Rms Displacement Research Articles

Modelling and Dynamic Analysis of Adaptive Neuro-Fuzzy Inference System-Based Intelligent Control Suspension System for Passenger Rail Vehicles Using Magnetorheological Damper for Improving Ride Index

The ride comfort and safety of passenger rail vehicles depend on the performance of the suspension system in attenuating vibrations induced by track irregularities. This paper investigates the effectiveness of an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based semi-active controlled suspension system using a magnetorheological fluid damper in reducing nonlinear lateral vibrations of a passenger rail vehicle. A complete rail vehicle model is developed, including the carbody, front and rear bogies, and the passive suspension system’s nonlinear stiffness and damping characteristics are considered from experimental data. The passive suspension model is validated through experiments, and an ANFIS-based controller is incorporated with the secondary vertical suspension system to improve ride behavior. Three semi-active suspension strategies are considered under varying speeds and track irregularities, and their effectiveness is compared to the nonlinear passive suspension system in terms of rms acceleration, rms displacement, ride quality, and comfort. The results shows that the ANFIS-based semi-active suspension system with a magnetorheological fluid damper outperforms the passive suspension system and semi-active strategies in all tested conditions. There is a reduction in rms acceleration by approximately 11.11% to 23.64% and rms displacement by about 5.36% to 32.06%. Moreover, it significantly improves ride quality (9.20% to 31.02%) and comfort (9.96% to 31.50%). The rms acceleration and displacement are reduced, and the Sperling ride index and Percentage Reduction Index values demonstrate that the ANFIS-based semi-active suspension effectively minimizes the impact of rail irregularities and vibrations, resulting in a significant gain in ride quality and passenger comfort.

Study on a three-dimensional variable-stiffness TMD for mitigating bi-directional vibration of monopile offshore wind turbines

Bi-directional vibrations of offshore wind turbine (OWT) exist due to the misalignment of wind and wave loadings, which induces the structural fatigue failure. At present, monopile offshore wind turbine (MOWT) is widest utilized in worldwide, which is adopted as the research objective in this study. A novel semi-active three-dimensional magnetorheological elastomer (MRE) based tuned mass damper is proposed to suppress a MOWT bi-directional vibration under misaligned wind, wave, seismic loadings. The proposed MRE-based TMD is installed in the nacelle, which presents dual-directional controllable stiffness properties. Its nonlinear behavior is depicted by bi-lateral Bouc-Wen model. A semi-active control framework is developed, in which current-dependent stiffness of MRE-based TMD is tuned for tracing real-time dominant frequency of the MOWT. The numerical results reveal that MRE-based TMD can effectively attenuate the bi-directional dynamic responses of MOWT under various operation conditions. Additionally, the semi-active MRE-based TMD outperforms passive TMD in reducing the peak and RMS displacement of the tower top in both fore-aft (FA) and side-side (SS) directions, especially in operational state. MRE-based TMD also presents strong robustness under the condition of structural stiffness degradation.

Melting of two-dimensional electron clusters in a magnetic field

The molecular dynamics method is applied to simulate the behavior of two-dimensional electron clusters of various shapes containing about 100 particles. The influence of a magnetic field on the effects of ordering and disordering (melting) in such clusters is studied. The field dependence of the rms displacements of particles in clusters is determined, and the trajectories of electron motion are found as functions of temperature and magnetic field. Ordering and disordering in clusters were fixed by the appearance of characteristic features in the rms displacements of electrons in the system. Hysteresis was observed in the field dependence of these displacements at a fixed temperature. The obtained data are compared with the results for root-mean-square displacements of electrons in a two-dimensional electronic infinite crystal. The qualitative agreement was found with these results; at the same time, the field dependence of root-mean-square displacements in an unbounded crystal is much weaker than in the clusters under study. The influence of the cluster shape on ordering transitions is studied, and it is found that the shape of a defect-free cluster does not affect the transition conditions. The distribution of electron velocities in clusters is studied for various magnetic fields.

