Vibration Cycle Research Articles

Development of a space-compatible packaging system for an integrated monolithic ultra-stable optical reference.

We report the development of a space-compatible packaging system for an integrated monolithic ultra-stable optical reference toward China's next-generation geodesy mission with low orbit satellite-to-satellite tracking. Building on our previous work, we optimized the mounting structure and thermal insulation mechanism using the finite element method. The comprehensive simulation results demonstrated the robustness of the entire packaging system with enough margins to withstand severe launch loads and maintain an ultra-high geometric cavity length stability. A long-term prediction of the vacuum maintenance around the cavity during in-orbit operation was conducted. An engineering prototype, within which an integrated monolithic optical reference has been mounted, was built based on our optimized design, and it has successfully passed typical aerospace environmental tests, including sinusoidal vibration (∼10g, 10-100Hz), random vibration (∼0.045g2/Hz, 10-2000Hz), and thermal cycling (0-45, 3 °C/min, lasting for 90h). The experimental thermal time constant of the prototype exceeded 9.5 × 104 s, enabling a temperature stability of 1.1 × 10-6K/Hz1/2 at 10 mHz on the optical cavity, with external active temperature control. The design is also suitable and useful for laboratory and terrestrial applications.

Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.

Identification of amplitude-dependent aerodynamic damping from free vibration data using iterative unscented kalman filter

This study presents an innovative approach employing an iterative Unscented Kalman Filter (IUKF) for the identification of amplitude-dependent nonlinear aerodynamic damping using wind tunnel free vibration data. The wind-structure interaction system is represented as a single-degree-of-freedom system, with the amplitude-dependent aerodynamic damping modeled as a polynomial function of structural displacement and velocity. The augmented state variables, encompassing structural vibration frequency and polynomial coefficients for aerodynamic damping, are concurrently estimated from free vibration data using the UKF technique. To enhance the robustness of the identification results against variations in initial conditions, the UKF is applied iteratively by assigning the estimated polynomial coefficients as new initial values for the state variables. Validation of the IUKF-based method is performed through a numerical example featuring a typical bridge deck sectional model, as well as experimental data from two spring-suspended sectional models experiencing vertical vortex-induced vibration (VIV) and torsional post-flutter limit cycle oscillation. The feasibility of identifying amplitude-dependent aerodynamic damping for amplitude range not covered by the displacement signal is examined.

Results of the cyclic triaxial testing on mechanically-biologically treated waste.

Accurate assessment of the dynamic strength characteristics of mechanically-biologically treated (MBT) waste is crucial for the construction and safe operation of landfill sites. Herein, samples of MBT waste from the Hangzhou Tianziling landfill were collected and subjected to consolidated undrained cyclic triaxial tests under four confinement levels and six cyclic stress ratios (CSRs). Under cyclic loading, the MBT waste exhibited a critical CSR. If the CSR exceeds the critical value, the MBT waste specimen rapidly undergoes deformation and failure. Dynamic strength of MBT waste decreases with an increase in the number of cyclic vibrations and increases with an increase in confining pressure. Considering the influence of cyclic vibrations and confining pressure, a formula for dynamic strength in terms of cyclic vibrations and confining pressure has been established. The dynamic shear strength parameter ranges for MBT waste were obtained under different seismic magnitudes. We compared the dynamic and static shear strength parameters of MBT waste and municipal solid waste. These study findings can serve as a reference for the dynamic stability analysis of MBT waste landfills.

Chip breakage in silk microfibre production using elliptical vibration turning

To overcome the precision limitation and environmental impact of current chemical-based production methods for manufacturing silk microfibres used for targeted drug delivery, this paper presents a high-precision, scalable, eco-friendly mechanical machining approach to produce such microfibres in the form of discontinuous chips obtained through elliptical vibration turning of silk fibroin film using a diamond tool. The length and waist width of fabricated microfibres can be precisely controlled. As each vibration cycle will produce one silk microfibre, complete and deterministic chip breakage becomes an essential and challenging task in this approach due to its unique two-phase structure. Thus, the hybrid FE-SPH numerical simulations and machining experiments were conducted to gain a pioneering and in-depth exploration of the chip-breaking mechanism in this process. It was found that applying a low depth ratio (ratio of the nominal depth of cut to the tool path vertical amplitude) and a high horizontal speed ratio (the nominal cutting speed versus the critical workpiece velocity) could effectively reduce the average tool velocity angle (the angle from the deepest cut to the tool exit point along the cutting direction). A smaller angle would enhance the diamond tool's shearing action and led to the reduction of hydrostatic pressure in the cutting zone and a consequent decrease in the ductility of silk fibroin due to its unique structure dominated by beta-sheet crystallites. The above adjustments collectively facilitated chip breakage. This paper, therefore, established a governing rule for the controlled and repeatable formation of microfibres based on the average tool velocity angle for the first time and revealed that the cutting chips would undergo complete and deterministic breakages once the angle approached below 22.6°. On this basis, the high-precision and scalable manufacturing of silk microfibres with precisely controllable length and waist width was ultimately achieved.

