Vibration Model Research Articles

Vibration characteristics of subway turnout area during vehicle deceleration and assessment of the model accuracy

Frog gaps and rail joints produces intricate wheel-rail contact conditions within subway turnouts, which results in intense vibrations. This study describes vibration tests conducted on several typical cross-sections of a turnout, which aimed at understanding the vibration transfer characteristics of typical section in turnout area. To separation the vibration signals from each carriage, wavelet analysis and peak detection algorithms were utilized. Using a 2D kernel density algorithm, representative data from the carriages were clustered, effectively isolating the influence of interference data. A coupled vehicle-turnout-tunnel-soil vibration analysis model was established, combining multiple spatial and temporal scales and the accuracy of its prediction was evaluated by comparing the calculated results to statistical test results.The test results indicate that when the train decelerated through the turnout, there was a significant variation in the vibrations of different train carriages, with a 13 dB difference in the total rail vibration levels. The rail joints and frog gap present in the turnout resulted in high vibration level in the tunnel walls. The main frequency of tunnel wall vibration in the frog gap section was 63 Hz, and the total vibration level was 84.9 dB. The accuracy of vibration response prediction was evaluated by comparing the calculated results to statistical test results using probability density functions, and the model errors were maintained within 10 % of the test data. The presented vibration testing and modelling results of vibration propagation characteristics in various directions for the subway turnout area will provide a foundation for selecting vibration mitigation measures.

A synchronization-induced cross-modal contrastive learning strategy for fault diagnosis of electromechanical systems under semi-supervised learning with current signal

Electromechanical systems is widely employed in the manufacturing industry, with fault diagnosis being critical for ensuring the reliable operation of them. Vibration signals exhibit distinct fault features, but their acquisition is subject to various limitations. Conversely, current signals, while easily measurable, typically manifest weak fault features. Therefore, selecting a signal for fault diagnosis necessitates a trade-off among cost, performance, and feasibility. To overpass these obstacles and enable flexible fault diagnosis in complex environments, this paper presents a novel contrastive vibration-current (CVC) framework that leverages synchronization information from multiple modalities to enhance the performance of single-modality models, primarily the current model. This allows the choice of any signal for monitoring during the deployment phase. Specifically, we first preprocess current signals using Clarke transformation to highlight their fault information. Subsequently, the vibration model employs semi-supervised learning to make full use of labeled and unlabeled samples. Additionally, a noise-resistant augment Mean Teacher is incorporated to enhance the robustness of the vibration model. Then, using synchronization-induced cross-modal contrastive learning (SICMCL), vibration and current features are aligned. And at the decision level, the current model leverages pseudo-labels derived from vibration. The results of experiments demonstrate that CVC excels when relying solely on single-modal signals, owing to the effectiveness of SICMCL. Moreover, for the current model, SICMCL is more beneficial in improving performance than true labels.

Nonlinear dynamic modelling and analysis of a rotating composite thin-walled beam considering ice coating

For rotating structures operating in severe weather conditions, ice coating phenomenon is an established issue that impairs the reliability and effectiveness of the structures by changing the dynamic behaviors. To explore the influence mechanisms of ice coating on the dynamic behaviors of rotating structures, this work presents an analytical dynamic model for nonlinear forced vibration of a composite thin-walled beam under both rotating and ice coating conditions. The ice coating is considered as C-shaped configuration which can affect the system parameters of the beam, especially aerodynamic performance. With effect of out-of-plane warping taken into account, the nonlinear dynamic equation of the beam is established using Hamilton's principle. The Galerkin discrete method together with the incremental harmonic balance method (IHB) as well as pseudo arclength continuation technique are adopted to obtain the periodic response of the nonlinear system. Then, a detailed parametric study on natural frequency, frequency-response and bifurcation behaviors is numerically conducted. Special attention is paid to the effects of ice coating, rotating angular velocity, inflow velocity and design parameters on the linear and nonlinear dynamic behaviors of the beam. Results reveal a prominent change in natural frequency, vibration amplitude and cusp bifurcation of multivalued region under the combined effects of ice coating and rotating motion. Such ice-induced changes exhibit the requirement of vibration control and optimization design consideration for rotating structures operating in icing coating conditions.