Development of a Time-Domain Simulation Code for Cross-Flow Vortex-Induced Vibrations of a Slender Structure with Current Using the Synchronization Model

In this paper, the numerical analysis method for the cross-flow vortex-induced vibration (CF VIV) analysis based on the proposed procedure for CF VIV analysis of slender structures is developed. In order to consider the changes in the incoming flow according to the static configuration of the slender structures due to the current, the proposed procedure has three stages. A slender structure is modeled as the lumped-mass line, and the dynamic relaxation method known as the numerical technique for a slender structure with large geometric nonlinearity is applied in the static analysis. The comparison studies with a commercial program are carried out to validate the developed code. The vortex-induced force on slender structures is considered with the synchronization model. To verify the developed CF VIV analysis procedure and numerical method for a slender structure, VIV analysis of the tensioned flexible risers under a uniform and shear current is performed. The simulated results of CF RMS displacement show good agreement with the results of the model test It is found that a tensioned riser vibrates with one dominant frequency in resonance with the nth mode, even though multi-frequencies components of the vortex shedding along the riser due to the shear current occurs.

Spring-controlled modified tuned liquid column ball damper for vibration mitigation of structures

Passive-tuned mass and liquid dampers are a popular choice among structural vibration control systems for being reliable, economical, and easy to implement. Therefore, meticulous and rigorous efforts have been devoted by researchers to develop various configurations of these systems for the enhancement of vibration mitigation efficiency, architectural flexibility, and versatility of application. However, experimental validation of these configurations has always been a challenging task for researchers. In this paper, an experimental validation has been conducted for the fused versions of tuned mass and liquid column damper known as tuned liquid column ball spring sliding damper (TLCBSSD) and tuned liquid column ball spring rolling damper (TLCBSRD). In these modified versions the ball inside the horizontal section of the damper has been attached with a spring. A series of shake table tests have been performed on 4 story frame structure under harmonic and seismic excitations to evaluate the vibration control performance of proposed dampers. The damper was placed on the top story of each experimental setup. A detailed discussion and analysis have been done based on the RMS acceleration, displacement, and inter-story drift of each story subjected to harmonic and seismic loadings for all test cases. Both proposed systems reduced the RMS response of the structure at resonant and seismic excitations. The vibration response has been significantly reduced for both systems, compared to reference TLCBD, at harmonic loadings including frequencies 0.65 Hz, 1.17 Hz, 1.30 Hz, 1.43 Hz, and 1.95 Hz, especially at resonant loading. Moreover, a detailed comparison between the normalized frequency responses from experimental and numerical studies has been presented. Overall, the proposed fused versions of tuned mass and liquid column ball systems have outperformed the reference TLCBD.

Performance of Structure Equipped AP‐TMD Compared with MTMD, ATMD, and PTMD against Earthquake Using Genetic Fuzzy Algorithm

During the past years, different control devices have been introduced and used to reduce the response of structures. This article presents the performance of active‐passive tuned mass dampers (AP‐TMDs) in the reduction of structural responses and a comparison between the uses of different controllers, including tuned mass damper (TMD), active tuned mass damper (ATMD), and multituned mass damper (MTMD). Analyzing and modeling the structure under four near‐ and far‐field earthquakes are performed in MATLAB and SIMULINK. Finally, the responses of controlled and uncontrolled structures equipped with these controllers are investigated. Fuzzy and genetic‐based fuzzy logic controllers are used to determine the control force of ATMD and AP‐TMD, respectively. In order to compare the performance of the dampers, the mass ratio of TMDs is fixed in all cases and is taken to be 5%. Damping of the structure is considered equal to 5%. The frequency and damping ratio of TMDs with maximum and RMS displacement optimization criteria are obtained. The mass ratio of TMDs in controlled structures with MTMD and AP‐TMD is calculated by numerical analysis. It can be inferred that using control force affects response reduction in both ATMD and AP‐TMD controllers significantly. In addition, using AP‐TMD can bring the merits of both passive and active systems by providing active control and reducing power requirements for control forces. All controllers are recommended for structural control although AP‐TMD reduced maximum and RMS displacement by about 50% in the best case, which has better performance than others. On the other hand, ATMD decreased RMS acceleration by 37.5% on average in four earthquakes compared to the uncontrolled structure.

