Vortex-induced Vibration Amplitude Research Articles

Coupling effects of top-end dynamic boundary with a planar trajectory of “8” on three-dimensional VIV characteristics

The top-end dynamic boundary of riser is usually generated by the motion of the moored floating body in marine environment, inducing the oscillation of equivalent fluid velocity and mechanical features of the riser, and further affecting its vortex-induced vibration (VIV). In this paper, the double-degree-of-freedom (2DOF) top-end dynamic boundary with a trajectory of “8”, which widely exists in fluid-structure interactions of ocean engineering, is studied. A series of tests for a riser model with the aspect ratio of 250 are conducted under the combination of the top-end dynamic boundary and uniform flow, whose three-dimensional (3D) VIV characteristics and behaviors are investigated in detail. The effect of amplitude and frequency of “8”-shape dynamic boundary on VIV is discussed, following which the relationship and difference among four top-end boundaries of “8”-shape, in-line harmonic, cross-flow harmonic and static forms are compared and analyzed. The results indicate that some periodically oscillatory phenomena involving time-varying frequency, mode transition and amplitude modulation are induced by the “8”-shape dynamic boundary. The periodic effect of dynamic boundary on VIV shows orthogonality, which means the cross-flow dynamic boundary is mainly responsible to the oscillatory characteristics in in-line VIV while the in-line dynamic boundary corresponds to cross-flow VIV. At the same time, the in-line dynamic boundary has a certain disturbance on the in-line vibration. The amplitude and frequency responses of in-line VIV could be enhanced by “8”-shape dynamic boundary at low or medium reduced velocity, further growing with the increase of boundary amplitude and frequency.

Effect of grid size and initial conditions on vortex-induced vibration of a circular cylinder

A direct-forcing immersed boundary (DFIB) method was used with an in-house parallelized C++ code to simulate the vortex-induced vibration (VIV) of a one-degree-of-freedom (1-DOF) elastically mounted circular cylinder in the laminar and turbulent flow regimes. The continuity and Navier–Stokes equations were solved numerically together with the equation of motion to study the VIV response of the cylinder in 3-D. The results were analysed and compared with published literature. The importance of conducting a grid independence study at multiple points inside the lock-in (synchronization) region for VIV simulations has been ascertained through detailed comparisons of coarser and finer grids in each of the flow regimes. In addition, for laminar flows, the effect of the grid on the evolution of the vibration response in the lock-in region was discussed. For turbulent flows, the effect of different initial conditions on VIV amplitude was studied, and a hysteresis phenomenon was observed in the initial and upper branches of the lock-in region. The need for multiple calculation methods of vibration amplitudes in turbulent flows was highlighted.

Three-dimensional nonlinear vortex-induced vibrations of top-tension risers considering platform motion

A novel three-dimensional (3-D) dynamic model considering nonlinearity of tension is proposed to explore in-line (IL), cross-flow (CF) and axial (AX) vortex-induced vibration (VIV) responses of riser under platform motion. The interaction between riser and external flow is simulated by the van der Pol equation, and the nonlinear equations of motion are established by Hamilton's principle and the Galerkin method, and solved by Runge-Kutta method. The influences of heave and swing motions of platform on VIV responses of the riser are investigated. It is found that for large velocity of external flow, the axial displacement of riser results in an increase in IL excitation mode and also an increase in IL oscillating displacement. When the riser is excited by swing motion of platform, with the increase of excitation amplitude, the maximum response amplitudes will also increase in all the three directions, and the amplitudes in high frequency domain increase more obviously. Combined effect of heave and swing motions of the platform results in the increase of VIV amplitudes in IL and AX directions, and combined action of forced and parametric excitations has little effect on response amplitude of riser in CF direction.

Experimental investigation of vortex-induced vibration of a flexible pipe in bidirectionally sheared flow

The existence of a bidirectionally sheared flow field caused by internal solitary waves has recently been confirmed according to a field survey in the South China Sea. A model test of a tensioned flexible pipe in bidirectionally sheared flow was performed in an ocean basin. The model was 28.41mm in diameter and 7.64m in length. The purpose of the model test was to understand the response performance and obtain benchmark data of vortex-induced vibration (VIV) in bidirectionally sheared flow. The test was performed on a rotating test rig to simulate bidirectionally sheared flow conditions. Fiber Bragg Grating (FBG) strain sensors were arranged along the test pipe to measure bending strains, and the modal analysis approach was used to determine the VIV response. Reduced velocities based on the tested first natural frequency in water reached 30.79. The cross-flow and in-line VIV amplitudes, response frequencies in statistics and time-domain analysis, traveling wave characteristics, phase synchronization and trajectories are presented in this article. The maximum root mean square (RMS) VIV amplitudes in the test reached 0.51 diameters and 0.18 diameters in the cross-flow and in-line directions, respectively. A relative low Strouhal number of 0.10 was found in the CF direction.

