Vibration Model Research Articles

Modelling of high frequency vibration of railway bogies’ subcomponent based on structural dynamics: A case study for lifeguard of metro bogie

The sub-components of railway bogie have been frequently reported to be subjected to the vibration fatigue due to the wheel/rail high frequency vibration. An efficiency numerical model is thus desirable to simulate the high frequency vibration of railway bogie, which can substantially enhance the design efficiency of railway bogie system considering the vibration fatigue. Therefore, this paper aims to proposing a modelling methodology for simulating the high frequency vibration of railway bogies’ subcomponents, and a lifeguard of metro bogie was taken as an example. Firstly, a field test measurement of lifeguard for the metro bogie was primarily introduced to demonstrate the high frequency vibration characteristics and the related failure mechanisms arising from the wheel/rail high frequency impact. Subsequently, a random vibration model for the railway bogie system and the lifeguard based on the rigid/flexible coupled dynamics were developed to simulate the high frequency vibration and the dynamic stress developed at the lifeguard. This method was subsequently employed in the structural optimization for the lifeguard. The results showed that the proposed methodology can effectively simulate the high frequency vibration of lifeguard of bogie system based on the measured axle box acceleration, and the optimized structure can effectively increase the service lifetime under the excitation of wheel/rail high frequency vibration.

Analysis of vibration responses in a large airport ground transportation centre caused by maglev and subway trains

This study aims to assess the vibration response of the ground transportation centre (GTC) at an airport integrated transportation hub during the starting and braking processes of underground maglev and subway trains. In this work, we considered the actual motion states of trains entering and exiting the GTC and calculated the traction characteristics of maglev and subway trains. On this basis, the vertical coupling vibration models for a medium- and low-speed maglev train-guideway and a subway train-floating slab track considering variable-speed motion, as well as the vehicle longitudinal motion models, were established, and the vertical and longitudinal fastener forces of the tracks were obtained accordingly. Finally, based on the two-step analysis method, the vertical and longitudinal fastener forces were simultaneously applied to the track–GTC–soil finite element model to evaluate the structural vibrations induced by maglev and subway trains. The results show that the amplitude of the vertical fastener force is an order of magnitude greater than that of the longitudinal fastener force, and the amplitude of the vertical fastener force caused by subway trains is greater than that caused by maglev trains. The starting process of both maglev trains and subway trains results in a greater vertical vibration response of the GTC than the braking process, with the impact of subway trains being greater than that of maglev trains. Within the same area, the vertical vibration level observed at structural column observation points is lower than that at slab observation points. When maglev trains and subway trains start simultaneously, the vibration level response at some points exceeds the specified limit of 75dB.

Influence of additional mass and connection of nonlinear energy sinks on vibration reduction performance

The broadband vibration reduction performance of nonlinear energy sink (NES) has attracted wide attention. However, the impact of the NES’s additional mass other than the oscillator and how it is connected to the primary structure has been ignored. More recently, it has been discovered that vibration attenuation through the cellular application of NES can achieve greater efficiency. However, the connection between NES cells and the primary structure, as well as between cells, has not been studied. In this study, by considering the additional mass of the NES cells, the influence of the connection modes of NES cells on the vibration reduction efficiency is investigated theoretically, optimally and experimentally for the first time. The forced vibration models of linear oscillator coupled with NES cells are established by viscoelastic connection and rigid connection respectively. The approximate analysis and numerical analysis show that the vibration reduction efficiency of NES cells is affected by the resonance frequency of the primary structure and the external excitation intensity and shows a nonlinear trend. With the change of the resonant frequency of the primary structure, the viscoelastic connection NES cells can almost always obtain higher vibration reduction efficiency than the rigid connection NES cells. The global bifurcation results show that the strongly modulated responses of the structure can be triggered by the viscoelastic connection. Moreover, the connection modes between NES cells also affect the vibration reduction efficiency. The optimal parameters of the connection damping and connection stiffness are obtained by the particle swarm optimization algorithm. Finally, the viscoelastic connection and rigid connection, and the effect of the connection mode between NES cells on the vibration reduction efficiency are compared by experiments. The conclusions of theoretical research are verified. This work can provide theoretical guidance for the engineering application of NES cells.