Transportation of Objects on an Inclined Plane Oscillating in the Longitudinal Direction Applying Dynamic Dry Friction Manipulations

A transportation system requires an asymmetry to achieve objects’ motion on an oscillating surface. Transportation methods based on vibrational techniques usually employ different types of asymmetries, such as temporal (time) asymmetry, kinematic asymmetry, wave asymmetry or power asymmetry. However, transporting an object on an inclined angle requires a relatively high net frictional force over each period of vibrational cycles due to the gravitational potential energy exerted on the object. This paper investigates the transportation of an object upward on an inclined plane that harmonically oscillates in its longitudinal direction. The novelty of this research is attributed to the upward motion of the object on the inclined plane, which is achieved by creating an additional asymmetry of the system through dry friction dynamic manipulations. For this reason, periodic dynamic dry friction manipulations have been employed to create the asymmetry of frictional conditions, resulting in a net frictional force that outweighs the gravitational force. A mathematical model has been developed using the Lagrange method, which describes the moving object’s motion. Moreover, the theoretical findings and results confirmed that the object’s velocity and direction can be controlled by dynamic dry friction manipulations. To demonstrate the technical feasibility of the proposed method, an experimental investigation was carried out where the results demonstrated that the control parameters significantly influence the characteristics of the directional motion of the moving object. This transportation method is beneficial for various modern industries engaged in transportation and manipulation tasks with objects spanning a broad range of sizes, including those operating at small scales for applications in lab-on-a-chip technology, micro-assembly lines, micro-feeder systems and other delicate component manipulation systems. The presented research advances the classical theories of vibrational transportation on inclined surfaces.

Theoretical and experimental investigation of ultrasonic cutting kinematics and its effect on chip formation and surface generation in high-frequency ultrasonic vibration-assisted diamond cutting

Ultrasonic vibration-assisted cutting (UVAC) is regarded as a feasible technology to machine difficult-to-cut materials. High-frequency ultrasonic vibration-assisted cutting (HFUVAC), with a working frequency of more than low and medium frequency (20–60 kHz), has been reported to improve material machinability and prolong tool life. This paper presents a comprehensive investigation of the ultrasonic cutting kinematics and the generated chip/surface formation process in HFUVAC of a 316l stainless steel workpiece. First, the ultrasonic cutting kinematics was analyzed and verified by comparing the experimental and theoretical surface texture under different nominal cutting speeds. Based on the ultrasonic cutting kinematics and the simulated strain/stress distributions, the chip and surface formation between conventional cutting (CC) and HFUVAC was analyzed. More importantly, the incremental cutting mode was defined when the cutting stroke, namely the effective cutting length in one vibration cycle was less than 800 nm. The results show that in the incremental cutting mode, defect-free surface was achieved due to suppressed large deformation and friction action. Finally, HFUVAC of the sinusoidal microstructure was performed under the incremental cutting mode, achieving optical requirements with nanometer-scale surface roughness and submicrometric form accuracy, which validates the technical feasibility in HFUVAC of micro-structured surfaces.

An abdominal vibration combined with walking exercise (AVCWE) program for older patients with constipation: Development and feasibility study.