Effect of Gear Tooth Cracks on the Dynamic Characteristics of Gear Transmission System of High-Speed Train

Abstract In order to study the dynamic characteristics of a high-speed train gear transmission system with cracks, time-varying meshing stiffness of gear teeth with different cracks was obtained using energy method. A torsional vibration model of the gear transmission system of a high-speed train was established. Based on the model, the ρ-value describing the change in stiffness was used to obtain the analytical solution of a system with crack faults. The influence of the degree of crack on the dynamic characteristics of a system under torque excitation of the driving end and load end was analyzed. In contrast with a normal gear system, a system containing a crack fault generated no harmonic response. Moreover, for a given set of working conditions, the degree of crack only affected the resonance amplitude and frequency of the system. These results form a robust guide for the detection of crack faults in the gear transmission system of a high-speed train.

Is there a finite mobility for the one vibrational mode Holstein model? Implications from real time simulations.

The question of whether there exists a finite mobility in the standard Holstein model with one vibrational mode on each site remains unclear. In this Communication, we approach this problem by employing the hierarchical equation of motion method to simulate model systems where the vibrational modes are dissipative. It is found that, as the friction becomes smaller, the charge carrier mobility increases significantly and a friction-free limit cannot be obtained. The current autocorrelation functions are also calculated for the friction-free Holstein model, and converged results cannot be obtained with an increase in the number of sites. Based on these observations, we conclude that a finite mobility cannot be defined for the standard Holstein model in the parameter regime explored in this work.

A hybrid vibration suppression strategy for redundant cable-driven parallel mechanisms

Suppressing the vibration of cable-driven parallel mechanisms (CDPMs) is of great significance for improving their performance such as positioning accuracy. In this paper, a hybrid vibration suppression strategy based on stiffness enhancement and input shaping is proposed to reduce the vibration of a CDPM in the process of moving. Firstly, the stiffness model and vibration model of the CDPM are established. Then, based on the stiffness model and the vector set [Formula: see text] that meets the requirements of the cable tensions, a stiffness enhancement algorithm is proposed to improve the stiffness of the mechanism by adjusting cable tensions. In order to reduce the vibration of the mechanism to the maximum extent, a hybrid vibration suppression strategy is proposed by combining the stiffness enhancement algorithm with the multi-modal input shaping technique. Finally, the effect of stiffness enhancement algorithm and hybrid vibration suppression strategy on reducing mechanism vibration is verified by experiments. The hybrid vibration suppression strategy proposed in this paper does not require additional components and therefore does not increase the cost of vibration suppression, and it has good performance.

A computationally efficient method for dynamic response analyses of accessory drive systems using harmonic balance method together with alternating frequency/time domain technique

Serpentine belt accessory drive system (SBADS) is a typical coupled vibration system with rigid body vibrations and continuum vibrations. Vibration behaviors of a SBADS consist of rotational vibrations of pulleys and tensioner arm and transverse vibrations of belt spans. In modeling of a SBADS, transverse vibration of a belt span consisting of time and space coordinates is discretized into multiple degrees of freedom with only time variable. As a result, number of degrees of freedom of a SBADS is large, and computational efficiency of dynamic responses of a SBADS is low. To solve this issue, a calculation method for nonlinear dynamic characteristics of a SBADS is proposed based on the harmonic balance method with alternating frequency/time domain technique in the paper. An engine front end accessory drive system is taken as a study example, the coupling vibration model of the SBADS is established, and hysteretic behavior of the tensioner is considered in the model. In addition, a dimensionality reduction method for the dynamic matrix is proposed based on local nonlinearity of the model. A calculation method for nonlinear dynamic responses of the SBADS is subsequently developed by combining the harmonic balance method and alternating frequency/time domain technique. Nonlinear dynamic responses estimated by the proposed method are validated by comparing with numerical simulations. Finally, amplitude-frequency responses of the SBADS are calculated using arc-length continuation method, and influences of nonlinear tensioner on frequency domain responses and internal resonance phenomena of the SBADS are analyzed.