The influence of the general vibration on the quality of the assessment of the pilot's physiological indicators

The article considers flight safety issues related to continuous monitoring of the pilot's functional state by using means of monitoring physiological health indicators, which is due to the complexity of flight work, accompanied by a whole range of unfavorable factors that reduce the efficiency of professional activity. The article studies the influence of the general vibration factor on the quality (accuracy) of the assessment of the pilot's physiological indicators recorded by non-invasive diagnostic devices in transmitted light. Such indicators include heart rate, fractional blood saturation level, and respiratory rate. A mathematical model of quasi-deterministic general vibration, which is the resultant of individual frequency components of corrected vibration acceleration directed along three axes of the Cartesian coordinate system, has been developed. Mathematical modeling of the effect of general vibration on the information photoplethysmographic signal has been performed and it has been shown that the effect changes the frequency-time structure of the signal and relative errors of the estimated physiological parameters appear – the level of fractional blood saturation (4.16 %), heart rate (4.78 %) and respiration (3.75 %). As a result of a practical experiment to analyze the effect of general vibration on the quality of assessment of the specified physiological parameters, it was found that, compared to the declared error of a pulse oximeter of ±2 %, the errors in determining the heart rate, fractional blood saturation and respiration rate increased by 3.221 %; 2.483 % and 1.906 %, respectively. The results of theoretical and practical studies have a strong pair correlation according to Pearson, the pair correlation coefficients were 0.72, 0.83, 0.76 for the results of measurements of heart rate, fractional blood saturation level and respiratory rate, respectively, which indicates the validity of the adopted simplifi ations in the development of the mathematical model. The obtained results can be used to develop devices for non-invasive diagnostics of the pilot's physiological indicators, functioning directly during the flight.

Research on Radial Vibration Model and Low-Frequency Vibration Suppression Method in PMSM by Injecting Multiple Symmetric Harmonic Currents

Driven by frequency conversion, the windings of a three-phase permanent magnet synchronous motor (PMSM) contain both odd and even harmonic currents. Due to the motor’s pole–slot conductance modulation, the interaction between the magnetic fields generated by these harmonic currents and the permanent magnet field results in harmonic radial vibrations of the motor. This paper analyzes the three-phase currents of the prototype and derives the radial magnetomotive force (MMF) spatiotemporal models for symmetric harmonic currents. By integrating Maxwell’s magnetic force formula and vibration response formula, the radial vibration models for symmetric harmonic currents are developed. The characteristics of vibrations caused by odd and even harmonic currents, as well as positive sequence and negative sequence harmonic currents, are analyzed separately. A cyclic sequence, low-frequency vibration suppression control method incorporating multiple harmonic current injections was designed. Experimental results of this method are compared with those obtained using an ideal sinusoidal current. Except for the second harmonic vibration, all other vibrations are significantly suppressed, with a maximum suppression rate of 92.28%. The total vibration level is reduced by 12.7619 dB, and the average torque is reduced by 0.67% with the total harmonic distortion of the current at 2.89%. The experimental results show that the vibration method in this paper has little influence on the average torque of the motor, the current distortion rate is small, and the vibration suppression effect is good.

Three-Dimensional Numerical Modeling of Train-Induced Vibration with Special References to Track Irregularities and Soil Stiffness

Three-Dimensional Numerical Modeling of Train-Induced Vibration with Special References to Track Irregularities and Soil Stiffness

Model of Dynamic Mechanical Parameters and Vibration Analysis in Hot Rolling

As the core equipment of metal shaping processing, the vibration problem of rolling mill seriously affects the product quality and production efficiency. To address the problem of the limited prediction of mill vibration due to small sample data in non-steady states, we propose to predict dynamic mechanical parameters (rolling force and rolling torque) based on the TCN-LSTM step strategy transfer model. The prediction accuracies of the TCN-LSTM step strategy transfer model under 1000 sets of training data reach 95.8% and 93.2%, respectively, and at the same time, it saves the time of training and regulation of the deep learning model and can better meet the needs of online prediction. The horizontal-torsion hot rolling vibration model is further established to quantitatively analyze the relationship between process parameters and mill vibration. The experimental results show that with the vibration suppression measures of 10% reduction of the rolling speed and 10% reduction of the entrance thickness, the horizontal vibration displacement amplitude is reduced from 0.687 × 10−4 m to 0.229 × 10−4 m, and the rotational displacement amplitude is reduced from 0.0273 m to 0.0117 m, which effectively suppresses the vibration of the mill and improves the stability of the rolling process.