Older patients with constipation are at higher risk for inadequate bowel preparation, but there are currently no targeted strategies. This study aims to develop an abdominal vibration combined with walking exercise (AVCWE) program and assess its feasibility among older patients with constipation. Phase I: Using the Delphi technique, eight experts across three professional fields were consulted to develop the AVCWE program. The experts evaluated and provided recommendations on demonstration videos and detailed descriptions of the preliminary protocol. Phase II: A single-arm feasibility study of the AVCWE program was conducted on 30 older patients with constipation undergoing colonoscopy at a tertiary hospital in China. A 10-point exercise program evaluation form and several open-ended questions were used to gather feedback from participants regarding the program. In both phases, content analysis was used to critically analyze and summarize qualitative suggestions for protocol modifications. Based on feedback from the expert panel, the AVCWE program developed in Phase I included two procedures during laxative ingestion: at least 5,500 steps of walking exercise and two cycles of moderate-intensity abdominal vibration (each cycle consisted of 10 min of vibration and 10 min of rest). The feasibility study in Phase II showed high positive patient feedback scores for the program, ranging from 9.07 ± 0.74 to 9.73 ± 0.52. The AVCWE program was developed by eight multidisciplinary experts and was well accepted by 30 older patients with constipation. Study participants believed that this program was simple, safe, appropriate, and helpful for their bowel preparation. The findings of this study may provide valuable information for optimizing bowel preparation in older patients with constipation.

Fluid–structure interaction simulation and optical fibre stress analysis of submarine cables in vortex‐induced vibration

AbstractUnder the current scouring, submarine cables are prone to be exposed, suspended, and even vortex‐induced vibration (VIV), threatening their mechanical and electrical properties. In this contribution, a finite element simulation model of 110‐kV single‐core optical fibre composite submarine cable is established. The natural frequency and resonant frequency of the model are obtained through wet mode analysis and harmonic response analysis. Then the VIV is simulated by the fluid–structure coupling method. Moreover, the stress extraction method of the torsional optical fibre position under the VIV is proposed. The results show that when the reduced speed is 2.57, the submarine cable appears beating vibration, which is composed of two vibrations with similar frequencies. When the reduced speed is 7.08, the vibration frequency is about 7.813 Hz, causing a rapid increase in vibration amplitude. The stress distribution of the torsional optical fibre presents a mirror image relationship at two moments separated by half a vibration cycle. Also, the frequency of stress change is the same as the frequency of VIV, which can judge whether the VIV occurs. The VIV range and position can be determined by the location where the stress changes the most.

Stability Deterioration Analysis of Toppling Dangerous Rock Mass under the Combined Effect of Vibration and Freeze-Thaw Cycles

To investigate the degree of stability deterioration in toppling dangerous rock mass under different action times, firstly, the vibration load generated by train travel in a single action and its decay law were studied, and the theoretical relational equation of rock strength deterioration under the action of vibration loading was obtained by analyzing the increase in half axle expansion of micro fissures inside the rock. Secondly, the freezing stress of the microfissures was determined according to the rock freezing and swelling theory, and the theoretical relational equation of rock strength deterioration under the action of freeze-thaw cycles was obtained by integrating the rock confinement and moisture migration conditions of the fissures wall. The stability coefficient of the toppling dangerous rock mass exhibited a rapid and then slow decreasing trend with increasing number of actions, which was non-linearly negatively correlated with the train running speed and the initial porosity of the rock, and non-linearly positively correlated with the freezing temperature. Controlling the freezing temperature and initial porosity of rock can significantly reduce the degree of deterioration in the stability of dangerous rock mass.

Fast texturing of micron grating on curved metallic surfaces using bending-torsional-coupled rotary ultrasonic side milling

Structural coloration by texturing micron gratings has been regarded as a promising approach for anticounterfeiting and functional decoration. However, the fabrication of micron gratings on curved surfaces is still challenging, restricting the application of structural colors. Taking advantage of the superior capacity of milling process in the machining of curved surfaces, this study proposes a novel texturing method for micron grating on curved surfaces by adopting bending-torsional-coupled rotary ultrasonic side milling (BTC-RUSM). The generation of gratings is governed by a “cutting and microforming combined process” in each vibration cycle induced by the bending-torsional-coupled vibration of the tool. The gratings with a spacing of 0.81 μm to 3.55 μm, controlled by the spindle rotation speed, are successfully fabricated. Structural coloration with colorful characters has been achieved on the curved surface.