Construction of environmental vibration prediction model for subway transportation based on machine learning algorithm and database technology

Vibrations generated in the metro transport environment are mainly caused by, vibrations generated by the interaction between the metro and the track during operation. and the change of vibration factors will affect the normal operation of the subway. However, it is difficult to have a model that can achieve the characteristics of high accuracy, fast computing speed and wide range of use in the traditional metro rail transportation environment prediction. Therefore, this research uses database theory and machine learning algorithms to predict the vibration of subway transportation environment. The experimental results show that the average difference between the whole prediction value and the real value is 1.4 dB, of which the maximum difference error value is 0.29%, the maximum error difference is 8.2%, and the approximate value is 6.2 dB, and the four averages predicted in 40 m are relatively small as 1.6 dB, and the average error value of prediction ability between 40 and 100 m is 1.72 dB, and the experimental prediction value and real value are in good agreement. The agreement between the experimental prediction and the real value is very good. Therefore, the model is able to predict the vibration model of the subway transportation environment with a high degree of agreement and accuracy.

Friction-induced vibration reliability and sensitivity analysis of a braking system

In this study, reliability and sensitivity analyses are performed for the behavior of friction-induced vibration based on automotive braking systems. In this paper, a friction-induced vibration model of the braking system is developed using Newton’s second law. The accuracy of the vibration model is verified through experiments. The displacement response of the braking system is theoretically derived by convolution integration. The function of maximum displacement is obtained by solving the stationary point of displacement response. Based on this function, the limit state function of the maximum limit of friction-induced vibration displacement is established, and the reliability and sensitivity of the friction-induced vibration of the braking system are evaluated by using the Mean Value First Order Second Moment (MVFOSM) method. The results show that the reliability of the braking system increases with the increase of the mathematical expectation of the equivalent stiffness and decreases with the increase of the mathematical expectation of the system friction coefficient, normal force, and damping ratio. In addition, the sensitivity of the reliability varies significantly with the mathematical expectation of the system friction coefficient and damping ratio. Therefore, the system friction coefficient and damping ratio are the key parameters for the reliability design of the braking system.

A nonlinear vibration model of fiber metal laminated thin plate treated with constrained layer damping patches

This paper explores the nonlinear vibration characteristics of fiber metal laminated thin plate(FMLTP) treated with constrained layer damping(CLD) patches. Additionally, based on the Jones-Nelson nonlinear material theory and the von Kármán geometric nonlinear theory, a theoretical model for FMLTP with CLD patches is established, considering material nonlinearity. Using the energy method, an energy equation is formulated and the nonlinear natural frequencies and vibration responses of the studied structure are iteratively determined through the Newton-Raphson method under various excitation amplitudes. Additionally, the modal damping ratios are calculated utilizing the complex modulus method. To validate the effectiveness of the model, a corresponding testing system is constructed, and tests are conducted on a 5-layer TA2/TC500 FMLTP treated with two pieces of CLD patches. The test results show excellent agreement with the theoretical results. Finally, the influences of different CLD patches treatment methods on the vibration characteristics of the FMLTP are discussed.

Analysis of torsional vibration characteristics for wind turbine drivetrain under external excitation

This work studies the torsional vibration characteristics analysis of the wind turbine drivetrain with the variation of internal parameter and external excitation. The electromechanically coupled torsional vibration model for wind turbine drivetrain is first established by taking into account the torsional vibration angle of the PMSG. Then, frequency response analysis of main parametric resonance is illustrated by multiple scale method, and the influences of the system parameters involving power factor angle, number of pole pairs, torsional stiffness, and wind speed excitation on the torsional vibration characteristics of wind turbine drivetrain are investigated. Moreover, the critical condition for homoclinic chaos in terms of the system parameters is derived by means of Melnikov’s method. The function relationship and the boundary curve of chaos threshold are obtained. Meanwhile, the effects of excitation amplitude and damping factor on the system transition to chaos are studied in detail. The analytical predictions including phase portrait, bifurcation diagram and Lyapunov exponent are investigated. The research results can offer a theoretical basis for further the parameter design and control of wind turbine drivetrain.