Vibration analysis of push-the-bit rotary steerable bottom hole assembly

With the development of oil and gas fields to the deep-sea, the rotary steerable system is widely used. Downhole vibration is an important factor affecting the performance of rotary steerable system. Currently, the lack of research on vibration during operation of rotary steerable system has affected the development of deep-sea oil and gas field development technology. In this paper, the dynamic model of the push-pull rotary steerable system is established based on the similarity principle. The model includes Bit-rock interaction model, Drillstring-borehole contact model and guiding force model of rotary steerable system, the trajectory and vibration of drill bit under different guiding forces are simulated. Then, the actual drilling experiment of the full-scale Push-The-Bit Rotary Steerable System (PTB-RSS) in the horizontal section is carried out. The acceleration and speed signals of the push-pull rotary steerable system in the process of applying guiding force are collected and verified with the calculation results of the dynamic model. It is found that the vibration frequency and amplitude of the Bottom Hole Assembly (BHA) gradually increase with the increase of the guiding force of the PTB-RSS during the drilling stage, which induce high-frequency torsional vibration to a certain extent. In addition, the dynamic simulation shows that when the guiding force of the rotary steerable system is increased to a certain extent, the vibration of the BHA gradually stabilizes, but the vibration amplitude does not decrease.

Comparative analysis of beam models for vertical rail vibrations under dynamic forces

Comparative analysis of beam models for vertical rail vibrations under dynamic forces

Effect of microstructure on dynamic response of ferrite matrixed steel at high strain rates

Dynamic response of steels at high strain rates are of great practical significance for understanding mechanical structures under extreme load conditions. To explore the relationship between structure and stress during dynamic deformation at high strain rates, steel specimens were prepared with varied microstructures of ferrite, ferrite and pearlite, and ferrite and spherical carbide. It is revealed that different microstructured steels exhibit drastically different characteristic of waves excited by the instantaneous impact of a servo-hydraulic tensile testing. It is also observed that a beat frequency response exists under dynamic deformation at certain high strain rates. It is therefore proposed that dynamic plastic deformation starts with stress fluctuation with a dislocation damped vibration model, and two successively excited waves are superimposed to form the beat frequency response.

Design of a lightweight broadband vibration reduction structure with embedded acoustic black holes in viscoelastic damping materials

Viscoelastic damping materials (VDMs) are valued for their high damping characteristics in vibration and noise control. However, they typically underperform at lower frequencies and add substantial mass to structures. This study introduces an innovative approach by embedding an acoustic black hole (ABH) structure within VDMs (ABH-VDM) to achieve lightweight and broadband vibration damping. Firstly, a finite element method-based vibration model is developed to analyse the propagation and attenuation characteristics of vibrations in a plate strip embedded with ABH-VDM. This analysis provides insights into the dynamic behaviour and damping effectiveness of the proposed structure. Secondly, the study investigates the vibration reduction capabilities and mass implications of ABH-VDM on large-scale plate structures. The influence of ABH structural parameters, including the power exponent, cutoff thickness, and array configuration, is systematically investigated to optimize damping performance. Finally, experimental validation confirms that ABH-VDM achieves an additional 1.4 dB reduction in vibration across the entire frequency spectrum, with a bandwidth extension of 900 Hz. Moreover, ABH-VDM reduces mass by 8.6 %, demonstrating its potential for lightweight vibration control in structural applications. This research contributes valuable insights into advancing lightweight and broadband damping solutions for enhanced vibration management in engineering systems.

