The influences of mass ratio and flexural rigidity in flow-induced vibrations of a circular cylinder with an attached flexible plate

In response to the vibration problem of helicopter fuselage caused by continuous rotor periodic excitation force, a nonlinear energy sink is considered to be installed on the main reduction transmission channel to reduce the vibration level of the fuselage. This article conducts an analysis of the influence of nonlinear energy sink structure parameters under harmonic excitation force, establishes a coupled dynamic model of helicopter main reduction/absorber/fuselage, and uses harmonic balance method and stability analysis theory to analyze the periodic solution and stability of the system. Using the vibration amplitude of the system as the evaluation criterion, the influence of damping, stiffness, and mass ratio on the vibration suppression effect of the nonlinear energy sink was explored. The results showed that as the damping of the nonlinear energy sink increased, the resonance frequency of the coupled system shifted to the left, and the vibration amplitude of the main reduction system increased; As the stiffness of the nonlinear energy sink increases, the vibration amplitude of the coupled system will first decrease and then increase, gradually approaching the vibration amplitude of the system without coupled dampers; The influence of mass ratio on system amplitude follows the same trend as the influence of stiffness. By optimizing, the structural parameters of the nonlinear absorber with good vibration suppression effect are ultimately obtained.

Influence of mass ratios between SiC particles and chopped carbon fibers on properties of C/SiC/SiO2 porous ceramics

We computationally study thrust generation and propulsive characteristics of an elastic plate pitching and/or heaving in free stream laminar flow. The pitching is considered about the leading edge, and the Reynolds number based on the plate length and free stream velocity is 150. An in-house fluid–structure interaction (FSI) solver is employed to simulate the large-scale flow-induced deformation of the structure along with active pitching and heaving in two-dimensional coordinates. The FSI solver utilizes a partitioned approach to strongly couple a sharp-interface immersed boundary method based flow solver with an open-source finite-element structural dynamics solver. We elucidate the mechanism of the thrust generation in the rigid and elastic plate by comparing the time-variation of thrust and work done by the plate, together with the wake signatures in the downstream. The time variation of the thrust is explained using first-order scaling arguments. The computed thrust as a function of pitching frequency for the rigid pitching plate shows a similar trend as compared to the published data of rigid foils, while the elastic plate exhibits a strong influence of the flow-induced deformation of the plate. They both exhibit reverse von Kármán-like vortex shedding in the downstream. We quantify the differences in propulsive characteristics of these two plate types as a function of pitching frequency. We found that there lies an optimum pitching frequency for the elastic plate for efficient propulsion, while the rigid one outperforms the elastic plate at larger pitching frequency. This is due to the fact that the elastic plate locks in to a higher mode of vibration at a larger pitching frequency. Furthermore, the influence of mass ratio, flexural rigidity, pitching amplitude, and Reynolds number on the performance of the elastic plate is also investigated. Finally, we study the combined effect of pitching and heaving on the propulsive performance. The pitching frequency for the maximum efficiency is lesser for the combined heaving and pitching plate as compared to only heaving or only pitching. Our results provide fundamental insights into the propulsive characteristics of the elastic pitching and/or heaving plates, which could help design autonomous underwater vehicles.

Results from a series of studies on the stream-wise vibration of a circular cylinder verifying Japan Society of Mechanical Engineers Standard S012-1998, Guideline for Evaluation of Flow-induced Vibration of a Cylindrical Structure in a Pipe, are summarized and discussed in this paper. Experiments were carried out in a water tunnel and in a wind tunnel using a two-dimensional cylinder model elastically supported at both ends of the cylinder and a cantilevered cylinder model with a finite span length that was elastically supported at one end. These cylinder models were allowed to vibrate with one degree of freedom in the stream-wise direction. In addition, we adopted a cantilevered cylinder model that vibrated with two degrees of freedom in both the stream-wise and cross-flow directions under the same vibration conditions as an actual thermocouple well. The value of the Scruton number (structural damping parameter) was changed over a wide range, so as to evaluate the value of the critical Scruton number that suppressed vibration of the cylinder. For the two-dimensional cylinder, two different types of stream-wise excitations appeared in the reduced velocity range of approximately half of the resonance-reduced velocity. For the stream-wise vibration in the first excitation region, due to a symmetric vortex flow, the response amplitudes were sensitive to the Scruton number, while the shedding frequency of alternating vortex flow was locked-in to half of the Strouhal number of vibrating frequency of a cylinder in the second excitation region. In addition, the effects of the aspect ratio of a cantilevered cylinder on the flow-induced vibration characteristics were clarified and compared with the results of a two-dimensional cylinder. When a cantilevered circular cylinder with a finite length vibrates with one degree of freedom in the stream-wise di-rection, it is found that acylinder with a small aspect ratio has a single excitation region, whereas a cylinder with a large aspect ratio has two excitation regions. Furthermore, the vibration mechanism of a symmetric vortex flow was investigated by installing a splitter plate in the wake to prevent shedding of alternating vortices. The vibration amplitude of acylinder with a splitter plate increased surprisingly more than the amplitude of a cylinder without a splitter plate. For a cantilevered cylinder vibrating with two degrees of freedom, the Lissajous figure of vibration of the first excitation region shows the trajectories of elongated elliptical shapes, and in the second excitation region, the Lissajous trajectories draw a figure “8”. The results and information from these experimental studies proved that Standard S012-1998 provides sufficient design methods for suppressing hazardous vibrations of cylinders in liquid flows.

