Vibration Phenomena Research Articles

Method for Constructing a Compact Component Mode Synthesis Model for Analyzing Nonlinear Normal Modes of Structures with Localized Nonlinearities

Abstract Nonlinear dynamics analysis is a crucial topic in mechanical and aerospace engineering. The analysis of nonlinear normal modes (NNMs) provides an effective mathematical tool for interpreting complex nonlinear vibration phenomena. Unlike the invariant normal modes of linear systems, NNMs often exhibit frequency-energy dependence and cannot be computed using the traditional eigen-decomposition method. Calculating NNMs relies on numerical methods that involve expensive iterative computations, especially for systems with numerous degrees-of-freedom. To relieve computational costs, this paper proposes a mode selection method for the component mode synthesis (CMS) technique to enable compact reduced-order modeling of structures with localized nonlinearities. The reduced-order model is then combined with a numerical continuation scheme to establish a low-cost NNM analysis framework. This framework can efficiently predict the NNMs of high-dimensional finite element models. The proposed framework is demonstrated on an I-shaped cantilever beam with localized nonlinear stiffness. The results show that the proposed approach can identify the key modes in the CMS modeling procedure. The NNMs of the nonlinear I-shaped beam structure can then be analyzed with a significant reduction in computational costs.

Mechanism of airfoil stall flutter: New insights from global linear stability analysis

Stall flutter is a self-excited aeroelastic vibration phenomenon that occurs in lifting systems near the stall angle of attack, characterized by the distinct single-degree-of-freedom behavior. Despite its significance, this phenomenon remains not fully understood and is often vaguely attributed to nonlinear effects. To address this gap, the present study aims to reveal the underlying fluid–structure interaction mechanisms of stall flutter through global linear stability analysis (LSA). For this purpose, a reduced-order model (ROM)-based aeroelastic stability analysis framework is established using the autoregressive with exogenous input method. The ROM-based aeroelastic model provides a low-order representation of the coupled dynamics near the equilibrium steady state and can accurately capture the stability characteristics of the fluid-elastic system. It is found that as the angle of attack approaches the static stall angle, a low-frequency weakly stable fluid mode emerges, whose frequency is sufficiently lower than that of the von Kármán vortex shedding. The interaction between this fluid mode and the structure mode ultimately leads to the instability of the aeroelastic system at high reduced velocities, which is the fundamental cause of stall flutter. Moreover, dynamic mode decomposition is employed to successfully extract the spatial coherent structures and frequency characteristics of this low-frequency fluid mode, thereby confirming the validity of the LSA results. Further analysis indicates that, as the angle of attack decreases, this low-frequency fluid mode gradually weakens and eventually degenerates into more stable non-oscillatory fluid modes, resulting in structural stabilization and the cessation of stall flutter. Overall, the linear dynamic model accurately predicts the onset of instability and the vibration frequency of the airfoil, which challenges the traditional nonlinear perspectives and supports the feasibility of using linear control theory for stall flutter suppression in future research.

A Review of Biomechanical Studies of Heart Valve Flutter

This paper reviews recent biomechanical studies on heart valve flutter. The function of the heart valves is essential for maintaining effective blood circulation. Heart valve flutter is a kind of small vibration phenomenon like a flag fluttering in the wind, which is related to many factors such as a thrombus, valve calcification, regurgitation, and hemolysis and material fatigue. This vibration phenomenon is particularly prevalent in valve replacement patients. The biomechanical implications of flutter are profound and can lead to micro-trauma of valve tissue, accelerating its degeneration process and increasing the risk of thrombosis. We conducted a systematic review along with a critical appraisal of published studies on heart valve flutter. In this review, we summarize and analyze the existing literature; discuss the detection methods of frequency and amplitude of heart valve flutter, and its potential effects on valve function, such as thrombosis and valve degeneration; and discuss some possible ways to avoid flutter. These findings are important for optimizing valve design, diagnosing diseases, and developing treatment strategies.

