Multi-frequency Response Research Articles

Quantitative Assessment of Sand Particulates in Gas-Water Slug Flow Using Deep Learning

Summary The weak collision response excited by micrometer-scale sand particulates is prone to overmixing with strong slug noise, significantly reducing the characterization and monitoring accuracy of sand particulate information in slug flows. Therefore, we developed a quantitative assessment method for sand particulates in slug flow that combines triaxial vibration monitoring and deep learning. First, a migration behavior characterization method of sand particulates is proposed combining nonlinear statistics, multifrequency coherence, and multiscale time frequency. The multifrequency response characteristics corresponding to the multiscale flow behavior of the sand-carrying slug flow were successfully characterized on the 2D time-frequency plane, namely, the mixed sand migration behavior [Intrinsic Mode Function 1 (IMF1)], liquid slug sand carrying (IMF2), forward liquid film and Taylor bubble sand carrying (IMF3), and reflux liquid film sand carrying (IMF4). Furthermore, the influence mechanism of gas superficial velocity (1.5–3.5 m/s), liquid superficial velocity (0.95–2.14 m/s), and sand content (0–20 g) on the triaxial vibration response of slug particulate flow with different migration behaviors is elucidated. Finally, a convolutional neural network (CNN)-gated recurrent unit (GRU)-self-attention mechanism (SATT) model for sand content assessment is developed based on the characterized multiscale migration behavior information and achieves an average recognition accuracy of 95.55% for data sets representing different sand migration behaviors in slug flow. This provides a new method for precisely identifying and monitoring sand production information of multiphase pipe flow.

Analysis of cracks development and damage evolution in red sandstone under dry-wet cycles based on temporal and frequency characteristics of acoustic emission

Utilizing the goafs of underground reservoirs (underground buildings) in western coal mines as storage spaces plays a crucial role in ecological environment protection and energy transition in mining areas. Hence, it is crucial to recognize the repeated erosion of reservoir water levels on the deformation and damage mechanisms of the roof and floor rock masses in the underground building dams. This paper intends to study the instability failure mechanisms and precursor responses of red sandstone samples with 0–3 dry-wet cycles during uniaxial loading-unloading under acoustic emission (AE) monitoring. The AE time-frequency features were analyzed, and the crack three-dimensional spatial extension and tensile-shear crack evolution were explored. The b-value and entropy value of AE events were presented for evaluating crack expansion damage status during loading-unloading. The findings suggest that the peak strength, elastic modulus, and crack thresholds of red sandstone exhibit a positive exponential decline with growing dry-wet cycles. Conversely, the peak strain and strain-softening modulus exhibit an opposite trend. With growing dry-wet cycles, AE signals from low-frequency, high-amplitude, and large-scale cracks decline, exhibiting a multi-frequency simultaneous response effect before sample instability. Meanwhile, the proportion and concentration of localization events with energy exceeding 104 aJ rise, and the failure instability gradually shifts from tensile-shear failure to tensile cracks. The sudden decline in b-value and the significant fluctuation in entropy value serve as short-term precursors to imminent rock instability failure, with the system energy following an ordered-disordered-ordered pattern. The research findings offer certain experimental foundation and novel judgment indicators for rock structure safety warning, including the stability of underground building dams, support for water-rich roadways, water hazard prevention, and utilization of abandoned mine spaces.

Artificial intelligence motivated flexible single-electrode mode multilayer triboelectric sensor for smart mobility systems

Triboelectric tactile sensing technique is increasingly coming into people’s lives to bring convenience, so that there is an urgent necessity for this technique to be applied to smart mobility to increase safety and enhance the mobility experience. Herein, a single-electrode mode multilayer triboelectric sensor (MTS) motivated by artificial intelligence (AI) is proposed, which consists of styrene-butadiene-styrene (SBS)/ poly (vinylida-ene fluoride-trifluoroethylene) (PVDF-TrFE) nanofibers (NFs) film as the friction layer and substrate, laser-induced graphene (LIG)/molybdenum disulfide (MoS2) as the charge trapping layer, and Ag as the electrode. The MTS exhibits remarkable sensing performance, such as a wide response range of 5–100 N, 0.4–2 Hz multi-frequency response capability, and non-contact sensing, as well as distinguished self-powered performance. To demonstrate the practical significance of the proposed MTS, two applications are explored specifically after equipping with AI, including: (i) a smart in-vehicle system is constructed, which consists of unlocking section and multifunctional control with early warning section. (ii) a smart car control system is implemented, which can carry out special tasks instead of humans. These applications provide reliable ways to promote the development of human-machine interaction and smart mobility, as well as help to make lifestyles and mobility smarter, safer and more convenient.