Nozzle jet flow-induced vibration of single circular cylinders and twin circular cylinders

Vortex-induced vibration (VIV) of two transversely vibrating cylinders in a side-by-side (SBS) arrangement is numerically investigated using a combination of direct-forcing immersed boundary and large eddy simulation techniques. The VIV responses of vibrating SBS cylinders at two reduced velocities (UR* = 4.0 and 6.0) are studied for a range of gap ratio 1.0 ≤g*≤ 3.0. Moreover, the influence of mass ratio, damping ratio, and Reynolds number in the amplitude response and efficiency of VIVACE (Vortex-Induced Vibration for Aquatic Clean Energy) from vibrating SBS cylinders are investigated at moderate Reynolds numbers (Re = 1000 and 10 000). The optimal gap ratio for UR* = 4.0 is in the range of 1.0 ≤g*≤ 1.2. Larger than this range, the VIV responses are close to single-cylinder responses. At UR* = 6.0, all gap ratios show lower responses than a single-cylinder case. The vibrating SBS cylinder with a larger damping ratio results in higher maximum VIVACE efficiency with a narrower UR* range for significant efficiency. With almost the same amplitude response, the SBS cylinders with a lower mass ratio result in lower VIVACE efficiency. Using the same mass-damping parameters, it appears that a low mass ratio could be desirable to increase the UR* range of significant VIVACE efficiency and pick the proper damping ratio to reach a high value of maximum VIVACE efficiency. The effect of flow conditions on the amplitude response and VIVACE efficiency of vibrating SBS cylinders with the same VIV parameters is not significant.

The flow-induced transverse vibration of a cylinder (diameter D*) with an attached flexible and elastic plate of high aspect ratio to its leeward side is investigated numerically at a low Reynolds number of 150 for a range of reduced velocities (Ur) using an in-house developed fluid solver based on curvilinear immersed boundary method strongly coupled with an open-source finite element-based structural solver. It was observed that an attached elastic plate of width B=B*/D*=0.1 and length L=L*/D*=1 suppresses large vibrations of the cylinder, but one with length L = 2, contrary to previous studies, amplifies vibrations up to five times of an isolated cylinder. Three regimes were observed: vortex-induced vibration (VIV), suppression, and galloping. In VIV regime for 3≤Ur≤7, lock-in was observed where the vortex shedding frequency from the plate-cylinder system was seen to slightly increase relative to that of static cylinder–plate system to match with the natural frequency of the cylinder and the plate. In this regime, the deformations of the elastic plate were large (max. 91% of L) and in high modes (up to fifth mode), leading to new vortex patterns. The transverse displacement of the cylinder–plate system was found to reach nearly twice of an isolated cylinder in this regime. For 7<Ur≤9, the cylinder–plate system was pushed into suppression regime, wherein its displacement was nullified because of lack of vorticity interaction and out-of-phase deformation. Beyond Ur = 9, the cylinder–plate system vibrated in the galloping regime, wherein it shed and generated forces as an asymmetric body creating an angle of attack with the incoming flow. The primary mode of deformation of the elastic plate progressively increased from second mode to third mode in galloping regime, and the transverse displacement of cylinder showed a linear increase with the increase in reduced velocity until Ur = 18. The vibration amplitude of the cylinder was higher in the galloping regime, but the vibrations of the plate were more intense (higher amplitude and mode) in the VIV regime. New vortex patterns were observed in the VIV and galloping regimes ranging from 2S mode till 2T mode including all the vortex pattern between them like 2S, 2P, 2Q, and P + T modes, which are reported for the first time.