Numerical Study of Vortex-Induced Vibration Characteristics of a Long Flexible Marine Riser

In ocean engineering, interactions between ocean currents and risers lead to regular vortex shedding on both sides of the riser, causing structural deformation. When the frequency of vortex shedding approaches the natural frequency of the structure, resonance occurs, significantly increasing deformation. This phenomenon is a critical cause of riser failure. Therefore, the dynamic response of flexible risers to vortex-induced vibrations (VIV) is crucial for their structural safety. This paper employs the finite-volume method to integrate over control volumes to solve for forces, such as pressure and shear stress, on the surface of the riser, while the finite-element method discretizes the continuous structural body into elements and nodes to solve for structural displacements and stresses. A strongly coupled method is utilized at each timestep to iteratively transfer load-displacement data between the fluid and structural fields, updating the boundary conditions of the fluid domain to achieve a bidirectional fluid–structure interaction simulation of vortex-induced vibrations in a seawater environment for flexible risers. The study finds that the three-dimensional flexible riser exhibits multi-frequency vibration phenomena and broadband vibration response characteristics under high flow velocity conditions. As the flow velocity increases, the vortex-shedding mode is observed to transition from the simple two single (2S) mode to the more complex pair + single (P + S) and two pair (2P) modes. In addition, the stiffness at the ends is enhanced by the fixed boundary conditions, and the coupling between the natural frequency of the ends and the vortex-shedding frequency triggers complex vortex-shedding phenomena in these regions. At higher flow velocities, these boundary effects result in more complex vortex-shedding modes and stronger vibration responses at both ends of the riser.

Impact of metro vibrations on people: critical aspects of designing vibration mitigation interventions

A methodology for assessing and mitigating the impact of metro infrastructure generated vibration and ground-borne noise on people is described. This methodology combines techniques for analyzing vibration measurements and predictive modeling to identify effective mitigation interventions. These interventions require working on existing railway track systems and involve interruption of service, unlike noise mitigation interventions that can be implemented without interfering with rail and road infrastructure. For this reason, it is important to identify the most effective mitigation techniques to minimize the impact on the population and simplify on-site implementation. The methodology was applied in Milan metro lines where the vibration level was estimated, and a vibration mitigation system was designed. The vibration phenomenon was quantified through accelerometric measurements taken in several buildings affected by the disturbance from vibration. The measured vibration levels were compared with reference level established by standards. The maximum difference obtained from this comparison was used as input data for the design of the mitigation intervention. The vibration mitigation interventions involve increasing the total mass and elasticity of the existing system. Their effectiveness was verified through numerical calculation using parametric software confirming the required amount of mitigation.

Applications of vibrational phenomena to evaluate the effect of hydrogen solution on the elasticity and fatigue properties of industrial metal plates

Understanding resonance phenomena in materials is crucial in many fields, from controlling noise in small mobile devices to designing seismic-safe large structures or in energy harvesting. Resonance depends on material elasticity and its shape, influenced by temperature. While controlling elastic properties can control vibrations, seeking practical alternatives is essential. This research focuses on introducing hydrogen into industrial metal materials as a method to control resonance conditions, which is particularly relevant in the context of the upcoming hydrogen society. Controlled amounts of hydrogen were introduced to industrial metal plates (Ti, W) using electrochemical methods to investigate changes in their resonance characteristics. The results indicate that the introduction of hydrogen into Ti resulted in a maximum 20% reduction in Young's modulus, while W exhibited a 10% decrease. Additionally, the recovery of their modulus by hydrogen desorption was confirmed. This confirms that the control of hydrogen allows the manipulation of the modulus of elasticity at constant temperature, controlling the resonance without changing the dimensions. Furthermore, similar evaluations were performed on high hardness steel. The results showed fatigue failure due to vibration, increased Young's modulus with the introduction of hydrogen, and an observed trend toward decreased life to failure.