Magnetically driven capsules with multimodal response and multifunctionality for biomedical applications

Untethered capsules hold clinical potential for the diagnosis and treatment of gastrointestinal diseases. Although considerable progress has been achieved recently in this field, the constraints imposed by the narrow spatial structure of the capsule and complex gastrointestinal tract environment cause many open-ended problems, such as poor active motion and limited medical functions. In this work, we describe the development of small-scale magnetically driven capsules with a distinct magnetic soft valve made of dual-layer ferromagnetic soft composite films. A core technological advancement achieved is the flexible opening and closing of the magnetic soft valve by using the competitive interactions between magnetic gradient force and magnetic torque, laying the foundation for the functional integration of both drug release and sampling. Meanwhile, we propose a magnetic actuation strategy based on multi-frequency response control and demonstrate that it can achieve effective decoupled regulation of the capsule’s global motion and local responses. Finally, through a comprehensive approach encompassing ideal models, animal ex vivo models, and in vivo assessment, we demonstrate the versatility of the developed magnetic capsules and their multiple potential applications in the biomedical field, such as targeted drug delivery and sampling, selective dual-drug release, and light/thermal-assisted therapy.

Modeling vortex-induced vibrations of branched structures by coupling a 3D-corotational frame finite element formulation with wake-oscillators

Branched structures are present in a diverse set of problems, from modeling branch pipe connections to simulating tree dynamics. Soft corals like the Bipinnate sea plume, have a branched geometry and are soft enough to bend under the waves. Due to their circular cross section, a vortex street forms in the coral’s wake inducing vibrations of its branches. Despite extensive studies on VIV in straight geometries, the three-dimensional (3D) dynamics of flexible branched structures remains uninvestigated. In this numerical and experimental study, we develop a novel formulation for the accurate computation of in-line and cross-flow VIV of frame structures undergoing large deformation. The finite element approach is used to model arbitrarily complex geometries of branched frame structures. Our formulation allows to model complex geometries with forks or sharp angles. The consistent 3D corotational formulation for frame elements computes the internal, inertial and hydrodynamic forces. A wake-oscillator approach models the near wake dynamics with fluctuating fluid forces on the structure in the in-line and cross-flow directions. The drag and lift coefficients follow distributed Van der Pol oscillators. Moreover, we implement the numerical resolution procedure in the open-source library ONSAS. The present formulation and numerical resolution procedure is validated by solving three examples, including comparisons with an analytical solution, a wake-oscillator, and experimental data from the literature. We also conduct experiments of a flexible and elastic cylinder clamped inside a water tunnel under a constant uniform flow. Amplitudes and power spectral density of the tip transverse displacements are compared with the model prediction. Finally, the proposed formulation is applied on a cylinder with two branches. The simulations demonstrate a multi-frequency response with higher amplitudes of displacements when additional branches are incorporated onto the cylinder, emphasizing the significance of considering VIV in nature and engineering applications for such geometries.

