Vibration Model Research Articles

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.

Effect of uncorrelated sources assumption on railway vibration modelling

In classical railway vibrations studies, wheel-rail contact points are considered as point sources uncorrelated from each other. This approach gives a more reliable source for vibration impact assessment studies along railways which can be based on in situ experimental measurements or on numerical models. This is also related to the fact that the combined wheel-rail roughness that cannot be perfectly known. This postulation allows using a line spectral force density combined with a line transfer mobility. However, all sources are generated by the same system (train, railway and ground) and are in reality correlated in some way. This paper investigates the effect of sources decorrelation on ground vibration estimation. Numerical models in time and frequency domain are used allowing comparisons for several identical configurations. Results are discussed in detail to understand the effect of sources uncorrelation approach.

Acoustic radiation of a fluid-saturated microperforated plate

It is known that fluid-saturated microperforated plates (MPP) dissipate energy and are substantially damped through thermoviscous dissipation taking place in the thermoviscous skin on the solid wall of the perforations. The aim of this work is to explore the acoustic radiation of a microperforated periodic cell to investigate the intercellular coupling and the complexity of near-field radiation, and to derive a criterion related to the near-field far-field transition. A numerical modeling using the finite element method is developed to solve the elastic and thermo-visco-acoustic (TVA) multiphysics problem. The TVA calculates explicitly the thermoviscous losses on the acoustic wave in the periodic cell studied. Numerical results show that the distance of the near-far field transition is significant at low frequencies, passing through a minimum for a frequency depending on perforation parameters (diameter and ratio) before increasing again as a frequency function. The radiated acoustic power and radiation efficiency are compared with those derived from the theoretical MPP vibration model. It is found that the microperforations and resulting added damping, around a characteristic frequency, reduce the acoustic radiation efficiency of the MPP compared to the corresponding non-perforated plate.

Research on digital vibration model of typical components in pipe system

The spatial distribution of pipe system is complex, long span and multi-point elastic support, so vibration analysis of pipe system is required in the pipeline design. This paper takes the pipe system as a typical component, based on the Timoshenko beam model, establishes a dynamic procedure for straight pipe elements that considers the axial flow rate of fluid, the pressure on the pipe wall, the Poisson coupling effect of fluid and pipeline structure, and the axial, transverse and torsional vibration. Through Laplace transform, the frequency simplified dynamic model is established. And the frequency transfer matrix model of straight pipe elements and the boundary constraint matrix of common boundary (such as fixed support) is established. Finally, the frequency domain transfer matrix model of different pipeline elements are set to the overall transfer matrix of the flow pipe system, providing a convenient means for rapid optimization of pipe system vibration.

Vibro-acoustic behavior of a permanent magnet synchronous electrical machine: Influence of rotor displacement on Maxwell's pressures

Electric machines are often perceived as silent, yet the noise they produce has become a significant issue. This paper presents a focused approach to understanding the source of this noise, aiming to enhance machine design. Our study centers on the vibratory model of a permanent magnet synchronous electric machine. The stator and rotor components (shaft, laminations, magnets, and flexible bearings) are modeled using finite element analysis. We calculate the magnetic forces from Maxwell's pressures, which are analytically determined using the subdomain method. A key aspect of our study is the consideration of dynamic eccentricity. The paper explores how the vibratory responses of the rotor affect theses stress and how to address the complexity of magneto-mechanical coupling. Our findings reveal that the magneto-mechanical coupling of the rotor directly and significantly impacts Maxwell's pressures, and has to be taken into account to characterize the dynamics of rotor and stator.

A novel multi-excitation transient vibration framework for coupling three- and one-dimensional pumped storage hydropower shafting systems

In vibration models of shafting systems, the hydraulic excitation is difficult to characterize due to the complex and changeable hydraulic factors. Thus, hydropower units are not well understood in terms of their dynamics and stability control under transient processes. A hydraulic–mechanical–electric multi-excitation transient vibration calculation framework is developed for analyzing the relationship between shafting vibration and internal flow regimes. First, the boundary data from penstocks, tailraces, and hydro-turbine are interacted with using one-dimensional and three-dimensional (1D–3D) coupling; Second, user-defined function secondary development is applied to achieve two-stage guide vane closure and the runner's variable speed rotation; Third, based on the computational fluid dynamics results, a multi-excitation vibration model is established to analyze shafting system characteristics. There is less than 1.2% error between the algorithm and the field test in terms of speed peak values. Under braking or reverse pumping modes, various vortice clusters are generated in the blade channel as well as the cascade, blocking the flow passage and leading to the runner's unbalanced force. Three sudden increases in vibration amplitudes of the shafting system have occurred in the radial direction under load rejection, each corresponded to the runner's stall rotations. The change trend in axial vibration amplitudes, however, is closely related to the change in axial hydraulic thrust. Furthermore, in braking and reverse pumping conditions, the axis trajectory is more complex under the action of multiple coupling factors than when only hydraulic factors are considered.

Modelling of wake-induced vibration of a long-span bridge with separated parallel nonidentical decks

The separated parallel decks design for long-span bridges can meet higher traffic demands, offering advantages in urban bridge design. However, when exposed to wind, the periodic wake shedding from the front bridge deck significantly affects the rear deck, leading to wake-induced vibrations (WIV). To address this issue, this study proposes and compares four models to comprehensively predict the wake-induced vibration of a long-span bridge with separated parallel nonidentical decks. The predictive capabilities of the four models for WIV are meticulously compared, and the reasons for the observed errors are analyzed. Ultimately, a model capable of accounting for the concurrent influences of wake-induced forces, instantaneous structural motion feedback, and non-linear self-excited forces is obtained. A series of wind tunnel tests are conducted to validate and evaluate the proposed models. Besides, this study encompasses an analysis of how structural damping and the deck layouts influence WIV. These findings bear substantial relevance to engineering practices confronted with similar challenges, thereby contributing to a deeper understanding of the intricate dynamics at play in such complex structural configurations.