Thermo-flexible coupled dynamics of composite laminated plates based on absolute nodal coordinate formulation

In this paper, a thermo-flexible coupled dynamic model of composite laminates is established by Absolute Nodal Coordinate Formulation (ANCF). In order to solve the problem of mesh mismatch and precision inconsistency between the displacement and temperature fields in the traditional thermo-flexible coupled modeling method, the ANCF hybrid element with integrated temperature description is constructed to achieve a unified description of the displacement and temperature fields. A new ANCF thin shell element with thermal effects is proposed. Based on the first law of thermodynamics, the heat capacity matrix, thermal conduction matrix, blackbody radiation matrix, internal heat source vector, and heat flux density vector caused by solar radiation for the ANCF thin shell element considering thermal effects are derived. The dynamic equation of ANCF composite laminates under a unified description is derived, and its dynamic model is established. The thermo-flexible dynamic response of ANCF composite laminates under thermal conduction, space thermal radiation, and solar radiation is analyzed by numerical simulation. The simulation results reveal the evolution process of the transient temperature field and the phenomenon of thermal-induced vibration, thus confirming that the thermal effects have an important influence on the dynamic behavior of ANCF composite laminates. The research provides a theoretical basis for the ground test of solar panels.

Research on the influence of rigid body modes on the operating vibration of arc gate

Abstract The 5# arc working gate of Jiangshan Wanyao Reservoir is composed of the suspension system of the gate and the steel wire rope, which has a serious vibration phenomenon when running without water. Firstly, the rigid body modal analysis of the gate suspension system is analyzed, the position size of key components such as gate support hinge shaft, gate motion guide embedded parts, and main beam position state is measured and evaluated on site, and the dynamic stress and vibration of the support arm are tested and analyzed during gate operation. It is concluded that the influence rule and weight of the steel wire rope on the rigid body mode of the gate, the torsional position of the gate, and the uneven operation condition of the side guide lead to the rigid body mode of the gate. It is suggested to improve the twisting state of the gate, adjust the unevenness of the embedded parts, and weaken the factors that induce the modal vibration of the rigid body.

Multiple-arc cylinder under flow: Vortex-induced vibration and energy harvesting

The shape of a cylindrical cross-section affects the vibrational performance. The vortex-induced vibration (VIV) phenomena of multiple-arc cylinders were numerically investigated to assess their impact on hydrodynamic energy harvesting and potential vibration suppression across a flow velocity range of 0.2 m/s to 1.4 m/s (1.767×104<Re<1.237×105). The study involves five types of multiple-arc cylinders: 4-arc, 8-arc, 16-arc, 24-arc, and circular cylinders. The accuracy of the numerical method was validated through comparison with experimental data. Specifically, increasing the number of arcs generally enhances overall energy conversion efficiency. Then, the VIV response and energy conversion results of the 24-arc cylinder are similar to those of the circular cylinder with maximum efficiency. Notably, the 4-arc cylinder achieves a global maximum amplitude of 0.074 m (A*=0.83) and a power output of 4.4 W with the new P+T mode, making it the most effective configuration for flow velocities between 0.7 and 0.9 m/s. For vibration suppression of multiple-arc cylinders, the appropriate arc structure effectively reduces amplitudes. The small vortices generated by the arc structures disrupt the separation of normal vortices from the boundary layer, leading to approximately a 50% reduction in amplitude responses for 8-arc and 16-arc cylinders.

Study on Self-Learning System for Milling Chatter Feature Based on Hybrid Preprocessing Model and Improved Convolutional Clustering

Milling chatter is a self-excited vibration phenomenon during the cutting process, typically occurring in machining operations with lower stiffness. It significantly impacts the machining precision and surface morphology of the workpiece. To summarize the vibration signal features under operating conditions and enhance the precision of the intelligent recognition model for milling chatter features, this paper proposes an adaptive learning model for chatter feature recognition based on the improved convolutional clustering algorithm. This study uses wavelet analysis to extract chatter features and improved convolutional clustering to identify chatter and stable cutting signals. This method selected appropriate mapping techniques based on differences in chatter signals under various conditions and uses convolution for feature extraction. Improve convolutional clustering evaluates sample similarity through energy transfer, less influenced by signal space structure compared to Euclidean or Mahalanobis distances. This method provides a unified criterion for evaluating different signal feature representation spaces, thereby improving the accuracy and efficiency of chatter sample recognition. The recognition accuracy of chatter phenomena at different spindle speed ranges reaches $95$ % and $96.3$ % respectively. The results show that this method can effectively distinguish between chatter signals and stable cutting signals.