Elliptical vibration chiseling: a novel process for texturing ultra-high-aspect-ratio microstructures on the metallic surface

Highlights Elliptical vibration chiseling is proposed based on a game-changing process principle for the high-efficient texturing of ultrahigh-aspect-ratio surface microstructures. Uniformed microstructures with an aspect ratio of 2–12 in the spacing scale of 1–10 μm have been successfully fabricated using elliptical vibration chiseling. The developed process model of elliptical vibration chiseling has been verified by the measured results of the microstructures’ geometric parameters. An inclined elliptical trajectory of tool vibration is more suitable for elliptical vibration chiseling than the standard elliptical trajectory. The deterministic process effects on the surface generation of microstructure in elliptical vibration chiseling have been demonstrated.

Study on mechanism of VIV causing limited amplitude vibration through LES for a 4:1 rectangular cylinder

Vortex-induced vibration (VIV) is characterized as a phenomenon of limited amplitude vibration. Understanding the basic nature and underlying mechanism of VIV is necessary for predicting the vibration amplitude. In this study, using Large Eddy Simulation (LES) of forced vibration, a detailed investigation of the flow pattern and wind load during VIV of a 4:1 rectangular cylinder is conducted. The results indicate that both vibration amplitude (y0/D) and wind speed (UR) significantly influence the flow pattern and wind load. Notably, an increase in vibration amplitude leads to a predominance of motion-induced force and a corresponding amplification of the fluctuating lift coefficient. Additionally, a decrease in the phase difference between lift force and displacement is observed, establishing this phase difference as a critical parameter for predicting vibration amplitude. Regarding wind speed, it is observed that as UR increases, the predominance of motion-induced force diminishes, resulting in a concurrent decrease in the fluctuating lift coefficient. Upon further investigation into the work performed by various forces within a single vibration cycle, it has been determined that as the vibration amplitude escalates, the work of the lift force (energy input WI) initially increases, then diminishes, whereas the work of the damping force (energy dissipation WO) continuously rises. The intersection of these two trajectories signifies the point of energy equilibrium between input and output, thereby establishing the vibration amplitude of VIV. The predicted vibration amplitudes, grounded in this principle, have been corroborated by experimental results.

Discretizing low-intensity whole-body vibration into bouts with short rest intervals promotes bone defect repair in osteoporotic mice.

Continuous administration of low-intensity whole-body vibration (WBV) gradually diminishes bone mechanosensitivity over time, leading to a weakening of its osteogenic effect. We investigated whether discretizing WBV into bouts with short rest intervals was effective in enhancing osteoporotic bone repair. Ten-week-old female mice were ovariectomized and underwent drill-hole defect surgery (Day 0) on the right tibial diaphysis at 11 weeks of age. The mice underwent one of three regimens starting from Day1 for 5 days/week: continuous WBV at 45 Hz and 0.3 g for 7.5 min/day (cWBV); 3-sbouts of WBV at 45 Hz, 0.3 g followed by 9-srest intervals, repeated for 30 min/day (repeated bouts of whole-body vibration with short rest intervals[rWBV]); or a sham treatment. Both the cWBV and rWBV groups received a total of 20,250 vibration cycles per day. On either Day 7 or 14 posteuthanasia (n = 6/group/timepoint), the bone and angiogenic vasculature in the defect were computed tomographyimaged using synchrotron light. By Day 14, the bone repair was most advanced in the rWBV group, showing a higher bone volume fraction and a more uniform mineral distribution compared with the sham group. The cWBV group exhibited an intermediate level of bone repair between the sham and rWBV groups. The rWBV group had a decrease in large-sized angiogenic vessels, while the cWBV group showed an increase in such vessels. In conclusion, osteoporotic bone repair was enhanced by WBV bouts with short rest intervals, which may potentially be attributed to the improved mechanosensitivity of osteogenic cells and alterations in angiogenic vasculature.