Pareto Optimal Design of the Tuned Mass Damper

Strong vibrations due to wind induced loads and earthquakes have undesirable effects on tall buildings and long-span bridges, and can cause discomfort, dizziness and anxiety for their occupants and users. The Single Tuned Mass Damper (STMD) is vibration control device used to mitigate strong motion. This study investigated the STMD from the perspective of multi-objective optimization. The main goal was to identify and characterize the Pareto set of optimal STMD parameters in terms of damping and stiffness. The optimization was performed using a multi-objective optimization algorithm based on gradient descent and successive bisecting of the search domain. <img src=image/14825382_01.gif> and <img src=image/14825382_02.gif> norms of the transfer matrices for structural displacement and acceleration were considered as design objectives. We found that for peak response reduction, irrespective of the excitation type, structural damping and STMD mass ratio, the Pareto set was linear and extended mainly in the direction of frequency ratio, while the damping ratio varied marginally within the set. For RMS displacement and peak acceleration minimization, the Pareto set was composed of two segments. Additionally, in all instances, the Pareto set was found to be bounded by the single-objective optimal STMDs for the considered design objectives. The implications of the findings were discussed and approximations of the Pareto optimal STMD were suggested.

Mechanical Design and Control System Development of a Rehabilitation Robotic System for Walking With Arm Swing.

Background: Interlimb neural coupling implies that arm swing should be included during gait training to improve rehabilitation outcomes. We previously developed several systems for production of walking with arm swing, but the reaction forces on the foot sole during usage of the systems were not satisfactory and there was potential to improve control system performance. This work aimed to design and technically evaluate a novel system for producing walking with synchronised arm and leg movement and with dynamic force loading on the foot soles.Methods: The robotic system included a passive curved treadmill and a trunk frame, upon which the rigs for the upper and lower limbs were mounted. Ten actuators and servocontrollers with EtherCAT communication protocol controlled the bilateral shoulder, elbow, hip, knee and ankle joints. Impedance control algorithms were developed and ran in an industrial PC. Flexible pressure sensors recorded the plantar forces on the foot soles. The criteria of implementation and responsiveness were used to formally evaluate the technical feasibility of the system.Results: Using impedance algorithms, the system produced synchronous walking with arm swing on the curved treadmill, with mean RMS angular tracking error <2° in the 10 joint profiles. The foot trajectories relative to the hip presented similar shapes to those during normal gait, with mean RMS displacement error <1.5 cm. A force pattern that started at the heel and finished at the forefoot was observed during walking using the system, which was similar to the pattern from overground walking.Conclusion: The robotic system produced walking-like kinematics in the 10 joints and in the foot trajectories. Integrated with the curved treadmill, the system also produced walking-like force patterns on the foot soles. The system is considered feasible as far as implementation and responsiveness are concerned. Future work will focus on improvement of the mechanical system for future clinical application.

Analyses of the Tympanic Membrane Impulse Response Measured with High-Speed Holography

The Tympanic Membrane (TM) transforms acoustic energy to ossicular vibration. The shape and the displacement of the TM play an important role in this process. We developed a High-speed Digital Holography (HDH) system to measure the shape and transient displacements of the TM induced by acoustic clicks. The displacements were further normalized by the measured shape to derive surface normal displacements at over 100,000 points on the TM surface. Frequency and impulse response analyses were performed at each TM point, which enable us to describe 2D surface maps of four new TM mechanical parameters. From frequency domain analyses, we describe the (i) dominant frequencies of the displacement per sound pressure based on Frequency Response Function (FRF) at each surface point. From time domain analyses, we describe the (ii) rising time, (iii) exponential decay time, and the (iv) root-mean-square (rms) displacement of the TM based on Impulse Response Function (IRF) at each surface point. The resultant 2D maps show that a majority of the TM surface has a dominant frequency of around 1.5 kHz. The rising times suggest that much of the TM surface is set into motion within 50 µs of an impulsive stimulus. The maps of the exponential decay time of the IRF illustrate spatial variations in damping, the least known TM mechanical property. The damping ratios at locations with varied dominant frequencies are quantified and compared.

Vibration control of offshore wind turbine under multiple hazards using single variable-stiffness tuned mass damper

With high flexibility and low damping, offshore wind turbines (OWTs) are prone to external vibrations such as wind, wave and earthquake, either attacked individually or as combined loading cases. This study proposes a semi-active variable-stiffness tuned mass damper (VSTMD) with magnetorheological elastomer (MRE) materials to mitigate undesired dynamic responses of OWT. A jacket supported OWT with MRE-TMD installed at the top of the tower is adopted as an example to demonstrate the effectiveness of the proposed design under multiple hazards. A semi-active frequency tracing algorithm is proposed through which the current-dependent stiffness of MRE-TMD is controlled by tracking the acceleration of OWT tower. The numerical results demonstrate that the semi-active MRE-TMD can effectively attenuate the dynamic responses of OWT under multi-hazard loadings, and it outperforms the passive TMD in reducing the peak and RMS displacements of tower structure. Robustness analysis of semi-active MRE-TMD is also validated by considering OWT sudden loss of partial stiffness under multiple-loadings.