Experimental investigation on the vortex-induced vibration of a rectangular 4:1 cylinder under skew winds

The characteristics of vortex-induced vibration (VIV) of a rectangular 4:1 cylinder are comprehensively investigated under different wind yaw angles (β = 0°, 5°, 10°, 15°, 20°, 25°, and 30°) and wind angles of attack (αm = +5°, +3°, and 0°) using wind tunnel tests. For the VIVs of a rectangular 4:1 cylinder, the lock-in regions, amplitudes, frequencies, hysteresis effects, and the applicabilities of independence principle (IP) for various cases are analyzed. Experimental results suggest that the maximum VIV amplitude and the onset wind speed for VIV respectively decreases and increases with increasing β. Hence, it is reasonable to assume that the most unfavorable state of VIV occurs for β = 0° for the rectangular 4:1 cylinder. However, the IP theory is inapplicable for predicting its VIV responses under skew winds. The maximum amplitude increases with the increase of αm, while the lock-in region shrinks with αm. For the rectangular 4:1 cylinder under skew winds, the experimental VIV response may provide a benchmark for checking the prediction accuracies of mathematical models and computational fluid dynamic simulations.

Vibration Assessment of a New Danube Bridge at Komárom

In this paper the vortex induced vibration of a cable-stayed bridge with a main span of 252 m was studied at construction stages. Structural FEM and aerodynamic CFD models were made in order to calculate the vibration amplitude of this slender structure. The damping of the pure steel structure and the effect of the tuned mass dampers were measured through on-site vibration tests. Based on the validated structural dynamics model and the simulated aerodynamic parameters, the vortex induced vibration amplitudes were evaluated and compared with the monitoring data gained from accelerometers and wind sensors attached to the stiffening girder during the most critical construction period.

An Air Velocity Monitor for Coal Mine Ventilation Based on Vortex-Induced Triboelectric Nanogenerator.

Air velocity of coal mine ventilation is an important consideration that may cause serious damage. This paper proposes a simple, low cost and effective air velocity monitor (AVM) for coal mine ventilation. The AVM uses the lock-in characteristic of vortex-induced vibration (VIV) to sense the air velocity. Amplitude of the VIV is converted into frequency signal of a vortex-induced triboelectric nanogenerator (VI-TENG) to improve the durability. Structure of the AVM are designed, and parameters of the AVM are optimized with experiments. For the upper and lower air velocity thresholds of 3.1 and 3.6 m/s, the optimized flexible beam length, slider weight, electrode space and electrode width are 42.5 mm, 0.4 g, 0.2 mm and 0.5 mm, respectively. Experiments also show that the output frequency of the VI-TENG could represent the amplitude of VIV well with the correlation coefficient of 0.93. Durability test demonstrates that the AVM generates stable output frequency in 120,000 cycles. A prototype and its controller are fabricated. Wind tunnel tests of this prototype show that it can give alarm when the gas velocity goes above the upper threshold or below the lower threshold. The proposed AVM could be a good solution for simple and effective coal mine ventilation alarm.

Vortex-induced vibration response characteristics of catenary riser conveying two-phase internal flow

Vortex-induced vibration (VIV) of the riser considering both external flow and multiphase internal flow is a complex fluid-structure interaction problem. Due to its flexible feature, steel catenary riser (SCR) may be more affected by internal flow than top-tensioned riser (TTR). Firstly, the semi-empirical time domain VIV model of riser with internal flow is introduced, and the theories of gas-liquid flow and solid-liquid flow are applied to modify the model. Then the VIV of TTR and SCR with internal flow are compared. Subsequently, the VIV of SCR with gas-liquid flow and solid-liquid flow are calculated, and their different effects are discussed. The results show that internal flow triggers higher-order modes of VIV and enlarges the fatigue damage in general. With similar length, internal flow has more significant impact on SCR than TTR. The increase of liquid volumetric flow rate, solid production and gas volumetric quality enlarges the modal order and fatigue damage. The increase of solid volumetric quality and solid density reduces the modal order and fatigue damage. Compared with gas-liquid flow, solid-liquid flow may decrease the VIV amplitude and reduce the fatigue damage.