Vortex induced vibration (VIV) of circular and square cylinders with flexible splitter plates is studied at low Reynolds numbers. Finite element based flow and structure solvers, coupled using a partitioned approach, are used for simulating the fluid-structure interaction. Effect of flexibility of an attached flexible plate on its ability to suppress the VIV of a circular cylinder is considered. Flexibility of the plate is found to adversely affect the reduction in amplitude of the vibration of the cylinder. Next, flow past two square cylinders with deformable splitter plates placed side-by-side is considered. Vibration response of the two plates is studied for different values of flexibility. Initially, the plates vibrate out-of-phase with each other, but eventually settle for an in-phase fully developed response. Large amplitude of vibrations in the fully developed response is observed when its dominant frequency is close to the first natural frequency of the plate vibrations.

Vibrational energy harvesters offer an alternative to batteries for the autonomous powering of low power electronic devices, such as wireless sensors. Velocity amplified electromagnetic generators (VAEGs) utilise the velocity amplification effect in order to increase the output power and operational bandwidth of an electromagnetic generator, compared to linear resonators. This effect is achieved through sequential collisions in a system of free-moving masses. The velocity amplification achieved is controlled by the number of masses or degrees-of-freedom (dofs) and the mass ratio between them. An experimental investigation into the influence of mass ratio and number of dofs on the operational bandwidth of a VAEG at low frequencies (< 30 Hz) is presented herein. VAEG systems with 2-, 3- and 4-dofs are analysed for mass ratios in the range of 3:1 to 20:1 under sinusoidal forced excitation. It is shown that 3- and 4-dof configurations offer broader bandwidths than 2-dof configurations, particularly at higher mass ratios. At lower mass ratios, the bandwidths of the 3- and 4-dof configurations decrease, while the bandwidth of the 2-dof configuration increases. At a mass ratio of 3:1, the bandwidth of the 2-dof configuration approaches that of the 3- and 4-dof configurations. The highest half-power bandwidth of 9.3 Hz was achieved by the 3-dof mass ratio 20:1 system, at an acceleration of 1 g. The total voltage harvested over the frequency range 7–30 Hz is at a maximum at a mass ratio of 5:1 for the 3- and 4-dof configurations, and at 3:1 for the 2-dof configuration. The findings of this investigation will be significant in the development of future reduced scale VAEGs.

SummaryIn this paper, the influence of mass ratio on the vibration control effects of tuned mass damper (TMD) on a super high‐rise building has been investigated. A 1/45 scaled model of a super high‐rise building was constructed, and the TMD with the mass ratio of 0.01, 0.02, and 0.03, respectively, was suspended on the top. Shaking table test and the corresponding numerical simulation were carried out to make a further understanding of the damping mechanism. The structural performance with or without TMD was comparatively studied. The results show that larger mass ratio can improve the control effects under frequent earthquake, but the control effects increase little with the increase of mass ratio under rare earthquake due to structural damages, accompanied by stiffness degradation and nonlinear behavior of the main structure. In addition, some suggestions on the mass ratio selection are also proposed to generalize its applications.

This paper investigates the effect of flexibly attached secondary systems (FSS) on the dynamic behavior of primary structures (PS) under harmonic and seismic ground excitations. An FSS affects the main structure during ground excitation differently than a secondary system that is rigidly attached to it. Small displacements in the FSS are used to derive the equations of motion that define the behavior of the PS and FSS. The analytical formulation presented is validated by a finite element (FE) study conducted in SAP2000. The influence of mass ratio, tuning frequency ratio, and excitation frequency ratio on the dynamic behavior of the PS is investigated. The results show that the combined system (PS+FSS) behaves as a modified single degree of freedom (SDOF) structure at higher tuning frequency ratios. The dynamic response of the structure is independent of the mass ratio at low tuning frequency ratio of FSS. Under seismic excitations, the flexible structure’s response reduces considerably as the mass ratio increases, compared to a stiff structure at a higher tuning frequency ratio. When the tuning frequency ratio is equal to one, smaller mass ratios of FSS increase the seismic performance of the stiff structure. A design methodology is proposed to measure the spectral acceleration of the primary structure by incorporating the effect of FSS in the design response spectrum. An analysis of the tuning frequency ratio and mass ratio on the modified design spectrum is also presented. Finally, the proposed design methodology is validated with an existing study.