Crisis-induced vibrational resonance in a phase-modulated periodic structure.

Double vibrational resonance is reported for a driven oscillator in a periodic structure of the Josephson junction type with high-frequency phase modulation. We identify two distinct phase modulation effects, namely, resonant induction and resonant amplification, leading to the appearance of a double resonance. We analyze these vibrational resonance phenomena theoretically and numerically, and we show that the origin of the induced resonance is traceable to a transition from periodicity to quasiperiodicity associated with an attractor-merging crisis.

Influence of Seal Structure on the Motion Characteristics and Stability of a Steam Turbine Rotor

Sealing aerodynamic characteristics are affected by the seal structure, and thus the stability of the rotor system is affected too. A 1.5-stage, three-dimensional, full-cycle model of the high-pressure cylinder of a 1000 MW steam turbine was established. The high eccentricity whirl of the rotor was realized using mesh deformation technology and the multi-frequency whirl model. The nonlinear steam-flow-exciting force of different sealing structures was obtained using CFD/FLUENT, and the motion equations with a nonlinear steam-exciting force were solved using the Runge–Kutta method. The motion characteristics and stability of the rotor system with different sealing structures were obtained. The results show that there are “inverted bifurcation” and “double bifurcation” phenomena in the bifurcation diagrams of different tooth numbers, boss numbers, and tooth lengths, and a 1/2 power frequency of different sealing structures goes through the process of weakening, disappearing, reproducing, and evolving into a 1/3 power frequency and a 2/3 power frequency. With the increasing load, the steam-flow-exciting force becomes stronger, and the multi-frequency vibration and dense frequency phenomena are significant. Under some load conditions, the change curves of three kinds of teeth in 1/3 and 2/3 power frequency vibrations are highly similar, and the tooth number has little influence on the system stability. Under the high load condition, with the boss number increasing, the chaos phenomenon is weakened. Increasing the tooth length is beneficial to the stability of the rotor.

Nonlinear resonance in an overdamped Duffing oscillator as a model of paleoclimate oscillations.

The cause of the dominant 100-kyr cycles in Earth's paleoclimate in the last 800 000 years has since long been debated. We analyze geological temperature proxy data and retrieve an anharmonic potential from time series data. The obtained potential has bistable features but has significant differences compared to the quartic potentials derived from theoretical energy-based models. Subsequently, we demonstrate the existence of vibrational resonance (VR) and nonlinear resonance phenomena at the combination tones of the driving frequencies in a simple bistable potential without self-sustained oscillations. We find that periodic forcing by the obliquity and frequencies similar tothose of the precession cycle can generate output dominated by 100-kyr cycles, thereby offering a mechanism for explaining the observations in geological data. While previous studies of VR have assumed one periodic driver to have a frequency much higher than the other, we show that for a range of amplitudes, both phenomena can occur at the orbital cycle frequencies. We find that the nonlinear resonance phenomenon is more robust to noise than VR between eccentricity and obliquity and emerges within a much larger range of amplitudes of forcing. Finally, we conclude that it is conceivable that nonlinear resonance between obliquity and precession might explain the spectral frequencies observed in the late Pleistocene.

Fuzzy PI vibration suppression control strategy for space double flexible telescopic manipulator with fractional disturbance observer