Dynamics of acoustically coupled single- and multi-port jet diffusion flames

The present experimental study investigated the dynamics of single- and multi-port gaseous jet diffusion flames exposed to acoustic excitation via a standing wave situated in a closed waveguide at atmospheric pressure. High-speed imaging of the oscillatory flame was analysed via proper orthogonal decomposition (POD), revealing distinct signatures in both mode shapes and phase portraits for transitions in the acoustically coupled combustion process. For Reynolds numbers between 20 and 100, and for low to moderate forcing amplitudes, the flame exhibited sustained oscillatory combustion (SOC) that was highly coupled to the acoustic forcing. Frequency analysis of the temporal POD modes accurately recovered the forcing frequency and its higher harmonics. At higher forcing amplitudes, a multi-frequency response was observed, resulting from a combination of the forcing frequency and much lower frequency oscillations due to periodic lift-off and reattachment (PLOR) of the flame, preceding a transition to flame blow-off (BO). For both single- and triple-jet flames, transitions from SOC to PLOR to BO were characterized by significant alterations in primary modal energetic content, deflection and eventual smearing in phase portraits, and the development of additional frequencies in modal spectra, although transitional behaviour for the triple jet flames involved additional complexity in the dynamics due to its structure. These features provide the potential for the development of reduced-order models that can characterize and predict acoustically coupled combustion behaviour.

Nonlinear dynamics of an artificial muscle with elastomer–electrode inertia: Modelling and analysis

Artificial muscles are dielectric elastomeric system that mimic the response of the natural muscle and are helpful in many bio-mimicking applications. The existing literature is based on the assumption that electrodes are compliant and are focused on materials with greater extensibility than biological matter. The present work deals with the modelling and nonlinear dynamic analysis of dielectric elastomers considering the elastomer–electrode inertia and damping effect for bio-mimicking. The distinguishing point of the proposed work is the appearance of terms related to the elastomer–electrode inertia effect in the governing equation. Further, the biological muscle’s nonlinear elastic behaviour is incorporated using the Fung material model. Equilibrium stretch variation with parameter exhibits cusp catastrophe. The effect of electrode inertia on the equilibria is examined. Single-well and double-well potential energy characteristics are obtained for constant voltage. The basin of attraction illustrates the sensitiveness of system dynamics on the initial state and damping. The system response, when subjected to time-varying voltage, is explored. Multi-frequency response exists due to harmonic, sub-harmonic, and super-harmonic resonance condition. The resonant frequency variation with geometry and inertia is presented. Time-varying voltage may lead to chaotic behaviour illustrated through the bifurcation diagram. The presence of a strange attractor and positive Lyapunov exponent in the chaotic region further justify the existence of chaos. Additionally, chaotic behaviour is obtained in the case of single-well and double-well potential. Also, the existence of similar attractors with same fractal dimension is shown. The inertia effect significantly changes the dynamic characteristic from chaotic to non-chaotic or vice-versa. The mechanical and electrical load may lead to chaotic or non-chaotic behaviour depending on the geometry of the elastomer. The chaotic region’s dependence on the damping value is also obtained. Our results show that electrode inertia significantly impacts the elastomer under quasi-static and dynamic conditions. The proposed work gives a foundation for precisely designing artificial muscle for practical applications like soft robotics, artificial arms, and different prosthetic implants.

Multifrequency Response Magnetoelectric Cantilever Beam Devices for Magnetic Field Energy Harvesting and Detection

Multifrequency Response Magnetoelectric Cantilever Beam Devices for Magnetic Field Energy Harvesting and Detection

Parameter Estimation Methods of Linear Continuous-Time Time-Delay Systems from Multi-frequency Response Data

Parameter Estimation Methods of Linear Continuous-Time Time-Delay Systems from Multi-frequency Response Data

Parametric resonance and bifurcation analysis of thin-walled asymmetric gyroscopic composite shafts: An asymptotic study

