Vibration Reduction Efficiency Research Articles

Influence of additional mass and connection of nonlinear energy sinks on vibration reduction performance

The broadband vibration reduction performance of nonlinear energy sink (NES) has attracted wide attention. However, the impact of the NES’s additional mass other than the oscillator and how it is connected to the primary structure has been ignored. More recently, it has been discovered that vibration attenuation through the cellular application of NES can achieve greater efficiency. However, the connection between NES cells and the primary structure, as well as between cells, has not been studied. In this study, by considering the additional mass of the NES cells, the influence of the connection modes of NES cells on the vibration reduction efficiency is investigated theoretically, optimally and experimentally for the first time. The forced vibration models of linear oscillator coupled with NES cells are established by viscoelastic connection and rigid connection respectively. The approximate analysis and numerical analysis show that the vibration reduction efficiency of NES cells is affected by the resonance frequency of the primary structure and the external excitation intensity and shows a nonlinear trend. With the change of the resonant frequency of the primary structure, the viscoelastic connection NES cells can almost always obtain higher vibration reduction efficiency than the rigid connection NES cells. The global bifurcation results show that the strongly modulated responses of the structure can be triggered by the viscoelastic connection. Moreover, the connection modes between NES cells also affect the vibration reduction efficiency. The optimal parameters of the connection damping and connection stiffness are obtained by the particle swarm optimization algorithm. Finally, the viscoelastic connection and rigid connection, and the effect of the connection mode between NES cells on the vibration reduction efficiency are compared by experiments. The conclusions of theoretical research are verified. This work can provide theoretical guidance for the engineering application of NES cells.

The Effect of Support Misalignment on Vibration Characteristics of Aero-Engine Rotor Systems under Ultra-High Operating Speeds

In order to ensure the vibration safety of rotor systems in the next generation of aero-engines and reduce the impact of misalignment faults, the effect of support misalignment on the vibration characteristics of rotor systems under ultra-high operating speeds is investigated in this paper. Firstly, an analytical excitation model of the rotor systems under ultra-high operating speeds is established, considering the impact of the support misalignment. Then, based on the model of the misaligned combined support system, the dynamic model of the flexible discontinuous rotor support system with the support misalignment is presented. Subsequently, based on the established model, the effects of support parameters and support misalignment amounts on the vibration characteristics of the rotor support system are analyzed. Finally, experimental validation of the research findings is conducted. The research result shows that the support misalignment increases the vibration response of the rotor, reduces the vibration reduction efficiency of the combined support system, and consequently decreases the vibration safety of the rotor support system.

Experimental and numerical study on dynamic response of a photovoltaic support structural platform with a U-shaped tuned liquid column damper

A tuned liquid column damper (TLCD) is widely used in offshore structures as a passive energy dissipation device to reduce the harm of wind, wave, and current loads to the safety of offshore platforms. This investigation explores the dynamic response and interaction mechanism of a photovoltaic support structural platform (SSP) equipped with a TLCD by experimental and numerical analysis. The vibration mitigation performance of the TLCD under varying liquid depth ratios, external excitation frequencies, and amplitudes is systematically evaluated. The experiments focus on assessing the structural dynamic response and wall pressure to determine the vibration reduction efficiency of the TLCD for structures with fundamental frequencies more than 2 Hz. The experimental results indicate that the TLCD can reduce the structural response maximally near the natural frequency (2.52 Hz) of the structure, with vibration reduction effectiveness ranging from 42.0% to 85.1%. Additionally, one develops a two-way fluid-structure interaction (FSI) model to investigate further the impact of hydrodynamic pressure caused by sloshing inside the TLCD on the SSP motion response, which providing a more detailed explanation for the different phenomena observed in the experimental results.