Synchronization characteristics and stable states of four co-rotating vibrators with balanced slanted elliptical trajectory

In the petroleum drilling and mining screening industries, our goal is to enhance excitation force, integrate circular screening with rectilinear transport to obtain the balanced slanted elliptical trajectory (BSET), and reduce screen mesh clogging. This work investigates the synchronization characteristics and stable states of four co-rotating vibrators. The novelty of this work lies in using a novel vibration model to achieve the BSET in the synchronization state and in further considering the influence of a new skewing angle between two eccentric rotors (ERs), which are few in previous vibration screening field. Initially, the vibration model is extracted from the designed prototype. Then, in accordance with Routh–Hurwitz criterion, the synchronization and stability are theoretically analyzed using small parameters of vibrator velocity and phase differences (PDs). The synchronization characteristics related to mechanical structures are discussed via numerical calculation and experimental verification. Results reveal that the synchronization implementation is adversely affected by the skewing angle, even leading to unordered behaviors. Achieving zero-phase or in-phase synchronization with four vibrators is only feasible with a larger symmetric distance and installation angle. This work can contribute a foundation for designing some new types of large vibration screening and material conveyance machines.

Multiple nonlinear vibration model of drilling string and mechanism of drilling speed increase in ultra-HPHT oil & gas wells

Multiple nonlinear vibration model of drilling string and mechanism of drilling speed increase in ultra-HPHT oil & gas wells

Method and Application of Spillway Radial Gate Vibration Signal Denoising on Multiverse Optimization Algorithm-Optimized Variational Mode Decomposition Combined with Wavelet Threshold Denoising

To address the noise issue in the measured vibration signals of spillway radial gate discharge, this paper utilizes the Multiverse Optimization Algorithm (MVO) to optimize the number of decomposition modes (K) and the penalty factor (α) in Variational Mode Decomposition (VMD). This approach ensures improved efficiency of VMD decomposition while maintaining accuracy. Subsequently, the obtained Intrinsic Mode Functions (IMFs) from VMD decomposition are classified based on Multi-scale Permutation Entropy (MPE). IMFs are divided into pure components and noisy components; the noisy components are processed with Wavelet Threshold Denoising (WTD), while the pure components are overlaid and reconstructed to obtain the denoised vibration signal of the gate. Comprehensive comparisons involving artificial signal simulations, gate flow-induced vibration model tests, and numerical simulations lead to the following conclusions: compared to other algorithms, the proposed combined denoising method (MVO-VMD-MPE-WTD) achieves the highest signal-to-noise ratio (SNR) in both the frequency and time domains for artificial signals, while yielding the lowest mean square error (MSE). In the gate flow-induced vibration model tests, the method significantly reduces noise in the vibration signals and effectively preserves characteristic information. The error in preserving characteristic information across model tests and numerical simulations is kept below 1%. Furthermore, compared to other optimization algorithms, the MVO demonstrates higher computational efficiency. The parameter-optimized combined denoising method proposed in this study provides insights into denoising measured vibration signals of hydraulic spillway radial gates and other drainage structures, and it opens possibilities for exploring more efficient optimization algorithms for achieving online monitoring in the future.

Vortex-Induced Vibration Performance Analysis of Long-Span Sea-Crossing Bridges Using Unsupervised Clustering

Vortex-induced vibration is a type of wind-induced vibration occurring frequently in large-span sea-crossing bridges under relatively low wind speeds, posing a threat to the structural fatigue performance and driving comfort. Identifying the instantaneous occurrence moments of vortex-induced vibration is a prerequisite for establishing a data-driven prediction model for vortex-induced vibration, and it is of great significance for the monitoring and early warning of vortex-induced vibration performance in bridges. To automatically detect the occurrence moments of vortex-induced vibration and establish a correlation model between vortex-induced vibration amplitude and environmental factors, this study proposes a fuzzy C-means clustering-based classification method. In order to detect the occurrence moments of vortex-induced vibration more finely, only short-term or even instantaneous structural vibration indicators were selected and transformed for distribution as clustering features. The entire detection process could be carried out unsupervised, reducing the manual cost of obtaining vortex-induced vibration information from massive monitoring data. Finally, actual vortex-induced vibration test data from a certain overseas bridge was utilized to verify the feasibility of this method. Based on the classification results, the correlation between vortex-induced vibration amplitude and environmental variables was determined, providing valuable guidance for predicting vortex-induced vibration amplitudes.