Nonlinear geometries and cross-sectional asymmetry can be among the most critical contributing factors affecting the performance and stability of composite shafts. The influence of these factors, which should be devoted to particular attention in the design of these systems and have not been investigated yet, are evaluated analytically in this study. The shaft is simply supported, made of orthotropic multi-layers, and spinning at a constant speed. To express the nonlinear system’s behavior, which is due to the large amplitude of the vibrations, it is assumed that the shaft is under the stretching assumption. Moreover, a rectangular cross-section is used to model the asymmetry that results in parametric excitation in the system. To accurately investigate the behavior of composite material, an optimal lay-up is employed. The gyroscopic coupling is included because of Rayleigh beam theory, and Euler’s angles are employed to achieve the angular velocities. The analytical study of the parametrically excited system, obtained by the method of multiple scales, is performed in two categories of resonant and nonresonant cases. In the nonresonant case, the analytical investigation suggests that the asymmetric shaft behaves like a symmetric one therefore, the parametric excitations do not have a significant impact. This claim is confirmed by numerical results. Also, the presence of the gyroscopic coupling and hollowness of the shaft causes the beating phenomenon in the system. However, in the resonant case, the presence of parametric excitation plays a pivotal role. The results also show that under certain conditions and despite the presence of damping, asymmetric balanced rotors can have a nontrivial stable amplitude. This response exists as long as the parametric excitation effects dominate the damping effects. Although damping reduces the vibrations’ amplitude, it can improve the stability of the system and eliminates unstable responses. Furthermore, the time response and frequency response curve of the system is carefully evaluated for various geometric design parameters and operation speed. Depending on the operating speed, the system can experience supercritical or subcritical pitchfork bifurcation. In addition, a detailed description of the system’s Campbell’s diagram, damping effect, and bifurcation is provided. Furthermore, it is proved that internal resonance cannot occur in the system. The accuracy of the analytical responses of the resonant case is compared with numerical ones. Stability of trivial and nontrivial responses is discussed in the time response and phase portrait of the system simultaneously. Finally, in the undamped system, multi-frequency responses are appeared as homoclinic and heteroclinic closed orbits.

Experimental study on dynamic responses of a tensioned flexible vertical cylinder under waves and combined current and waves

The two degree-of-freedom (2DOF) dynamic responses of a flexible vertical cylinder under waves only and combined current and waves in a finite water depth were experimentally studied. The cylinder has multi-frequency response in both in-line (IL) and crossflow (CF) directions under waves. The response frequencies in the IL direction are multiples of wave frequency. The CF response frequencies include the multiples of wave frequency and the natural frequency of the cylinder, indicating that the CF response is controlled by both the wave actions and the vortex shedding. When the natural frequency of the cylinder is a multiple of the wave frequency, the CF vibration has the largest amplitude. A top tension can suppress the CF response more than the IL response amplitude, and the suppression effect increases with the increase of the top tension. With the decrease of the water depth, the response amplitudes in both directions decrease. Under combined current and waves, the IL response amplitude increases with the increase of KC number and the primary frequency of IL response is still the wave frequency. For a current velocity where VIV occurs, the superimposition of waves on current reduces the CF response amplitude because the vortex shedding frequency moves away from the natural frequency. The multi-frequencies of CF response are related to both the natural frequency of the cylinder and the wave frequency. The trajectories of the cylinder are mainly dependent on the ratio of the natural frequency to the wave frequency under waves or combined current and waves. There can be 2–6 cycles in the CF direction for each IL cycle with different wave frequencies and the top tension.

State estimation of a lithium-ion battery based on multi-feature indicators of ultrasonic guided waves

Ultrasonic non-destructive testing technology has been applied to battery state estimation applications to ensure the safety of the energy storage system. However, the accuracy and robustness of battery state estimation should be improved. In this paper, the state estimation of a lithium-ion battery based on multi-feature indicators of ultrasonic guided waves is studied. Piezoelectric ceramic ultrasonic probes with a fixed angle are used as the transducers. Eleven feature indicators of ultrasonic signals are analyzed. The appropriate feature indicators for battery state estimation are determined based on sensitivity analysis and correlation analysis. Considering the frequency response characteristics of the probe and the battery, the multi-frequency response characteristics of the battery are analyzed. Finally, seven feature indicators with multi-frequency excitation are selected. Subsequently, an adaptive machine learning model is designed to estimate the battery state. Based on the experimental results, the root mean square error (RMSE) of the battery state of charge (SOC) estimation result is less than 2.36 %. The applicability of the proposed method is verified by battery fully charged and non-fully charged experiments. Meanwhile, the method can quickly diagnose the side reaction process under abuse conditions such as overcharge and overdischarge, which provides a new method for non-destructive battery state evaluation.