Vortex-induced vibration characteristics of two open girders: A comparison of experimental and numerical investigation

Open girder sections are vulnerable to vortex-induced vibrations (VIV) because of their bluff aerodynamic characteristics. A comparative investigation was conducted by wind tunnel tests and numerical simulation. Firstly, based on sectional model wind tunnel tests, the VIV performance of semi-open girder and separated edge-boxes open girder was studied with consideration of the influence of the equivalent mass, wind attack angle and damping ratio. The aerodynamic parameters Scruton number ( S c) and Strouhal number ( S t) of two girders were analyzed contrastively. In addition, VIV amplitudes corresponding to the real bridge girders were calculated by the linear and nonlinear theories. Then, flow fields around two semi-open girder sections were investigated on the basis of computational fluid dynamics. The results show that vertical and torsional VIVs of two open girders are observed, at +3°and +5° wind attack angles. There were two vertical VIV regions and the maximum amplitude in the second vertical VIV region is significantly larger than that in the first one. For the semi-open girder and separated edged-box open girder, the vertical VIV amplitudes at +5° wind attack angle is 115% and 75% larger than at +3° wind attack angle, respectively. The damping ratio could obviously mitigate the VIV of two girders and VIV amplitudes are decreased linearly with the S C number increases. There are vortexes above the girder deck at the opening position of the semi-open girder and the separated edge-boxes open girder. The oblique web and wind faring may break the large vortex into several smaller vortexes at the opening position, thus optimizing the vortex vibration performance of the girder. A thicker shear layer is formed at separated open-girder during the development of airflow towards backward of bridge deck, due to the effect of railings and the blunt boxes on the lower surface.

Vortex-Induced Force Model and Reliability Analysis of a Steel Box Girder with Projecting Slab in a Cable-Stayed Bridge

To study the vortex-induced force (VIF) model of a steel box girder with projecting slab, a cable-stayed bridge with a main span of 160 m was taken as the research object in this study. First, a computational fluid dynamics (CFD) numerical simulation method was used to calculate the amplitude characteristics of vortex-induced vibration (VIV) of the steel box girder with projecting slab, and the calculated results were compared with those of wind tunnel tests. Then, the time–history of VIF of the bridge girder was extracted based on the validated numerical simulation results, and a new mathematical model of VIF for the steel box girder with projecting slab was established according to the residual values between the reconstructed and target values. On such a basis, the steady VIV amplitude expression of the bridge girder was deduced according to the principle of the work done by the damping terms in the VIF model. Finally, the performance function of the maximum VIV amplitude was established with six random variables. Furthermore, the failure probability of VIV was calculated by the maximum entropy principle combined with the multiplicative dimensional reduction method, and the sensitivity of each random variable was analyzed as well. The results show that the lock-in region, VIV amplitudes and vibration frequency of the bridge girder calculated from the numerical simulations agree well with those from the wind tunnel tests, and the maximum amplitude occurs at the oncoming wind speed of 7.2 m/s. In addition to the most important fundamental-frequency component, there also exist double- and triple-frequency components in the time–history of VIF of the bridge girder, which implies the VIF exhibits certain nonlinear characteristics. According to the proposed expression of the steady VIV amplitude of the bridge girder, the steady amplitude decreases as the absolute value of parameter [Formula: see text] increases, but it increases with the increase of the parameter [Formula: see text]. The failure probability of VIV of the bridge girder is calculated to be 0.9616 based on the performance function with six random variables. Besides, it is found that the damping ratio [Formula: see text] has great effects on the reliability of VIV, while the vertical bending frequency [Formula: see text] exerts less effects.