Vortex-induced vibration and energy harvesting of cylinder system with nonlinear springs

Vortex-induced vibration is a common fluid–structure coupling phenomenon in ocean engineering. As a nonlinear stiffness structure caused by anisotropic deformation and support gap, nonlinear spring is of great significance in the field of vortex-induced vibration. Based on the structural dynamics equations and the wake oscillator model, the vibration model of the 2-Degree of Freedom cylinder system with the nonlinear stiffness spring is established. The stiffness ratio, mass ratio, and damping ratio of the cylinder system are changed, and the amplitude and frequency response are analyzed to obtain the effect of nonlinear spring on vortex-induced vibration. The results show that the cylinder system with a nonlinear stiffness spring can maintain a high vibration amplitude in a large Reynolds number range, and the smaller the mass ratio, the more significant the effect is. When m*=1.5, the amplitude of the cylinder system in a cross flow is greater than 0.6 at Re = 180 000–480 000. The energy harvesting in the vortex-induced vibration of cylinder systems with nonlinear stiffness springs is also studied. The efficiency depends on the damping ratio and Reynolds number. When the damping ratio is constant, the energy harvesting efficiency increases first and then decreases with the Reynolds number increases. When m*=1.5, the energy harvesting efficiency of the cylinder system is 19.27% with Re= 35 000 and damping ratio ξ=0.155. As a kind of renewable energy, energy harvesting in vortex-induced vibration is a potential development direction in the future energy field.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety. This paper proposes the strongly nonlinear acoustic metamaterial (NAM) method to mitigate aeroelastic vibration in supersonic wing plates. We employ the cantilever plate to simulate the practical behavior of a wing. An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory. The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods. While presenting the flutter and post-flutter behaviors of the NAM wing, we emphasize more on the pre-flutter broadband vibration that is prevalent in aircraft. The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%–90%, while the post-flutter vibration is reduced by over 95%, and the critical flutter velocity is also slightly delayed. As clarified, the significant reduction arises from the bandgap, chaotic band, and nonlinear resonances of the NAM plate. The reduction effect is robust across a broad range of parameters, with optimal performance achieved with only 10% attached mass. This work offers a novel approach for reducing aeroelastic vibration in aircraft, and it expands the study of nonlinear acoustic/elastic metamaterials.

Vibration modeling and simulation analysis of wind turbine flexible tower based on BP neural network

Vibration modeling and simulation analysis of wind turbine flexible tower based on BP neural network

Analysis of the effect of nonlocal factors on the vibration of nanobeams

Abstract Currently, the Eluer-Bernoulli beam nonlocal theory does not fully consider the effects of foundation deformation and axial force on the beams, and cannot accurately reflect the real mechanical properties of nanobeams. The primary objective of this study is to introduce a novel computational method designed for an enhanced characterization of the vibrational behavior of nano beams. Initially, this method incorporates the influence of foundation deformation on beam bending, accounts for the effects of axial forces, integrates Eringen's nonlocal theory, and establishes a modified Euler-Bernoulli beam theory model for the first time, accompanied by a degradation validation of the model. Subsequently, the Laplace transform and Hasselman's complex mode synthesis method are utilized to solve the model, providing the first derivation of the state-space transfer function for the nano beam vibration model based on the modified Euler-Bernoulli beam theory that includes axial force effects. Lastly, the study elucidates the impact of nonlocal factors and various parameters on the vibration characteristics of nanobeams. The results show that the order n increases, and the peak frequency value moves in the direction where the nonlocal factor tends to zero. When the order n is less than 6, the frequency peak is mainly concentrated in the interval where the nonlocal factor is greater than 0 and less than 0.1. At the same order, the beam length increases, and the peak frequency moves in the direction of increasing non-local factor. The modified geometric parameters and the foundation beam stiffness parameters have a greater effect on the peak of the beam's vibration mode in the higher order case and a lesser effect in the lower order case. The larger the nonlocal factor, the larger the peak of the vibration mode. The foundation beam stiffness parameter also has an effect on the direction of the peak vibration mode at the 1st and 2nd orders. The research results will help to predict the vibration behavior of nano beams under different conditions more accurately and provide an important reference for related applications.

Analysis of Vibration Characteristics of Spatial Non-Uniform Tensioned Thin-Film Structures Based on the Absolute Nodal Coordinate Formulation.

Due to their lightweight characteristics, spatial thin-film structures can generate vibrations far exceeding their film thickness when subjected to external loads, which has become a key factor limiting their performance. This study examines the vibration characteristics of tensioned membrane structures with non-uniform elements subjected to impacts in air, leveraging the Absolute Nodal Coordinate Formulation (ANCF). This model takes into account the wrinkling deformation of thin films under pre-tension and incorporates it into the dynamic equation derived using the absolute node coordinate method. A detailed discussion was conducted on the influence of non-uniform elements, situated at different locations and side lengths, on the vibration characteristics of the thin film. The analytical results obtained from the vibration model were compared with the experimental results, validating the effectiveness of the vibration model. This provides a theoretical foundation for the subsequent vibration control of thin films.