(Invited) Investigating Defects in the High-k/Ingaas System at Cryogenic Temperature

III-V RF devices operating at cryogenic temperature are highly desirable for application areas such as space communication or quantum computing. In the case of quantum computation, integration of the readout and control electronics close to the quantum bit (Qubit) stage is needed to allow scaling of the number of Qubits needed for practical applications. Many characteristics of high frequency operation at cryogenic temperature in novel III-V devices are not fully understood. In this study, we will focus on the behaviour of defects at or near the interface between the high dielectric constant (high-k) oxide and InGaAs semiconductor at cryogenic temperature and how it may affect the full device operation at low temperature.The thermal budget constraints associated with the processing III-V semiconductor devices prohibit the use of high temperature thermal treatments to reduce oxide defect densities in the high-k. This leads to defective oxides presenting higher instability, variability, and degradation issues than in the Si/SiO2 system. The methods developed to investigate defects in the Si/SiO2 metal oxide semiconductor (MOS) system generally attribute the divergence in capacitance voltage (CV) and conductance voltage (GV) from the ideal CV and GV characteristics mostly to interface state defects (ITs) [1], which is not the case of the III-V MOS system. As a consequence, attempts to fit the multi-frequency CV and GV response of III-V MOS structures in the weak inversion regime, using interface states alone, cannot recreate the experimental data.In this study, we present an advanced MOS defects characterisation method capable of discerning between the contributions of oxide defects (sometimes labelled ‘border traps’) and ITs. The method relies on the fully physics based simulation of MOS systems, including inelastic tunnelling from the semiconductor to localized defects in the oxide [2] to reproduce the experimental multi-frequency CV and GV characteristics. The simulations include physical models accurately describing the carrier capture/emission processes by oxide traps, and which incorporate tunneling into the dielectric in conjunction with lattice relaxation at the interface/border trap sites [3, 4]. The results will show that the simulations are able to reproduce the room temperature experimental data (both CV and GV) of InGaAs/Al2O3 MOS structures in all bias regions. This new method enables the precise extraction of the density, energy and spatial distribution away from the interface of electrically active oxide defects from different experimental results.Results will also be presented showing how the multi-frequency CV and GV response of n-InGaAs/Al2O3 and p-InGaAs/Al2O3 MOS structures change with reducing temperature. Measurements at 223K show a marked reduction in the CV and GV dispersion with frequency in the accumulation and depletion regions, consistent with a phonon assisted tunnelling interaction of electrons and holes with defects in the Al2O3. Reduction in the measurement temperature to 10K still demonstrates a residual dispersion of the capacitance and conductance with frequency, which is more marked in the case of the p-InGaAs/Al2O3 MOS structure. The models and trap distributions extracted from room temperature will be applied to the reduced temperature measurements (233 K and 10 K) to investigate the validity of the models and to gain further understanding of defect behaviour and associated device implications at cryogenic temperatures.[1] E. H. Nicollian and J. R. Brews, “MOS Physics and Technology,” John Wiley & Sons, New York, 1982.[2] A. Palma, et al. Phys. Rev. B Condens. Matter Mater. Phys., 56 (15), pp. 9565-9574 (1997).[3] E. Caruso, et al. IEEE Trans. Electron Devices, 67 (10), pp. 4372-4378 (2020)[4] G. Sereni, et al. “IEEE Trans. Electron Devices, vol. 62, no. 3, pp. 705–712, (2015).

Modeling and analysis of a three-degree-of-freedom piezoelectric vibration energy harvester for broadening bandwidth

This study proposes a multi-frequency response piecewise-linear piezoelectric vibration energy harvester (MFRPLP-VEH) by combining the linear multi-frequency resonance and nonlinear vibration bandwidth broadening methods to improve the working frequency bandwidth and environmental robustness of the piezoelectric vibration energy harvester. A theoretical model is established based on the electromechanical coupling and the dynamic response of the MFRPLP-VEH. The energy harvesting performance and broadening width efficiency of the MFRPLP-VEH were obtained through an experimental verification platform, where the resonant frequencies of the three beam are 28.9, 33.6, and 38.6 Hz, respectively. Furthermore, the operating frequency range is widened by 90.9% at an external excitation acceleration of 10 m/s2. The energy generated by the MFRPLP-VEH is 194% of the energy generated by its linear counterpart under the same excitation conditions. The numerical and experimental results verify the accuracy of the theoretical model and the broadband working frequency range of the MFRPLP-VEH.