Vortex-induced vibration of a flexible fluid-conveying riser due to vessel motion

As vessel motion and internal flow can exert impact on vortex-induced vibration (VIV) of flexible risers, it is of great significance to take these two factors into consideration while VIV is investigated. Therefore, crossflow (CF) VIV of a flexible fluid-conveying riser is studied when vessel motion is considered. The governing equation is firstly discretized based on finite element method and solved by Newmark-β method. Then, validation is conducted by comparing with experimental data. Subsequently, CF VIV response of a flexible riser is explored with consideration of both vessel motion and internal flow. The results show that regardless of low and high Keulegan-Carpenter (KC) numbers, vessel motion can have a notable effect on top tension and CF VIV characteristics. Variations of CF VIV amplitude, vibration frequency as well as top tension frequency are affected by both vessel motion and internal flow. With the increase of internal flow velocity, CF VIV amplitude is changed while mode jump occurs concomitant with frequency transition. Besides, both vessel motion and internal flow velocity can have an impact on energy allocation along the flexible fluid-conveying riser. Noteworthy is that although both vessel motion and internal flow can exert an impact on top tension and VIV response, the effect induced by vessel motion still plays a dominated role.

Evaluation the possibility of vortex-induced resonance for a multistage pressure reducing valve.

A multistage pressure reducing valve is presented in this paper. The pressure reducing components are specially designed to not only control the flow rate but also effectively prevent the cavitation vibration. However, when the fluid flows through the pressure reducing components, the divergence and shedding of the vortices in the flow field seriously affect the stability of the valve and cause vortex-induced vibration. Especially, the main frequency of the vortex shedding is in the same frequency range as the modal frequency of the valve, the vortex-induced resonance of the valve occurs. It seriously affects the safety of a control system. In this paper, by monitoring the lift coefficient of the vortex cross flow in the valve, the frequency spectrum information of the lift coefficient is used as the novelty indexes to indicate vortex-induced vibration of the fluid in the valve. The main frequency and amplitude of vortex-induced vibration are obtained. The factors affecting the vortex-induced vibration of the fluid are analyzed. The results indicate that vortex-induced vibration is the most serious when the valve is opened or closed. The variation of the flow velocity and the pressure difference have obvious effects on vortex-induced vibration of the valve. The intensity of the variation affects the main frequency and amplitude of vortex-induced vibration. Using thermal-fluid-solid coupling modal analysis instead of traditional modal analysis, the modal frequency under the working state of the valve is obtained. It is compared with the main frequency of vortex shedding, and vortex-induced resonance does not occur in the multistage pressure reducing valve.

Extraction of aerodynamic damping and prediction of vortex-induced vibration of bridge deck using CFD simulation of forced vibration

This study presents computational fluid dynamics (CFD) simulation of forced vibration of a bridge deck for extraction of amplitude-dependent aerodynamic damping in the vicinity of vortex lock-in region. The coordinate system fixed on the oscillating body is used to bypass the requirement of mesh updating. The three-dimensional flow around the vibrating deck is assumed to be homogeneous in spanwise direction and simulated using the efficient high-order spectral element/Fourier method. The aerodynamic damping is extracted from the simulated lift and then used to estimate the steady-state vortex-induced vibration (VIV) amplitude for given wind velocity and structural parameters. A good match of VIV amplitudes between simulations and wind tunnel tests validates the accuracy of simulation. The VIV mechanisms are discussed from the vortex shedding modes, distributions of dynamic pressure and energy transfer from flow to bridge deck. The leading-edge vortex shedding rather than Karman vortex shedding is identified to be responsible for the VIV. The hysteresis of VIV is observed which is related to the mode change of impinging leading-edge vortex and leading-edge vortex shedding. Finally, a novel forced vibration technique with a varying amplitude is proposed that permits extraction of aerodynamic damping by a single CFD run with improved efficiency.

Suppression of vortex shedding and vortex-induced vibration of a circular cylinder using screen shrouds

Experiments were conducted in wind tunnels to investigate the one degree of freedom (1DOF) vortex-induced vibration (VIV) and vortex shedding of a circular cylinder controlled with various screen shrouds in the sub-critical Reynolds number regime. The screen shrouds, made of stainless steel screen meshes with porosities β = 37%, 48%, 61%, and 67%, were fitted concentrically outside the bare circular cylinder. The diameter ratio between the outer screen shrouds and the inner bare cylinder was fixed at 2. The VIV responses and force coefficients of the screen shrouded cylinders were first examined in a wind tunnel to quantify the effectiveness of the screen shrouds on VIV suppression. It was found that the screen shrouds significantly suppressed the maximum VIV amplitude, delayed the onset of the VIV and narrowed the lock-on region. The maximum VIV amplitude was suppressed by 90% using the β = 67% screen shroud. To further understand the effect of the shrouds on vortex manipulation, the wake characteristics of the screen shrouded cylinders with β = 37% and 67% were then examined in a wind tunnel using hot-wire anemometers over a streamwise range x* = 5−40. Phase-averaging analysis revealed that the large-scale vortices were not formed until x* = 10 or 20, before which only small-scale vortical structures were identified in the shear layers of the shrouded cylinders, indicating that the screen shrouds successfully delayed the formation of the large-scale vortices. This result was entirely different from the formation of the large-scale structures found in the bare cylinder wake. In addition, the strength of the vortical structures in the former two wakes was much weaker than that in the latter, indicating attenuated large-scale vortices in the screen shrouded cylinder wakes. After the formation of the large-scale structures, the vortices decayed slower in the screen shrouded cylinder wakes than that in the bare cylinder wake.