Experimental study on characteristics of vortex-induced vibration of a twin-box girder and damping effects

To investigate the characteristics of vortex-induced vibration (VIV) of the twin-box girder, we carried out the VIV wind tunnel tests. The VIV of the twin-box girder occurs in the range of 4.680≤Ur≤6.113, with the maximum dimensionless VIV displacement RMS(y)/D=0.03308 at reduced velocity at Ur=5.949. It is interesting that the VIV suddenly disappears at Ur=6.276 at the loading stage, and the large amplitude VIV does not occur at the unloading stage, which indicates that the vibration trajectory with the variation of reduced wind velocity shows significant asymmetry characteristic. In the lock-in region, as the aerodynamic lift force increases, both the phase lag and the VIV displacement show an increasing tendency with the reduced velocity. Flow visualization results show that strong alternately shedding vortex generates around the gap during the VIV. Under the effects of the vortex in the gap, the size of the separation bubble increases with the increase of vibration amplitude, and the wake width becomes wider. As the damping ratio increases, the amplitude of VIV displacement shows a decreasing tendency, the lock-in region becomes narrower and the reduced velocity corresponding to the max VIV displacement decreases. Moreover, the maximum RMS displacement of vertical VIV decays exponentially as the damping ratio increases.

Performance comparison of particle tracking velocimetry (PTV) and particle image velocimetry (PIV) with long-exposure particle streaks

Particle tracking velocimetry (PTV) and particle image velocimetry (PIV) are popular experimental methods to quantitatively measure flow fields. In many practical applications, hardware limitations result in longer exposure times, causing particle images to elongate into particle streak images. In this study, the performances of PTV and PIV in relation to particle streak images are evaluated systematically by means of both synthetic and experimental images. For the synthetic images, particle streak images are created via the integration over time of the standard Gaussian approximation of particle images, plus the effects of exposure time, and parameters such as particle image diameter, intensity, and density were investigated in terms of the velocity fields of a 1D uniform flow and the rotational 2D Hill’s vortex. The results show that PTV performs well for short exposure times, and its peak-finding criteria can be verified for nondimensional exposure times up to 10. As the increases from 10 to 70, the reliability of the PTV algorithm drops significantly, while the yield drops only slightly. Longer exposure times cause an increase in the number of RMS displacement errors; the PTV algorithm is more likely to fail when particle diameter, image intensity and particle density are larger. The displacement error of PTV RMS ranges from 0.064 pixels to 0.157 pixels. In comparison to PTV, PIV is more robust in relation to streak images with long-exposure times, and not sensitive to the effects of particle image diameter and intensity. The RMS dispersion errors for PIV range from 0.015 pixels to 0.316 pixels. A comparison of the RMS displacement errors exhibited by PIV and PTV shows that where the seeding of particles is not an issue, PIV is more robust, and can handle long-exposure streak images. The results of experimental streak images show that PIV produces lower RMS dispersion error values at low Reynolds numbers, whereas it produces more significant errors for high Reynolds numbers. At regions of low seeding density, PTV can resolve local fluid motions with superior accuracy, but it is vulnerable to high exposure time. Based on these results, where a longer exposure time is a requirement for an application, the use of PIV is recommended, by virtue of its robustness to image streaking, provided that a good seeding and high particle image density are available. For applications such as some microscale flows or flows with separation or recirculation regions, PTV is more capable of fulfilling their requirements.

Effect of Surface Modification of a Titanium Alloy by Copper Ions on the Structure and Properties of the Substrate-Coating Composition

To improve the strength properties, adhesion, and the thermal cycling resistance of ceramic coatings, the titanium alloy surface was modified with copper ions under different processing times. It is found that at the maximum processing time, the thickness of the alloyed layer reaches 12 μm. It is shown that the modified layer has a multiphase structure in addition to the main α and β–titanium phases with the intermetallic compounds of the Ti-Cu system. The parameters of the fine structure of the material are investigated by the X-ray diffraction analysis. It has been found that when the surface of the titanium alloy is modified, depletion occurs in the main alloying elements, such as aluminum and vanadium, the crystal lattice parameter increases, the root-mean-square (rms) displacements of the atoms decrease, and the macrostresses of compression arise. A multilevel micro- and nanoporous nanocrystalline structure occurs, which leads to an increase in the adhesion and the thermal cyclic resistance of the ceramic coating based on Si-Al-N.