Modular Multilevel Converter Impedance Computation Based on Periodic Small-Signal Analysis and Vector Fitting

Instability and oscillation issues originating in high-voltage direct current (HVDC) systems comprising modular multilevel converters (MMCs) are gaining increasing interest in the research community. To detect such phenomena in advance, considerable effort has been devoted recently to developing MMC models for small-signal analysis. The derivation of such models is a challenging task due to the topology and complex control structure of MMCs, which results in them having a multi-frequency response. To address this issue, scholars developed methods based on dynamic phasors and harmonic state-space modelling, which, however, require extensive pen-and-paper computations. In this paper, the periodic small-signal analysis (PAC) is adopted to determine numerically several MMCs transfer functions. Such functions can be computed between any electrical circuit node or input/output port, without the need to recast the three-phase average MMC model to derive a linear equivalent one, possibly in the DQ-frame. We show how vector fitting allows converting these functions to equivalent algebraic representations, which can be profitably used to design MMCs and study their stability following some parameter changes. To showcase this feature, we exploit one of these transfer functions to detect DC-side instability in a point-to-point HVDC system.

Applying a Multi-Method Framework to Analyze the Multispectral Acoustic Response of the Seafloor

Improvements to acoustic seafloor mapping systems have motivated novel marine geological and benthic biological research. Multibeam echosounders (MBES) have become a mainstream tool for acoustic remote sensing of the seabed. Recently, “multispectral” MBES backscatter, which is acquired at multiple operating frequencies, has been developed to characterize the seabed in greater detail, yet methods for the use of these data are still being explored. Here, we evaluate the potential for seabed discrimination using multispectral backscatter data within a multi-method framework. We present a novel MBES dataset acquired using four operating frequencies (170, 280, 400, and 700 kHz) near the Doce River mouth, situated on the eastern Brazilian continental shelf. Image-based and angular range analysis methods were applied to characterize the multifrequency response of the seabed. The large amount of information resulting from these methods complicates a manual seabed segmentation solution. The data were therefore summarized using a combination of dimensionality reduction and density-based clustering, enabling hierarchical spatial classification of the seabed with sparse ground-truth. This approach provided an effective solution to synthesizing these data spatially to identify two distinct acoustic seabed classes, with four subclasses within one of the broader classes, which corresponded closely with seafloor sediment samples collected at the site. The multispectral backscatter data also provided information in likely, unknown, sub-surface substrate differences at this site. The study demonstrates that the adoption of a multi-method framework combining image-based and angular range analysis methods with multispectral MBES data can offer significant advantages for seafloor characterization and mapping.

Effects of nonlinearity of restoring springs on propulsion performance of wave glider

Wave glider is an unmanned surface vehicle that can directly convert wave energy into forward propulsion and fulfill long-term marine monitoring. A previous study suggested that the wave motion and stiffness of restoring springs mounted on the hydrofoil are the main factors affecting the propulsion performance of the wave glider. In this paper, the dynamic responses and nonlinear characteristics of the underwater propulsion mechanism considering the nonlinear stiffness of restoring springs are investigated based on a fluid–rigid body coupled model. Firstly, models of propulsion mechanism with different kinds of restoring springs are proposed, and the linear and nonlinear characteristics of the restoring spring are considered. Then, a fluid–rigid body coupled model of a wave glider is developed by coupling the rigid body dynamics model and hydrodynamic model. Dynamic responses are simulated by the numerical analysis method, and the nonlinear characteristics with different restoring springs are illustrated by the time/frequency domain motion response and phase diagram analysis. The effects of the wave excitation frequency, wave heights and the location of the connection point of springs on the propulsion performance of the wave glider are analyzed. The results show that multi-frequency responses occurred in the propulsion system, and the nonlinear restoring spring on the hydrofoil can provide a larger restoring moment to avoid excessive pitch angle and is more suitable for different sea conditions, which provides a reference for developing propulsion mechanisms with high performance in complex marine environments.