The space double flexible telescopic manipulator (SDFTM) with time-varying length, is called the space flexible manipulator and can carry out reciprocating linear telescopic motion along its axis. It possesses characteristics such as lightweight flexibility, small space occupation, large turning radius, and a wide working range. These features can assist astronauts in performing complex tasks in dangerous outer space environments and offer broad application prospects. However, due to the highly nonlinear and time-varying length characteristics of the space flexible manipulator, its dynamic modeling becomes more complex and challenging. Moreover, during the rotation of the space flexible manipulator, its inherent flexible behavior can trigger vibration phenomena, significantly impacting the execution accuracy of on-orbit tasks. Therefore, proposing control methods to address vibration issues is an effective approach. Thus, achieving stable and precise operation of the space flexible manipulator necessitates the precise establishment of its dynamic model and the development of high-precision control algorithms, which have become key research directions. Firstly, a time-varying dynamic modeling method of the space manipulator is proposed by combining the Lagrange principle and flexible beam vibration theory. Unlike the traditional method, which only considers the limit length of the space manipulator under static conditions, the dynamic process of the space manipulator presented during actual operation is fully considered, which greatly improves the modeling accuracy. Then, a time-varying model based on the fuzzy PI real-time control strategy (FD-FZPI) with fractional order disturbance observer (FO-DOB) is proposed. Based on the robust stability principle, a more accurate FO-DOB is proposed based on integer order DOB, coupled with a fuzzy PI controller to compensate for the external disturbance and modeling error of the space manipulator. Finally, numerical simulation analysis is carried out, and the results show that the average parameter difference between the time-varying dynamic model and the static dynamic model can reach about 5.2 %, which indicates the accuracy of the proposed dynamic modeling method. At the same time, the proposed FD-FZPI control strategy achieves about 14.6 % performance improvement over the traditional DOB-PI control method, indicating that the proposed control strategy can effectively suppress the flutter fluctuation of the space manipulator and achieve accurate and stable dynamic tracking.

Coupled vibration characteristics and optimization design of the cylindrical-exponential ultrasonic concentrator

Abstract In this study, the vibrations of cylindrical-exponential ultrasonic concentrators are investigated, with the objective of improving energy transfer efficiency. Traditional analyses, often one-dimensional, have been found to inadequately consider the effects of height on vibration behaviour. To address this gap, the equivalent elasticity method is employed to provide a more comprehensive understanding of vibrational phenomena. The coupled vibration of the concentrator is regarded as an interaction between a longitudinal vibration and a plane radial vibration. A mechanical coupling coefficient is introduced, establishing a link between these vibrational modes. Equivalent circuits for radial and longitudinal vibrations are derived, and input impedances are presented as functions of resonance frequency and mechanical coupling coefficient. These analyses enable an exploration of the impact of geometric dimensions on the vibrational characteristics. To validate our theoretical model, the finite element method is used to simulate the coupled vibration and the results confirm the efficacy of the approach.

Dynamic response characteristics of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission system considering wear effect

To illustrate the impact of tooth surface wear on the dynamic response of the cylindrical gear transmission system with variable hyperboloid circular-arc-tooth-trace (VH-CATT), a nonlinear dynamic model of VH-CATT cylindrical gear that considers wear effect was developed in this article. Firstly, according to the analysis conducted through the finite element method, the time-varying meshing stiffness of VH-CATT cylindrical gear is calculated, and the time-varying meshing stiffness considering wear is characterized by introducing wear fault characteristics. Then, the load ratio is introduced to represent the relationship between the error amplitude and the excitation load. By using the error amplitude as the bifurcation parameter, this parameter describes how the excitation load affects the dynamic characteristics of the VH-CATT cylindrical gear. Finally, the bifurcation diagram and maximum Lyapunov exponent of the VH-CATT cylindrical gear transmission system under various wear depths are computed using the fourth-order Runge-Kutta method. At the same time, the response state of the VH-CATT cylindrical gear is verified by phase diagram, Poincaré mapping and time history diagram. The findings indicate that the vibration amplitude of the VH-CATT cylindrical gear system increases as the error amplitude increases. The vibration phenomenon of VH-CATT cylindrical gear transmission system with wear fault is more obvious, and the system enters the bifurcation and chaos effect state in advance. Therefore, the wear of the tooth surface will lead to the decrease of the gear meshing stiffness, which will lead to the increase of the vibration amplitude of the system, resulting in the phenomenon that the dynamic response state of the system is advanced. The research results will provide a theoretical basis for high-quality VH-CATT cylindrical gear transmission and gear nonlinear dynamics research.