Event-triggered semi-active TLCD for ground motion-induced vibration control

One potential drawback of tuned liquid column dampers (TLCDs) is their relatively low control efficiency during the initial stage of structural vibration caused by external excitations. This is because satisfactory control effects can only be achieved when the liquid inside TLCD is fully oscillating, which is not the case during the initial stage. To solve this problem, in this study, an event-triggered semi-active technique is creatively proposed to improve the vibration reduction efficiency of TLCDs during the initial stage. The fundamental idea of the proposed approach is to provide an initial displacement to the liquid column via baffles, and then release the constraints on the initial liquid displacement at an appropriate time to achieve the rapid activation of TLCDs. A strategy from the standpoint of phase difference between liquid column motion and structural motion is proposed to determine the triggering conditions (i.e. when to release the constraints). The effectiveness of the proposed semi-active system is examined under both harmonic and stochastic excitations. The results show that the proposed strategy successfully improves the vibration suppression performance of TLCDs in the early stage of structural vibration.

Experimental study on the influence of radial internal clearances of the rolling bearings on dynamics of a flexible rotor system

To investigate the impact of radial internal clearance of rolling bearings on the dynamic response of a flexible rotor system in a turbo-shaft engine, a dynamic similarity model of the power turbine rotor was established. Experimental research was then conducted. Four rolling bearings supporting the rotor were examined, with dynamic response tests carried out under varying radial internal clearances. The influence of the radial internal clearance on the dynamic characteristics of the rotor system was studied using the controlled variable method. The amplitude, orbit, and asynchronous vibration were analyzed through time-domain signal comparison, waterfall diagrams, and spectral analysis. The experimental results demonstrate that: (1) Adjusting the radial internal clearance of the bearings can significantly reduce the dynamic response of the flexible rotor system, with a maximum observed displacement response reduction of 88%. (2) The efficiency of vibration reduction is closely related to the axial location of the bearing. (3) Optimal radial internal clearance is not necessarily achieved at the maximum or minimum values. (4) The "locked-up" frequency phenomenon, which increases the resonance opportunities of the rotor system, can be mitigated by adjusting the radial internal clearance of different bearings. This research is of great significance and engineering value for understanding, diagnosing, and preventing excessive vibration in flexible rotor systems.

Study on Vibration Reduction Effect of the Building Structure Equipped with Intermediate Column–Lever Viscous Damper

Generally speaking, the traditional lever amplification damping system is installed between adjacent columns in a building, which occupies a significant amount of space in the building. In contrast to amplification devices in different forms, the damper displacement of the intermediate column damper system is smaller, and the vibration reduction efficiency is lower. In light of these drawbacks, this study proposes a new amplification device for energy dissipation and vibration reduction, which is based on an intermediate column–lever mechanism with a viscous damper (CLVD). Initially, a specific simplified mechanical model of CLVD is derived. Subsequently, an equivalent Kelvin mechanical model of CLVD is derived to intuitively reflect CLVD’s damping and stiffness effect. The damping ratio added by CLVDs to the structure is calculated according to that model; the additional damping ratio and additional stiffness are utilized to calculate the displacement ratio Rd and shear force ratio Rv of the structure with CLVDs to the structure without CLVDs. Rd and Rv are introduced to evaluate the vibration reduction effect of the structure with CLVDs, and the effects of various parameters (such as intermediate column position, beam’s bending line stiffness, lever amplification factor, damping coefficient, and earthquake intensity) on Rd and Rv are analyzed. The results indicate that when the ratio of the distance from the intermediate column to the edge column to the span of the beam is 0.5, CLVD owns the optimal vibration reduction effect. Increasing the beam’s bending line stiffness is beneficial for CLVD to control structural displacement and shear force; when the leverage amplification factor is too large, the CLVD provides the structure with stiffness as the main factor, followed by damping. Additionally, when the ratio of the displacement amplification factor to the geometric amplification factor satisfies fd/γ = 1/21−0.5α, the CLVD has the optimal displacement control effect on the structure. After that, measures are provided to optimize the CLVD in different situations in order to effectively control the inter-story displacement and the story shear force of the structure. Consequently, a nine-story frame is taken as an example to elaborate the application of CLVDs in the design for energy dissipation and vibration reduction. The results reveal that the CLVD scheme adopting the proposed optimization method can effectively enhance the displacement amplification ability of CLVDs, resulting in an additional damping ratio of up to 12%. At the same time, the inter-story displacement was reduced by almost 40% under fortification earthquakes. Through the research in this study, designers can obtain a new choice in structural vibration reduction design.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior, the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression, and has attracted a lot of attention. In this paper, an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks (NESs) for the first time. The proposed asymmetric tristable NES (ATNES) is composed of a pair of oblique springs and a vertical spring. Then, the three stable states, symmetric and asymmetric, can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs. The governing equations of a linear oscillator (LO) coupled with the ATNES are derived. The approximate analytical solution to the coupled system is obtained by the harmonic balance method (HBM) and verified numerically. The vibration suppression efficiency of three types of ATNES is compared. The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states. In addition, compared with the symmetrical tristable NES (TNES), the ATNES can effectively control smaller structural vibrations. In other words, the ATNES can effectively solve the threshold problem of TNES failure to weak excitation. Therefore, this paper reveals the vibration reduction mechanism of the ATNES, and provides a pathway to expand the effective excitation amplitude range of the NES.