Flow-induced vibration analysis of two unequal-diameter flexible cylinders in staggered configuration from a hydrodynamic force perspective

This paper presents an experimental study on the hydrodynamic features of two unequal-diameter flexible cylinders in staggered arrangement subject to flow-induced vibration (FIV). Five position angles (α = 15°, 30°, 45°, 60°, and 75°) are defined between the tandem (α = 0°) and side-by-side (α = 90°) cases with the centre-to-centre spacing being fixed at P = 6.0d, where d is the diameter of the small cylinder. The time-varying strains obtained from the experimental tests are converted into displacements, and then the hydrodynamic force coefficients of the two cylinders are derived using an inverse analysis method. It is found that the variation trends of the cross-flow (CF) hydrodynamic coefficients with the reduced velocity do not demonstrate qualitative differences from those of their isolated counterparts except in the mode transition regions. The downstream cylinder experiences stronger influence from the upstream cylinder on its CF hydrodynamic characteristics especially at small α. The more frequent mode transitions in the in-line (IL) direction lead to the multi-frequency responses associated with changes in the IL hydrodynamic coefficients. The typical wake-induced flutter (WIF) phenomenon is observed when Vrs = 5.01, 8.77 and 16.28–25.05 for the downstream small cylinder in Case I and α = 75°. The influence of the characteristics of the WIF phenomenon on the hydrodynamic force is evident because of the nonexistence of the high-frequency components in the oscillations.

Numerical study on the characteristics of vortex-induced vibrations of a small-scale subsea jumper using a wake oscillator model

Vortex-induced vibrations (VIVs) of a small-scale subsea jumper has been studied numerically using a wake oscillator model. The dynamics of the jumper is described based on the linear Euler–Bernoulli beam theory and a wake oscillator model is uniformly distributed along the jumper to model the hydrodynamic force acting on it. The dynamics of the coupled system has been solved using the finite element method and the responses of the jumper subjected to uniform flows in different directions have been analysed. Some important characteristics of jumper VIVs, such as multi-frequency multi-mode response, single-frequency multi-mode response as well as uncoupled cross-flow and in-line VIVs without dual resonance, have been identified and the underlying mechanism have been explored. One unique character of the jumper mode is that some segmental elements of the jumper would undertake significant rigid body motions in their axial directions. A qualitative comparison shows that these axial rigid body motions of the segmental elements may influence the hydrodynamic force and could play an important role in the reliable prediction of the jumper VIV.

An experimental investigation of vortex-induced vibration of a curved flexible cylinder

Vortex-induced vibration of a curved flexible cylinder placed in the test section of a recirculating water tunnel and fixed at both ends is studied experimentally. Both the concave and the convex orientations (with respect to the incoming flow direction) are considered. The cylinder was hung by its own weight with a dimensionless radius of curvature of $R/D=66$ , and a low mass ratio of $m^{*} = 3.6$ . A high-speed imaging technique was employed to record the oscillations of the cylinder in the cross-flow direction for a reduced velocity range of $U^{*} = 3.7 - 48.4$ , corresponding to a Reynolds number range of $Re= 165 - 2146$ . Mono- and multi-frequency responses as well as transition from low-mode-number to high-mode-number oscillations were observed. Regardless of the type of curvature, both odd and even mode shapes were excited in the cross-flow directions. However, the response of the system, in terms of the excited modes, amplitudes and frequencies of the oscillations, was observed to be sensitive to the direction of the curvature (i.e. concave vs convex), in particular at higher reduced velocities, where mode transition occurred. Hydrogen bubble flow visualization exhibited highly three-dimensional vortex shedding patterns in the wake of the cylinder, where there existed spatial and temporal evolution of the vortex shedding modes along the length of the cylinder. The time-varying intermittent vortex shedding in the wake of the cylinder was linked to the spanwise travelling wave behaviour of the vortex-induced vibration response. The observed spatially altering wake corresponded to the multi-modal excitation and mode transition along the length of the cylinder.