Enhanced toughness-thermal stability synergy and mechanisms of dual-phase Nb alloys by tuning C concentration

Nb alloy has become a promising material in aerospace due to high melting point, low density and excellent processing properties. Nevertheless, the mismatched mechanical properties and thermal stability of single-phase BCC-Nb made the aircraft unable to resist cyclic vibration loads under the action of heat/force/flow. Here, after solid solution, quenching and two-stage aging, an FCC/BCC dual-phase Nb alloy with a discontinuous grain boundary (GB) carbide network skeleton was formed. The results show that interstitial C atoms precipitate from BCC-Nb matrix resulting in volume shrinkage and form discontinuous carbide at GB, which stimulates the phase transition of BCC expansion to FCC near GB. Wherein, discontinuous GB carbides help pin the GB and dislocations, impede grain growth, and change the deformation from local to the entire network skeleton. Meanwhile, the gap provides a channel for the dislocation to pass through the GB. Additionally, the FCC provides the multi-slip system to transfer the dislocation. The results show that the yield strength, tensile strength, elongation, fracture toughness and elastic modulus of Nb alloy are increased by 79.99 %, 34.52 %, 164.22 %, 204.76 % and 1.27 %, respectively. This unique microstructure is expected to guide the design of the next generation of high-performance Nb alloys.

Mechanical enhancement and high linearity health monitoring of composite materials based on CNTs/PSF/PI film sensor with ultra-low SWCNTs doping content.

A new type of embedded composite material health monitoring nano-sensor is designed to ensure that the unique material advantages of nanofillers can be maximized. The carbon nanotubes (CNTs)/polysulfone (PSF)/polyimide (PI) thin film sensor in this paper is obtained by the self-assembly of a PSF/PI asymmetric porous membrane which is prepared by a phase inversion method through vacuum filtration of SWCNTs. It is a new structure for a practical CNT sensor that can take into account both 'composite health monitoring and damage warning' and 'composite mechanical enhancement'. The new structure of the CNTs/PSF/PI film sensor is divided into two parts. The upper part consists of small-aperture finger-like holes filled with SWCNTs (the SWCNT content is 0.0127 mg cm-2). The lower part consists of large-aperture cavities conducive to resin infiltration, which enhance the interface bonding force between the sensor and the composite material. This unique structure allows the CNTs/PSF/PI film sensor to change the influence of the embedded sensor from 'introducing defects' to 'local enhancement', and the mechanical strength of the enhanced specimen can reach up to 1.68 times that of the original specimen, and the service interval can reach 2.01 times that of the original specimen. In addition, the CNTs/PSF/PI film sensor also has good sensitivity (GF = 2.54) and extremely high linearity (R2 = 0.9995), and has excellent follow-up and interface bonding ability. It can also maintain excellent fatigue resistance and stability over 46 500 vibration cycles, which provides new research ideas and research methods for the field of composite-life monitoring sensors.

Three-dimensional mechanical characteristics analysis of bolted joints and loosening mechanism

Bolted joints are widely used in various industries. However, in challenging conditions such as shock, vibration, and temperature fluctuations, threads can loosen, leading to equipment damage and accidents. Scholars have introduced self-locking thread designs like wedge-shaped self-locking threads and stepped threads to improve anti-loosening performances. While experiments support their effectiveness, previous research primarily focused on optimizing thread structure parameters, and the studies of loosening mechanism are not in-depth enough, which restricts the development of anti-loosening bolted joints. This paper proposes a parametric modeling approach to create 3D elastic–plastic finite element models of bolted joints with different thread profiles. This approach allows for a comprehensive analysis of structural behavior, stress distribution, and load conditions, enabling the in-depth examination of the mechanical properties for thread loosening. A novel arc-lock anti-loosening threads design is proposed. Arc-lock threads are found to provide superior load distribution uniformity, increased normal force, and enhanced frictional resistance. Furthermore, the correctness of the finite element results is validated through photoelastic experiments and transverse vibration experiments. Results show that under a preload force of 225.5kN, the assembly of M24 Grade 10.9 bolts with Grade 10 nuts exhibit RMSE (Root Mean Square Error) values of 11.25, 9.02, and 8.76 for regular threads, wedge-shaped threads and arc-lock threads, respectively. Arc-lock threads demonstrate a more uniform stress distribution. In transverse vibration experiments under fully tightened conditions, regular threads loosened at the 2326th vibration cycle, while wedge-shaped self-locking threads and arc-lock threads maintained the preload percentages of 91.24% and 93.51%, respectively. These findings offer a scientific basis for understanding anti-loosening mechanisms in bolted joints and inform anti-loosening thread design.