High-mode vortex-induced vibration of stay cables: monitoring, cause investigation, and mitigation

Herein is described a case study using long-term field monitoring data from a cable-stayed bridge to investigate the cause of high-mode vortex-induced vibration (VIV) observed in stay cables. Wind characteristics and dynamic responses of girders and stay cables were analyzed to investigate two possible vibration sources–interactions with girders and vortex shedding. To this end, a modal decomposition procedure that included automated peak picking and successive band-pass filtration was proposed. These novel steps revealed a relationship between the shedding frequencies of stay cables and corresponding critical wind velocities. The main cause of large-amplitude VIVs was diagnosed using a novel damping identification procedure that consisted of automated modal decomposition, temporal correlation, and optimization-based curve fitting techniques. The damping identification results demonstrated how the modal VIV amplitudes of stay cables have a strong dependency on damping capacity. The effectiveness of Stockbridge dampers in mitigating high-mode cable VIVs was subsequently examined through field application and comparison analysis during a typhoon. The unique interaction between stay cable vibrations and the buffeting response of bridge girders observed during this period was additionally discussed.

Effects of end condition and aspect ratio on vortex-induced vibration of a 5:1 rectangular cylinder

A series of wind tunnel tests were carried out to study the end condition and aspect ratio effects of a sectional model on the vortex-induced vibration (VIV) of a 5:1 rectangular cylinder. Five aspect ratios varying from 9 to 32 as well as eight endplates with different sizes were examined in the tests. Static and elastically mounted sectional models were employed to measure the surface pressure and VIV response of the cylinder, respectively. Sectional fluctuating lift forces, shedding frequency, as well as their spanwise distribution and correlation on the sectional model were obtained and discussed. Results indicated that the aspect ratio had a significant effect on VIV amplitudes, and small aspect ratios tended to remarkably underestimate the VIV amplitudes. There existed an end interference region with a length of 6–8 D, where the sectional lift forces could be, on average, half the value for the non-interference region. Besides, the aspect ratio was positively related to the spanwise correlation of sectional lift forces. Both end condition and VIV had little effect on the length of the end interference region. In the VIV ‘lock-in’ range, with the increasing reduced wind velocity the fluctuating lift force first increased and reached a maximum value earlier than the VIV amplitude, and after that further increase of reduced wind velocity led to decreased fluctuating lift force (toward a value even smaller than that of the stational model). This complicated variation of sectional lift forces implied that vortex shedding was highly nonlinear and self-limiting. Finally, an empirical method based on the test results was explored to account for the influence of aspect ratio on VIV amplitude.

Experimental investigation of the effect of high damping on the VIV energy converter near the free surface

The vortex induced vibration (VIV) energy converter is a novel device to extract hydrokinetic energy from ocean currents. The flow velocity near the sea level is relatively higher, which makes ocean surface currents more exploitable. However, due to the influence from free surface (such as wave impact, etc.), the total system damping of the converter increases rapidly. Therefore, this study focuses on the effect of high damping on the converter near the free surface. The experiments are carried out in a towing tank to measure the VIV responses and energy conversion performance. The VIV energy converter is operated at high damping by changing the load resistor from infinity to 30Ω. Correspondingly, the damping ratio increases from 0.38 to 0.50. The main conclusions are: (1) High damping suppresses the VIV amplitudes. (2) Three typical VIV branches can't be distinguished when at high damping. (3) The VIV frequency increases with damping and approaches the vortex-shedding frequency of a stationary cylinder (Strouhal frequency). (4) When the damping ratio increases from 0.38 to 0.50, the maximum converted power decreases from 1.37W to 0.66W. (5) The optimal efficiency ηVIV = 29% is achieved at the beginning of the VIV region.