Distributed control of a plate platform by NES-cells

Nonlinear energy sink (NES) has become a good passive vibration control technique with great potential. For a huge structure, it is unpractical to control the vibration by just one NES, let alone the structure has multi-modes. In this work, a technique who uses distributed nonlinear energy sink cells (NES-cells) to control the multi-modal resonance of the floating raft is proposed. The floating raft is simplified as a corner-point supported plate. Natural modes of it guide the distribution of NES-cells to make NESs locate on the position with strong vibration, which enhances the coupling ship between the plate platform and NES-cells. An example of installing NES-cells guiding by the first-two modes of the corner-point supported plate is presented in this paper. It is compared with the vibration reduction effect by a single NES. To make a fair comparison, total mass of NES-cells is the same with that of the single NES. The results show that NES-cells can deal with multi-modal vibration reduction better. The experimental results also fully illustrate this view. At the same time, the reaction of each NES-cell to the plate is effectively dispersed while comparing with the single NES, which decreases the stress at the attachment points and is more suitable for engineering applications. The number of NES-cells also has an effect on the vibration reduction efficiency. When the design parameters are fixed, there exists an optimal number to make the vibration reduction efficiency tend toward saturation. The multimodal vibration control of the plate platform is effectively solved by the proposed NES-cells technique. It also provides guidance for other practical engineering problems.

Research on the effect of rail vibration suppression using the stiffness-damping interventional rail vibration reduction device

This study introduces the Stiffness-Damping Interventional Rail Vibration Reduction Device (SDIRVRD) as a means to enhance rail vibration suppression. It compares the SDIRVRD with the traditional tuned rail damper (TRD) in terms of their vibration suppression mechanisms. The research investigates the influence of the SDIRVRD’s stiffness and damping parameters on the dynamic response of the vehicle and track. It also conducts a comparative analysis of track and vehicle vibration responses before and after the installation of the SDIRVRD, evaluating its effectiveness in reducing both track system and vehicle vibrations. The field test validates the theoretical calculations, and the vibration reduction efficiency is quantified using the insertion loss value. Key findings include the superiority of the SDIRVRD over the TRD in vibration reduction under equivalent damping ratio conditions. The SDIRVRD significantly reduces rail acceleration, displacement, and velocity admittances, with a notable suppression effect on pinned-pinned rail vibration. The stiffness and damping of the SDIRVRD play a crucial role in enhancing its vibration reduction effect, but after the stiffness exceeds 2 kN/mm and further increases the stiffness of the SDIRVRD, the enhancement of its damping effect on the vehicle-track system’s vibration diminishes significantly. The SDIRVRD reduces acceleration vibration levels in the vehicle and track system by approximately 2–3 dB. Insertion Loss measurements show significant vibration reduction in the rail across most frequency domains.

