), and improved ELM combined with preprocessed least squares QR decomposition (PLSQR + ELM). Three crucial parameters, mass damping ratio α, Reynolds number (Re) and mass ratio m*, are extracted by the partial least square (PLS) method to characterize VIV. The results show that the prediction accuracy of all algorithms is acceptable in the absence of noise, with the ELM-type being the highest. When noise is taken into account, PLSQR + ELM is the most efficient and robust. A new linear relation between the VIV amplitude Y* and log10(α/Re) is proposed, which is demonstrated to be better than published ones.

Study on water hammer effect and tubing string vibration in high-pressure high-production gas wells

The transient internal flow in high-pressure high-production gas wells generates severe water hammer and tubing string vibration, which accelerates fatigue damage, joint wear, thread loosening, and other wellbore integrity problems. Based on the analysis of transient flow in gas wells, a mathematical model for fluid pressure surge and the induced tubing string vibration is developed and validated by similarity experiments. This method considers fluid-structure interaction, initial loads of tubing string, and compressibility of natural gas, and can fill the gap in quantification of water hammer pressure and tubing sting dynamic load in high-pressure high-production gas wells. On this basis, the effects of valve closure time, production rate, liquid content, and tubing string structure on transient flow and tubing string characteristics are analyzed systematically. The calculations show that wellhead pressure increases rapidly, and pressure wave propagates along tubing string to induce vibrations in the string after an instantaneous shut-in at the wellhead. During this transient process, fluid pressure and axial stress at wellhead reach their maximum valves. Owing to the fixed constraint effect of wellhead and downhole packer, the lack of restrictions on tubing distant from wellhead and packer enhances the severity of axial vibration. As valve closure time increases, the maximum wellhead pressure, tubing vibration displacement, and velocity gradually decrease. Therefore, the most direct way to control water hammer effect and tubing string vibration is to extend the shut-in time or prevent a rapid shut-in of gas well. The methods used in this study and the results obtained therein can serve as both a theoretical framework and practical foundation for the prediction and control of water hammer effect and tubing string vibration in high-pressure high-production gas wells.

Variable stiffness-based vibration prediction for full coupling model of gearbox

Vibration is a problem worthy of attention in gearbox design. In the case of high speed and heavy load, vibration may be more significant, so some methods are needed to predict the vibration of the gearbox. At present, most vibration prediction methods have the problems of few research parameters, low fidelity and a large amount of calculation. In this paper, a fully coupled finite method model of variable stiffness gearbox based on lumped parameter method (LPM) is proposed, and the vibration prediction of gearbox housing is carried out considering time-varying meshing stiffness (TVMS), transmission error and other factors. Firstly, a new stiffness calculation method was proposed based on finite element theory and potential energy method, which can accurately solve the TVMS of fault gear. At the same time, the comprehensive meshing error of gear was solved. At then, the TVMS and comprehensive meshing error of the healthy gear and fault gear were brought into the dynamic equation of two-stage spur gear to obtain meshing force. After that, the meshing force was used as an excitation to solve the vibration of the gearbox housing. Finally, the vibration regularity of the health gearbox and fault gearbox was compared. The sensitivity of each gear shaft to the vibration caused by fault and the vibration regularity of different bearing seats of the same gear shaft was explored. The effectiveness of the simulation results was verified by experiments.

Water in Crystals: A Database for ML and a Knowledge Base for Vibrational Prediction

Water in Crystals: A Database for ML and a Knowledge Base for Vibrational Prediction

An efficient three-dimensional dynamic stiffness-based model for predicting subway train-induced building vibrations

The prediction of train-induced vibration in buildings constructed above the subway is a challenging problem due to its sophisticated system and time-consuming calculation. This paper proposes an efficient three-dimensional (3D) dynamic stiffness-based model (DSM) to predict subway train-induced building vibrations. The DSM has the capability to analytically explore the axial, bending, and torsional vibrations of columns and beams, as well as the flexural and in-plane vibrations of floors and walls induced by the moving train, which few studies have focused on before, and has high computational efficiency compared to the traditional finite element method (FEM). In the DSM, the dynamic stiffness matrices of floors, walls, columns and beams are formulated by the stiffness theory firstly. Then, the global dynamic stiffness matrix of the building is determined following an assembly procedure and the vibration responses of the building can be calculated by the dynamic stiffness equation in the frequency domain. Further, the calculation accuracy and efficiency of the DSM are validated by comparison with a 3D finite element model. Finally, the DSM is used to predict the train-induced vibrations of a building constructed at a subway station based on a subway train-slab track coupled dynamics model. Results show that the building vibrations induced by the moving train are significant in both vertical and horizontal directions and the steel-spring floating-slab track can effectively suppress the train-induced building vibrations.

A review on different regulation for the measurement of transport noise and vibration

Transport noise and vibration have a negative influence on the environment, human health, and quality of life. The measurement and analysis of transport noise and vibration are required by the regulations and guidelines that various countries have set in order to manage and mitigate these effects. This review paper provides an overview of the requirements for the measurement and analysis of vibration and noise in transportation in different countries. The paper examines the measurement and analysis parameters, methods, and standards used in the United States, Europe, Australia and Japan. The review finds that although the requirements for measurement and analysis vary between countries, there are common parameters and methods used worldwide, such as sound pressure level and frequency spectrum measurements, noise and vibration impact assessment, prediction, and control measures. A comprehensive understanding of the measurement and analysis requirements for transport noise and vibration in different countries is essential for ensuring compliance with regulations, mitigating adverse impacts, and promoting sustainable transport development.

Empirical prediction of blast-induced vibration on adjacent tunnels

The blast-induced vibration during excavation by the drilling and blasting method has an important impact on the surrounding buildings/structures and auxiliary equipment. In particular, with the development of tunnel engineering, the impact of blasting vibration on tunnel construction has attracted extensive attention. Based on literature data statistics, this paper first explored the performance of several commonly used empirical equations in predicting the propagation and attenuation characteristics of blasting vibration on adjacent tunnels. Secondly, the relationships between the empirical parameters of the blasting vibration prediction equation and the geological strength index (GSI) of tunnel surrounding rock were discussed, and two new blasting vibration prediction equations based on site rock GSI were established to approximately predict blast-induced vibration on adjacent tunnels. Finally, the application feasibility of the established prediction equation in practical engineering was discussed based on field test data. The research results show that under the condition of multiple groups of data, the prediction performance of various prediction models does not differ significantly. With the increase of the GSI of the surrounding rock mass of the adjacent tunnel, the site coefficients β and k of the blasting vibration prediction equation in predicting PPV (peak particle velocity, resultant velocity) both show a decreasing trend as a whole. The site coefficient k is generally within 3,000. Two new empirical prediction equations of blasting vibration propagation and attenuation on adjacent tunnels under different site conditions were established: Eq. (14) for PPV and Eq. (15) for PPVi (max) (maximum value of the three component velocities; i = x, y, z represent peak component particle velocity). The verification analysis of five sites shows that these two equations have a certain practical application value. Compared with other empirical equations, these two equations do not need regression fitting blasting vibration data, they only used the GSI of the site rock mass, and they are more easy to use in the field when there is a lack of monitoring data.