Flow-induced oscillations of vocal-fold replicas with tuned extensibility and material properties

Human vocal folds are highly deformable non-linear oscillators. During phonation, they stretch up to 50% under the complex action of laryngeal muscles. Exploring the fluid/structure/acoustic interactions on a human-scale replica to study the role of the laryngeal muscles remains a challenge. For that purpose, we designed a novel in vitro testbed to control vocal-folds pre-phonatory deformation. The testbed was used to study the vibration and the sound production of vocal-fold replicas made of (i) silicone elastomers commonly used in voice research and (ii) a gelatin-based hydrogel we recently optimized to approximate the mechanics of vocal folds during finite strains under tension, compression and shear loadings. The geometrical and mechanical parameters measured during the experiments emphasized the effect of the vocal-fold material and pre-stretch on the vibration patterns and sounds. In particular, increasing the material stiffness increases glottal flow resistance, subglottal pressure required to sustain oscillations and vibratory fundamental frequency. In addition, although the hydrogel vocal folds only oscillate at low frequencies (close to 60 Hz), the subglottal pressure they require for that purpose is realistic (within the range 0.5–2 kPa), as well as their glottal opening and contact during a vibration cycle. The results also evidence the effect of adhesion forces on vibration and sound production.

Functional force stimulation alters motor neuron discharge patterns.

Beneficial effects have been observed for mechanical vibration stimulation (MVS), which are mainly attributed to tonic vibration reflex (TVR). TVR is reported to elicit synchronized motor unit activation during locally applied vibration. Similar effects are also observed in a novel vibration system referred to as functional force stimulation (FFS). However, the manifestation of TVR in FFS is doubted due to the use of global electromyography (EMG) features in previous analysis. Our study aims to investigate the effects of FFS on motor unit discharge patterns of the human biceps brachii by analyzing the motor unit spike trains decoded from the high-density surface EMG. Eighteen healthy subjects volunteered in FFS training with different amplitudes and frequencies. One hundred and twenty-eight channel surface EMG was recorded from the biceps brachii and then decoded after motion-artifact removal. The discharge timings were extracted and the coherence between different motor unit spike trains was calculated to quantify synchronized activation. Significant synchronization within the vibration cycle and/or its integer multiples is observed for all FFS trials, which increases with increased FFS amplitude. Our results reveal the basic physiological mechanism involved in FFS, providing a theoretical foundation for analyzing and introducing FFS into clinical rehabilitation programs.

Flow-induced vibrations of ten tandem cylinders at low Reynolds number

Flow-induced vibrations of ten cylinders in tandem arrangement are numerically investigated by using the immersed boundary method with a low Reynolds number (Re = 100). Seven spacing ratios L/D (where L = center–center spacing between tandem cylinders and D = diameter of the cylinder) are selected from 1.1 to 4.0, and the reduced velocity Ur ranges from 2.0 to 13.5 with an increment of 0.5. Small (L/D < 2.0) and large (L/D > 2.0) spacing ranges are identified, both including two types of responses: wake-induced vibration (WIV; Ur = 2.0–9.0∼10.5 for a small L/D and Ur = 2.0–6.0∼6.5 for a large L/D) and wake-induced galloping (WIG; Ur > 9.0∼10.5 for a small L/D and Ur > 6.0∼6.5 for a large L/D). The largest vibration amplitude of each cylinder is obtained in the WIG region for the small L/D condition. The presence of downstream cylinders suppresses the vortex shedding of upstream cylinders and thus postpones the vibration of upstream cylinders at a small Ur, whereas the downstream cylinder enhances the vibration at a larger Ur due to the wake interference. For a small L/D, three flow regimes with the extended-body, reattachment, and co-shedding patterns are successively presented as Ur increases. For a large L/D, four types of flow regimes, namely, EB-2S (the extended-body with “2S” pattern), RT-2S (the reattachment with “2S” pattern), TR-2S (two-row vortex street with “2S” pattern), and CS-VS (co-shedding with variation shedding), are classified. Two new vortex shedding patterns, “2G (two counter-rotating vortices shed from each side per vibration cycle)” and “2C (two co-rotating vortices shed from each side per vibration cycle),” have been identified. In the WIV region, there is only one dominant vibration frequency for upstream cylinders (C1–C7), while a sub-harmonic frequency emerges and dominates C8–C10 when L/D is large. The fluctuating lift force spectra show a broad-band frequency distribution due to the irregular positions of the vortex generation and merging, and the dominant frequency in the WIG region decreases consecutively from C1 to C10.