Vibration Control of Marine Top Tensioned Riser with a Single Tuned Mass Damper

The study of the Tuned Mass Damper (TMD) on Top Tensioned Risers (TTRs) through the application of numerical analysis is of great significance for marine engineering. However, to the best knowledge of the author, neither the in-field riser data nor the ocean current data used in published papers were from engineering design, so the research results provide limited guidance to the actual engineering project. In view of this problem, this study designed a single TMD to suppress the vibration of the engineering TTR under the action of the actual ocean current. First, the dynamic model of a riser-TMD system was established, and the modal superposition method was used to calculate the model. The non-resonant modal method of the flexible structure was used to design the TMD parameters for the engineering riser. Ocean current loading in the South China Sea was then applied to the riser. The vibration of the riser without and with TMD was compared. The result showed that TMD could effectively reduce the vibration response of the riser. When compared without TMD, the maximum value of displacement envelope and the RMS displacement were reduced by 26.70% and 17.83% in the in-line direction, respectively. Moreover, compared to without TMD, the maximum value of displacement envelope and RMS displacement were decreased by 17.01% and 22.05% in the cross-flow direction, respectively. In the in-line direction, the installation position of TMD on the riser was not sensitive to the effect of the displacement response; meanwhile, in the cross-flow direction the installation position of TMD on the riser was more sensitive to the effect of the displacement response.

Nonlinear dynamic response analysis of marine risers under non-uniform combined unsteady flows

Considering the top-end platform surge induced by periodic wave, the encountered flow field of marine risers under the actual marine environment is approximate to a combined sheared and sheared-oscillatory flow, which is non-uniform in both time and spatial domains. A published time domain force-decomposition model is proposed to predict the riser's nonlinear dynamic response under non-uniform combined unsteady flows. A 90 m flexible riser is chosen as the simulated object, and a large amount of the combined flow cases with different oscillation periods and combined ratios are designed. With the fundamental study on a steady sheared flow case, the structural dynamic response characteristics under non-uniform combined flows are investigated systematically. The overall dynamic response presents travel wave pattern, and the high-frequency response is easier to be excited for the riser's top and bottom segments. Some time-sharing response characteristics like amplitude modulation, frequency transition and mode jumps are captured, and they are affected by the flow field parameters significantly. Under the long oscillation period cases, the intermittent dynamic response follows the accordant periodicity with the current velocity. While under the short oscillation period cases, the unstable structural vibration occurs persistently without clear regularity. The combined ratio also influences the RMS displacement, excited frequency bandwidth and travel wave propagation velocity evidently. Associated with VIV mechanism analysis, the individual response characteristics under different flow field parameter combinations are explained reasonably.

Influence of He-ion irradiation of ceramic AlN

The paper presents results of studying the effect of irradiation of low-energy helium ions on structural properties and morphology of AlN polycrystalline ceramics. On the basis of X-ray diffraction patterns, dependences of the change in stresses in the structures of types I and II, as well as the magnitude of atoms displacements from lattice sites as a result of irradiation, were determined. According to the data obtained, with small irradiation fluences, characteristic of a low concentration of implanted helium ions and defects in the structure, the change in the magnitude of displacements and stresses is insignificant. An increase in fluence above 1017 ion/cm2 leads to a drastic change in distortions and deformations in the structure, as well as to an increase in the value of rms displacement of atoms from the lattice sites. It has been established that the greatest decrease in microhardness and resistance to stress is observed for samples irradiated with fluences above 1017 ions/cm2, which are characterized by the formation of a large concentration of defects and impurity inclusions. The decrease in microhardness is due to the formation of regions of disorder and helium bubbles, as well as a decrease in the density of ceramics and the degree of crystallinity.