A Data-Driven Model for Predictive Modeling of Vortex-Induced Vibrations of a Long-Span Bridge

Vortex-induced vibration (VIV) of long-span bridges can be of large amplitude, which can influence serviceability. Therefore, it is important to predict the response of vortex-induced vibration to aid the management of long-span bridges. A novel data-driven model is proposed to predict the time history of the dynamic response of VIV events. Specifically, the proposed model consists of gated recurrent unit (GRU) neural networks and the Newmark-beta method. GRU neural networks can perform accurate sequential prediction, and the Newmark-beta method can complement the physical meaning of the middle output of the proposed model. To aid the accurate prediction of the amplitude of VIV events, the proposed model employs weighted mean square error as the loss function, which can put more emphasis on the amplitude. The proposed model is validated on measured VIV events of a long-span suspension bridge. The weighted mean absolute percentage error and Pearson correlation coefficient of the trained model indicate the effectiveness of the proposed model.

Coupling effects in borosilicate glass leaching: A study on La/V doping

Borosilicate glass could solidify high-level radioactive waste (HLW), and the research on the leaching behavior can optimize the composition, thereby improving its stability and durability. In this work, the leaching behaviors of borosilicate glass in the presence of La/V and their coupling effects were investigated. The results revealed significant coupling effects among La3+, VO43−, and CO2 in an aqueous environment. The existence of LaCO3OH and zircon-type LaVO4 was confirmed by grazing incident X-ray diffraction spectra, and their structures were characterized by infrared and Raman spectra in which the vibration models of CO32−, La-O bond, and VO43− were identified. At the initial leaching stage, orthorhombic LaCO3OH and zircon-type LaVO4 crystals emerged on the glass surface. While the formation of lanthanum-containing layers slowed down the initial leaching rate, it also enriched lanthanum on the glass surface. This enrichment posed a potential risk of leakage since lanthanum was previously uniformly dispersed in the glass network. Therefore, the doping and coupling effects in the design of glass compositions should be considered. The crystallization process, induced by coupling effects between the compositions of borosilicate glass and the solidified waste, plays an important role in understanding the leaching behaviors of nuclear glass.

Bifurcations and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms

For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [ Li & Chen, 2007 ] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of the corresponding phase portraits are identified and analyzed. Under different parameter conditions, exact homoclinic and heteroclinic solutions, periodic solutions, compacton solutions, as well as peakons and periodic peakons, are all found explicitly.

Vibration frequency and mode localization characteristics of strain gradient variable-thickness microplates

Based on the modified strain gradient theory and Kirchhoff–Love assumptions, a free vibration model is established for variable-thickness microplates with three material length scale parameters, and the corresponding Euler–Lagrange equation is derived. Keeping the microplate volume constant, three kinds of thickness variations along the X-direction are considered: linear, parabolic, and cubic variations. Further, a C2-type four-node 36-degree-of-freedom variable-thickness differential quadrature finite element is developed to solve the resulting variable-coefficient boundary value problem by combining the Gauss–Lobatto and differential quadrature rules. Galerkin approximate solution for fully simply supported microplates is provided as a benchmark for numerical method verification. The convergence and accuracy of the model are verified through several examples. Finally, the vibration frequencies of the microplates under different thickness variation types, taper ratios, thickness ratios, material length scale parameters, and boundary conditions are examined through parametric analysis. Also, the influence of each factor on the mode localization of the microplates is quantitatively characterized by the modal assurance criterion (MAC) for the first time. The numerical results show that the thickness variation has a minor effect on the vibration frequency but a significant influence on the mode shape when the volume of the microplate is constant. The strain gradient, taper ratio, and discontinuous boundary have a remarkable effect on the distribution of higher-order mode shape contour lines and the regions where vibration localization occurs.

Modeling, mechanics and experimental investigation of perpetual vibration of serial-chain direct-drive flexible robotic system