Vortex-induced vibration of a flexible rectangular cylinder: Experimental investigation and comparative study of theoretical models

The vortex-induced vibration (VIV) of slender flexible structures is usually estimated based on two-dimensional aerodynamic parameters determined by sectional model wind tunnel tests. Before converting such test results into a prototype flexible structure, many complicated factors, such as the spanwise correlation of aerodynamic force and vibration mode shape, should be considered. In this study, wind tunnel tests of a 5:1 rectangular taut strip model and its sectional model with the same geometry were first conducted to analyze the relationship between the VIV amplitude of the flexible structure and sectional model. The results showed that the taut strip model sustained an approximately 15% higher VIV amplitude than the sectional model, indicating that the VIV amplitude could be underestimated if the sectional model test results were directly used. Next, based on the identified spanwise correlation function of the 5:1 rectangular cylinder, several existing VIV response estimation approaches based on Scanlan's semi-empirical vortex-induced force (VIF) model were examined and compared. Finally, an improved approach was proposed by which the correlation coefficients based on the partial spanwise correlation theory could be approximated with more comprehensive consideration of the spanwise correlation, allowing for a more accurate evaluation of the VIV amplitude for flexible structures.

Incorporation of subcritical Reynolds number into an aerodynamic damping model for vortex-induced vibration of a smooth circular cylinder

Vortex-induced vibration (VIV) of a circular cylinder is known to be affected by the Reynolds number, while this effect has rarely been considered in VIV modeling. This paper attempts to incorporate the Reynolds number into an aerodynamic damping model for simulating the VIV of a circular cylinder with a smooth surface immersed in a smooth flow. Aerodynamic damping parameters within the Reynolds number range of 500 ∼ 33000 (i.e., the TrSL1 and TrSL2 regimes) are identified according to the griffin plots and existing forced vibration experimental data. The model can simulate the peak VIV amplitudes of an elastically supported rigid circular cylinder at different mass-damping parameters in the TrSL1 and TrSL2 regimes. Both experimental results and numerical simulations demonstrate that the peak VIV amplitude of a low-damping cylinder is highly dependent on the Reynolds number, while the dependency is decreased by increasing the mass-damping parameter. The results suggest that the Reynolds number effect is significant in the VIV analysis of a lightly damped cylindrical structure, while the role of Reynolds number seems insignificant for a moderate-damping or high-damping cylindrical structure. For a flexible circular cylinder, the proposed model is expected to predict slightly higher peak VIV amplitudes because the aerodynamic damping effects are overestimated at some segments along its length.

Influence of porous media coatings on flow characteristics and vortex-induced vibration of circular cylinders

The aerodynamic parameters and flow field characteristics of cylinders with and without a porous media coating (PMC) were experimentally investigated in a wind tunnel. This research explored the potential of using a PMC to control vortex-induced vibration (VIV). The PMCs were manufactured with four pores-per-inch values (PPI = 15, 20, 30, and 40) and three depths, (d/D=0.125, 0.25, and 0.5, where d is the depth of the coating and D is the diameter of the bare cylinder). The instantaneous drag and lift forces were measured in static tests. The results showed that all the PMCs could decrease the fluctuation of the forces. The root-mean-square lift force was reduced by up to 98% with a coating of PPI = 15 and d/D=0.5 at Re = 5.2×104. The flow fields were visualized using a particle image velocimetry (PIV) system and analyzed with time-averaged velocity fields, wake velocity profiles, and turbulence kinetic energy distributions. For PMCs with smaller PPI values and greater depths, the wake vortex formed further away from the cylinder. Then the dynamical responses were tested for elastically supported models. Not all the PMCs could suppress the VIV. When PPI < 30, the PMC decreased the VIV amplitude. For each PPI, a greater depth resulted in a lower amplitude. The VIV amplitude for a coated cylinder was reduced to 4% of that for the bare cylinder. When PPI > 30, the PMC enhanced the VIV, with a greater depth resulting in a higher amplitude. When PPI = 30, the PMC could either increase or decrease the VIV amplitude, depending on the depth. The flow fields around the oscillating cylinder were also analyzed to reveal the effect of the PMC on the wake vortex shedding behavior.