Natural vibrations of fluid in a well connected with the reservoir by a system of radial fractures

The problem of natural vibrations of a fluid in a horizontal well with multiple fractures obtained by hydraulic fracturing is considered. A mathematical model of the natural vibrations of fluid in a horizontal oil well connected to the reservoir by a system of radial hydraulic fractures is constructed and the frequency characteristics of the natural vibrations of fluid as functions of the hydraulic fracture and reservoir parameters are determined. Using a numerical analysis of the frequency characteristics of vibrations, the effect of changes in the fracture width, the number of fractures, and the reservoir permeability on the natural frequencies is demonstrated.

Nonlinear forced vibration of the FGM piezoelectric microbeam with flexoelectric effect

In this paper, based on the extended dielectric theory, Euler beams theory and von Karman’s geometric nonlinearity, a nonlinear FGM piezoelectric microbeam model is established with flexoelectric effect. The governing equations, initial conditions and boundary conditions are obtained by applying Hamilton’s principle and then solved by combining the differential quadrature method (DQM) and iteration method. The innovation of this paper is to construct a nonlinear forced vibration model of piezoelectric microbeams. The coupling response between the inverse flexoelectric effect and the inverse piezoelectric effect is investigated. Various effects are examined, including the functional gradient index m and transverse distributed load q affecting the distribution of electric potential. Results indicated that the functional gradient index m, beam thickness h, and span-length ratio L/h have a significant impact on the dimensionless deflection of the FGM microbeam. The influence of the flexoelectric effect on dimensionless deflection increases with the decrease of scale. In addition, transverse load q and the functional gradient index m also have a significant impact on the distribution of electric potential. This paper will provide useful theoretical guidance for the design of micro-sensors and micro-actuators.

Optimization of the Suspension System of Passenger Cars using the Vibration Model Multi-Objective Method

Optimization of the Suspension System of Passenger Cars using the Vibration Model Multi-Objective Method

Analysis of dynamic levitation process of the particle chain in a nonlinear standing wave field.

This research delves into the dynamic behavior of acoustic levitation of the particle chain in a nonlinear standing wave field. Experimental acoustic levitation control tests reveal bifurcation and jump phenomena during dynamic adjustments to resonant cavity height. Employing the 10-particle chain experiments and the COMSOL simulation models, the Sine-Gordon 2D vibration model is established to study the dynamic deformation process of the particle chain. The study uncovers the nonlinear interaction of particle lateral vibrations, horizontal acoustic radiation force, and conical wave fields that generate the jumping standing wave field. Notably, the fourth particle acts as a prominent jumping critical point in the secondary standing wave field, facilitating the derivation of the particle chain's nonlinear levitation dynamics. This discovery provides us with a new method to regulate the particle chain system.

A Novel Application of Computational Contact Tools on Nonlinear Finite Element Analysis to Predict Ground-Borne Vibrations Generated by Trains in Ballasted Tracks

Predictive numerical models in the study of ground-borne vibrations generated by railway systems have traditionally relied on the subsystem partition approach (segmented). In such a method, loads are individually applied, and the cumulative effect of the rolling stock is obtained through superposition. While this method serves to mitigate computational costs, it may not fully capture the complex interactions involved in ground-borne vibrations—especially in the frequency domain. Recent advancements in computation and software have enabled the development of more sophisticated vibrational contamination prediction models that encompass the entire dynamics of the system, from the rolling stock to the terrain, allowing continuous simulations with a defined time step. Furthermore, the incorporation of computational contact mechanics tools between various elements not only ensures accuracy in the time domain but also extends the analysis into the frequency domain. In this novel approach, the segmented models are shifted to continuous simulations where the nonlinear problem of a rigid–flexible multibody system is fully considered. The model can predict the impact of a high-speed rail (HSR) vehicle passing, capturing the key intricacies of ground-borne vibrations and their impact on the surrounding environment due to a deeper comprehension of the occurrences in the frequency domain.