Experimental and numerical investigation of the track structure elasticity induced by resilient fastener on vehicle-track interaction and train running stability

The resilient fastener slab track (RFS track) has found extensive application in urban railways, effectively mitigating vibration and noise resulting from train operations. However, the structure elasticity of the RFS track is higher than the normal slab track (NS track), which can affect train running stability and cause abnormal vibration phenomenon. This paper explores the track structure elasticity on vehicle-track interaction and train running stability through experimental tests and numerical simulations. The vibrational properties of the RFS track and the NS track are obtained through field tests. A 3D metro vehicle-track coupled dynamics model is developed and utilized to simulate the dynamic performance of metro vehicles moving on different track structures. The impact of track structure parameters upon the vehicle-track interaction and train running stability are discussed. The findings indicate that the track structure elasticity can reduce train hunting stability and cause abnormal vibration phenomena in metro vehicles under certain conditions. The reasonable matching of the fastener lateral and vertical stiffness can not only accomplish vibration attenuation but also minimize the impact on train running stability. In addition, the rail surface wear and track gauge variation also exert influence on the running stability and dynamic performances of metro vehicles.

Optimal control problem governed by a kind of Kirchhoff-type equation

In this paper, we consider an optimal control problem governed by a kind of Kirchhoff-type equation, which plays an important role in the phenomenon of beam vibration. Firstly, the existence of solution to the state equation is proved by the variational method. Secondly, for the given cost functional, we get that there exists at least an optimal state-control pair via the Sobolev’s embedding theorem under the constraint of the state equation. Next, the necessary optimality condition for the optimal solution is derived by using the cone method. Finally, we give the pointwise variational inequality, minimum principles and an equivalent necessary condition for the optimal control problem according to the discussion of the variational inequality.

Study on the effect of valve openings and multi-stage throttling structures on the pressure and temperature during CO2 pipeline venting processes

The venting operation is an important measure for rapidly eliminating the risk of overpressure in CO2 transportation pipelines. However, the low-temperature phenomenon and vibration generated by the rapid discharge can affect structural reliability. Multi-stage throttle structures have been proven to effectively alleviate vibration phenomena, but their impact on low temperatures remains unclear. In this study, venting tests were conducted on eight groups of single-stage and two-stage throttle structures based on a large-scale pipeline. The results indicate that the nonlinear variation of the valve resistance coefficient when the valve opening changes is the fundamental reason affecting the downstream temperature. Two-stage throttle structures can effectively mitigate the low-temperature conditions in certain spaces within the pipeline. For the remaining low-temperature sections, three-stage throttle structures can provide effective compensation. However, this significantly reduces the pressure drop rate in the main pipeline, contradicting the original purpose of the venting operation. Additionally, considering the temperature of the throttle structure and the pressure within the main pipeline, this study recommends increasing the valve openings for the two-stage throttle structure. The results of this study provide important references for the design of throttle structures and the formulation of on-site venting schemes, with strong prospects for engineering applications.

Study of Resonance between Bogie Hunting and Carbody Mode via Field Measurements and Dynamic Simulation.

By addressing the phenomenon of carbody abnormal vibrations in the field, the acceleration of the carbody and bogie was measured using accelerometers, and the diamond mode of the carbody was identified. The equivalent conicity of the wheelset and the acceleration at the frame end indicated that the shaking of the carbody was caused by bogie hunting. In the SIMPACK simulation, the acceleration frequency and amplitude at the frame end and midsection of the side beam were calculated. The lateral deformation amplitude of the side beam in the finite element model was extracted, and a modal shape function for the diamond-shaped mode was established. By utilizing the modal vibration equation, the modal generalized forces of the carbody were computed, revealing that, during carbody shaking, the yaw damper force contributed significantly among the forces of the secondary suspension, with the phase difference between the front and rear bogies approaching 180°. This insight offers a novel perspective for subsequent active control strategies. Subsequently, these modal generalized forces were applied as external excitation to a coupled vibration model encompassing both the carbody and transformer. Aiming to reduce the acceleration amplitude at the side beam, the transformer was treated as a dynamic vibration absorber, allowing for the optimization of its lateral suspension parameters. As a result, the lateral and vertical acceleration amplitudes at the side beam were concurrently reduced, with the maximum decrease reaching 58.5%, significantly enhancing the ride comfort.