The domain of Flexible Robotic Systems (FRS) is an exciting ensemble of global robotics research of the present decade, which unfurls various real-time data like rheology, vibration, sensor fusion, and non-linear coupled dynamics for control. As some of these features, especially strain-induced deflection and vibration, are inherent in FRS, the design and prototype development of multiple degrees-of-freedom flexible robots is highly challenging. The paper addresses the aforementioned design paradigms of FRS through logical understanding by giving importance to the manufacturable design-variables. Further, these design issues for the firmware of higher-order FRS have been explained with a focus on the novel design and hardware development of a prototype multi-link serial-chain FRS fitted with a miniaturized gripper at the free end. Besides hardware realization, the paper brings out an interesting feature in experimental robotics, namely, the evaluation of the natural frequency of vibration of a flexible manipulator using real-time data on dynamic strain produced within its body. This niche methodology gets propelled by the data from multiple strain-detecting sensors placed judiciously over the links of the FRS. Guided by this lemma, a novel theoretical analysis of the optimal placement of strain-sensors over the external surface of the FRS is described. Additionally, the paper dwells on a novel scheme for dynamic analysis as well as control system logic for the developed FRS. This research provides a complete canvas of design, modeling, firmware development, and experimental ab initio evaluation of perpetual in-situ vibration of a typical serial-chain FRS

Dynamic performance of multi‐layered composite sandwich open cylindrical shells with double‐layered soft cores

AbstractIn this paper, the dynamic performance of Multi‐layered Sandwich Composite Cylindrical Open Shells (MSCCOS) with double‐layered soft cores is analyzed for the first time by adopting the First‐order Shear Deformation Theory (FSDT). For accomplishing this aim, vibration differential equations of MSCCOS are derived based on Hamilton's variance principle. Then, the closed‐form Navier solution is introduced to obtain the numerical results of differential equations. Subsequently, the effectiveness and accuracy are discussed by several comparisons. Ultimately, the dramatic effect of different structural and material parameters on natural frequencies and associated loss factors is investigated and described vividly. Because shear deformation and rotary inertia of all layers are considered in vibration differential equations, thin and moderately thick MSCCOS could be researched, and some interesting discoveries for the dynamic performance of MSCCOS are derived.Highlights A vibration model of five‐layered composite open shell was obtained. The optimal structure parameters maximizing the damping properties are shown. Dynamics properties of five‐layered composite open shell are presented.

Modeling of construction vibration impacts in transit project applications

This presentation explores some of the challenges related to predicting the vibration impact from construction activities associated with new mass transit infrastructure. Pre-construction assessment methods are examined and compared against as-measured construction vibration monitoring data. Practical considerations and limitations of construction vibration monitoring are also discussed, citing examples, and insight from the ongoing projects, especially in the Greater Toronto Area.

Modeling of free vibrations and resonant frequencies of simply-supported submerged horizontal plate.

A theoretical approach was applied to study the vibration of simple-supported submerged horizontal plate. The derived analytical solution was used to determine natural frequencies for a horizontal plate vibrating in fluid. The investigations were conducted for a very wide range of material density and elasticity modulus covering all materials used in engineering practice. Analysis shows that plate vibration frequency decreases with increasing plate width and draft, and decreases with decreasing plate thickness. Moreover, the results show that a substantial effect on vibration of submerged plate has mass of water above plate. The results also show that plate vibration frequency decreases with increasing plate material density and decreases with decreasing elasticity modulus. The dominant factors affecting the vibration of the submerged plate are the plate width, the plate thickness, and elasticity modulus. For moderate and low values of elasticity modulus, vibration frequency is becoming lower than frequency of water waves. This is very important because wave frequencies overlap with the natural plate vibration frequencies, which may lead to resonance and failure of a structure. The problem is that the overlap of plate vibration frequencies and wave frequencies occurs for very wide range of wave and plate parameters. Laboratory experiments confirm theoretical results.

Simulation and analysis of core barrel vibrational modes associated with neutron noise phenomena in WWER-type reactors

This survey focuses on an approach to address various vibrational modes of the core barrel in a hexagonal-structured reactor core. The core barrel vibration is considered one of the main mechanical vibrations in a high-power nuclear reactor, initiating core component malfunctions and safety issues. Here, a well-reasoned method is proposed to handle the triple vibrational modes of such core barrels, whether individually or in combination with fuel assembly vibrations. The modeling of core barrel vibrations involves modifying the lattice water width for boundary fuel assemblies and correlating it with external reactivity in the time-dependent calculation. The radial and axial distributions of neutron noise amplitude, phase, and spectrum are further analyzed for several scenarios using the designed neutron noise simulation tool, DYNOSIM. The outcomes support using the suggested methodology to simulate neutron noise in hexagonal cores due to different modes of core barrel vibration.