<div class="htmlview paragraph">In 1344 car-to-car side collisions, the risk of serious or fatal injury to the occupants of struck vehicles seem to increase proportionally to the difference in mass ratios in favor of the striking vehicle.</div> <div class="htmlview paragraph">However, in-depth analysis of 63 collisions during which the impact occurred on the side panel of the passenger compartment reveals that the difference in mass ratios is not the principal determinant of injury severity.</div> <div class="htmlview paragraph">The frequency and severity of injuries correlates better with the amount of intrusion of the side panel, a type of intrusion which occurs almost systematically, and even at low impact speed, when the bumper and structure in front of the side rail of the striking car override the rocker panel of the struck car.</div> <div class="htmlview paragraph">We shall show the relationship between the severity of chest, abdominal and pelvic injuries sustained by occupants seated perpendicularly to the intruding panel and the following parameters:</div> <div class="htmlview paragraph"> <ul class="list disc"> <li class="list-item"><div class="htmlview paragraph">mass ratio</div> </li> <li class="list-item"><div class="htmlview paragraph">compatibility of the relative heights of the stiffest elements involved in the impact</div> </li> <li class="list-item"><div class="htmlview paragraph">impact speed</div> </li> <li class="list-item"><div class="htmlview paragraph">ΔV of the struck car</div> </li> <li class="list-item"><div class="htmlview paragraph">intrusion</div> </li> </ul> </div> <div class="htmlview paragraph">We shall indicate the structural modifications which might improve protection of occupants involved in side collision with another car.</div>

The effectiveness of splitter plate as suppression device in reducing the flow-induced vibration (FIV) of a circular cylinder was conducted experimentally. The parameter used in this experiment is the gap separation between splitter plate and the circular cylinder (G/D). The control element of gap separations are varied from 0.5 to 2.0. The experiments were conducted in the wind tunnel which was free from external wind conditions at Aeronautical and Wind Engineering Laboratory (AEROLAB), UTM Kuala Lumpur. A supporting structure was designed and fabricated with the purpose to allow free vibration induced by wind on the circular cylinder. The results were analysed through the response of amplitude and power spectral density of the circular cylinder with splitter plate and compared with bare circular cylinder. For the gap separations of G/D = 1.0, 1.5 and 2.0, the vibration of the circular cylinder were successfully suppressed. The optimal distance for gap separation was at G/D = 1.5 with suppression effectiveness of 82%. For G/D = 0.5, on the contrary, the vibration of the circular cylinder was amplified. As conclusion, splitter plate can function to suppress as well as amplify the vibration of cylinder, depending on the gap separation.

This research examines the influence of a linear buffer on the impact load experienced during the high-speed water entry of slender projectiles, employing both experimental and numerical simulation methods. Experiments were carried out using a custom-designed high-speed water entry testing platform. In this setup, projectiles were propelled by an air gun, and their water entry dynamics were recorded with a high-speed camera. The results show that implementing a linear buffer significantly reduces the impact load during water entry. Compared with the prototype projectile, the impact load of the projectile equipped with a buffer can be decreased by up to 91.34%. The investigation further determined that buffer stiffness and the mass ratio between the projectile's body and head play crucial roles in determining the impact load. Within the effective range of buffer stiffness, lower values, and mass ratios are associated with enhanced load reduction. As the velocity of water entry increases, the effect of buffer stiffness on peak impact load weakens, while the influence of mass ratio becomes more prominent. These findings have important engineering implications for designing high-speed water entry systems, providing a viable strategy for reducing impact loads and improving safety and reliability.

This study thoroughly examines the impact of the coupling effects of wind-rain load on the structural behavior of the television tower, and the effective vibration control method is employed to mitigate the dynamic response of the structure. A refined finite element model of the tower was developed, and the dynamic response characteristics of the structure under varying wind speeds and rain intensities are further investigated. Based on parameter analysis, the influence of mass ratio and frequency ratio on the damping efficiency of tuned mass damper (TMD) was revealed. The results demonstrate that compared to wind load alone, the node displacement increases more significantly near the top of the tower under wind-rain load. When the basic wind speed reaches 40 m/s, the TV tower will be damaged due to the extreme compressive stress of the 45 units on the compression side exceeding the yield strength of the members. Under extreme weather loads, the members on the compressive side at a height of 60 meters are most susceptible to yielding and entering the plastic deformation stage. The overall vibration reduction effectiveness of TMD increases with higher mass ratios, with a mass ratio of 1.5 % identified as optimal. Regarding the reduction of top displacement of the tower, the effectiveness of TMD varies with frequency ratio, showing an initial increase followed by a decrease; optimal vibration control is observed at a frequency ratio of 0.9.