An experimental study on flow-induced vibration of three and four side-by-side long flexible cylinders

Multiple flexible cylinder structures, such as marine risers and cables, are key equipment for the production and transportation of oil and gas in offshore engineering. Till now, little information is available on flow-induced vibration (FIV) of more than two side-by-side flexible cylinders. Though some FIV characteristics of multiple flexible cylinders can be predicted based on the knowledge of two flexible cylinders undergoing vortex shedding, there are still some other characteristics that remain unrevealed, which require further experimental investigations on more than two flexible cylinders. In this paper, the FIV of three- and four-cylinder system in a side-by-side arrangement with a distance of 6.0D between cylinder centerlines was experimentally studied in a towing tank. The flexible cylinder models with mass ratio of 1.90 and aspect ratio of 350 were mounted horizontally and towed along the tank to simulate the uniform flow. The towing velocity ranged from 0.05 to 1.0 m/s and the corresponding Reynolds number varied from 800 to 16000. The experimental results were discussed in detail, including the maximum RMS displacement amplitudes, dominant frequencies, dominant modes, time-varying displacements at the measurement points, displacement response spectra, spanwise evolutions of the RMS displacement and space-time varying displacement contour. It can be found that the multi-mode response characteristics of the three-cylinder system in a side-by-side arrangement are obviously distinct from those of the four-cylinder system due to the effect of complex wake flow behind the cylinders. These findings are very meaningful for the design of a group of flexible cylinders in engineering applications.

Comparing ADCP data collected during a seismic survey off the coast of Newfoundland with analysis data from the CONCEPTS operational ocean model

ABSTRACTOceanographic data collected during seismic surveys have potential to provide a significant resource for oceanographic research. In this paper, acoustic Doppler current profiler (ADCP) data collected during the Chevron 2011 North East Grand Banks survey are analysed. The survey took place in a 32,000-km2 area in the North East Grand banks, Orphan Basin region in water depths ranging from 100 to 1500 m and notably, the survey area is crossed by the offshore branch of the Labrador current. Data quality is evaluated by comparing velocities before and after ship turns where we find no significant velocity bias. The ADCP data are compared to data products from the CONCEPTS global ice ocean prediction system operational ocean model. ADCP data and model output agree qualitatively with the model reproducing the long-term fluctuations seen in the data. At higher frequencies between 0.3 and 2.0 cycles/day, the model tends to under-represent the current velocities by about 20%, but the spectral peak associated with inertial oscillations is well resolved. Comparisons of drift track predictions based on the ADCP observations and model output show rms displacement differences of 8 km after 24 h and ∼10 km separations for drift tracks with length under 50 km.

Vibration control of offshore wind turbine using RSM and PSO-optimized Stockbridge damper under the earthquakes

In this inquisition, a passive damper namely Stockbridge Damper (SBD) has been introduced to the field of vibration control of Offshore Wind Turbine (OWT) to reduce the earthquake excitations. The dynamic responses of the structure have been analyzed for three recorded earthquakes and the responses have been assessed. To find an optimum SBD, the parameters of damper have been optimized using Response Surface Methodology (RSM) based on Box-Behnken Design (BBD) and Particle Swarm Optimization (PSO). The influence of the design variables of SBD such as the diameter of messenger cable, the length of messenger cable and logarithmic decrement of the damping has been investigated through response variables such as maximum displacement, RMS displacement and frequency amplitude of structure under an artificially generated white noise. After that, the structure with optimized and non-optimized damper has been analyzed with under the same earthquakes. Moreover, the comparative results show that the structure with optimized damper is 11.78%, 18.71%, 11.6% and 7.77%, 7.01%, 10.23% more effective than the structure with non-optimized damper with respect to the displacement and frequency response under the earthquakes. The results show that the SBD can obviously affect the characteristics of the vibration of the OWT and RSM based on BBD and PSO approach can provide an optimum damper.

Analysis on multi-frequency vortex-induced vibration and mode competition of flexible deep-ocean riser in sheared fluid fields

Multi-frequency vortex-induced vibration of flexible riser in lineally sheared fluid fields with different shearing parameters is explored by using the numerical approach. By combining the finite element method with a hydrodynamic model, the approach can consider mode competition based on modal energy and can carry out nonlinearly simultaneously dynamic response in time domain. Our analysis shows that multi-frequency VIV may occur both in non-uniform and uniform fluid fields. And, the behaviors of multi-frequency VIV are different from single-frequency VIV. Because several modes are involved and compete with each other, and consequently the determination of modal excitation region become more complicated. As the towing speed (or the shearing parameter) increases in sheared flow, the average RMS displacement does not regularly rise (or drop), but slightly fluctuates owing to changes of the participating mode and its excitation region. On the other hand, the average RMS stress gradually rises owing to higher-order modes being included. Moreover, it is found that the dominant frequency distributing along structural span significantly changes with the towing speed, and the length of the first dominant frequency gets smaller due to larger shearing parameter along with more intense competition between the participating modes.