Torsional vibration attenuation of a closed-loop engine crankshaft system via the tuned mass damper and nonlinear energy sink under multiple operating conditions

In recent years, nonlinear energy sink (NES), as a nonlinear dynamic vibration absorber (NDVA), has been widely studied due to its high robustness and broadband vibration attenuation effectiveness, compared with the traditional linear dynamic vibration absorber (LDVA). In the area of crankshaft torsional vibration reduction, the external excitation of a closed-loop crankshaft model changes with the variation of speed, which puts forward higher requirements for wide-band torsional vibration attenuation. This study attempts to explore the feasibility of NES replacing the traditional linear tuned mass damper (TMD) for engine crankshafts in possible practical engineering application by studying a four-cylinders diesel engine crankshaft. Firstly, a multi-inertias nonlinear closed-loop self-excited coupled oscillation model (M-NCSCO) of crankshaft is established, and the correctness of the model is verified through comparison with those from experiments. Based on this, the crankshaft is coupled with optimal TMD (O-TMD), general NES (G-NES), and optimal NES (O-NES), respectively. An improved Newmark–β method is proposed to solve the nonlinear dynamic model numerically. The effects of NES and TMD on the vibration attenuation behavior of the crankshaft are studied under different engine operating conditions (including power, injection timing, single cylinder flameout, and load). The results show that the vibration attenuation efficiency and robustness of G-NES are 7.90% and 3.47% higher than that of O-TMD when considering the above four typical working conditions comprehensively. After further optimization of G-NES, the vibration reduction efficiency of O-NES is improved by 3.1% compared with G-NES.

Vibration reduction of floating raft system based on nonlinear energy sinks

Floating raft vibration isolation systems have been plagued by multi-frequency vibration and vibration suppression for the low-frequency range. In this paper, the floating raft vibration control strategy using multiple distributed nonlinear energy sinks (NESs) is proposed for the first time. In the modeling, three kinds of distributed NESs, namely, being connected to the power units only, to the raft and elastic base only, and to the entire substructure of the system, are considered. Based on this five-degree-of-freedom dynamic model, the natural frequencies and modes are analyzed. The approximate analytical analysis of the nonlinear model is carried out, and the correctness of the approximate solution is verified numerically. The vibration reduction efficiency of the three NES distribution models is demonstrated. The results show that the distributed NESs can effectively control the vibration of the floating raft system for all modes. The vibration problem of the floating raft system for the low-frequency range is perfectly solved. Furthermore, with a small additional weight ratio, different NES distribution models can be used to achieve the vibration damping of the floating raft system for low-order or high-order modes. In conclusion, this paper provides a novel and efficient control strategy for floating raft vibration.

Analysis and improvement of human-induced vibration comfort of articulated steel pedestrian bridges

The effect of different pedestrian densities (0.2, 0.5, 1, 1.5 and 4.6 persons/m2) on a pedestrian bridge is studied, the comfort level is evaluated according to the acceleration peak, and the most sensitive part of the acceleration response employs tuned mass dampers (TMDs) for vibration control. The study shows that the bearing capacity level of the pedestrian bridge with articulated piers meets the standard. Compared with a pier rigid connection system, the structural dynamic characteristics of pier articulation do not change much, and the vertical frequency and peak acceleration in the span are slightly smaller. The comfort evaluation results of the bridge with articulated piers are the same as those of the bridge with a rigid pier. The TMD setting can effectively reduce the human-induced vibration time response, the vibration reduction efficiency can reach 52%, and the comfort level changes from CL2 to CL1 after vibration reduction.

The active control study of a damped two-level smart spring system

The vibration reduction performance of a damped two-level smart spring system is studied. The governing equations of the smart spring system are reduced to a first-order ordinary differential equation of matrix form. An active control algorithm employing the relative velocity relationships between the primary and auxiliary systems to prevent the movement of the controlled object is applied in the simulation. Different excitation types are considered to fully examine the validity of the control law. Responses of the controlled object under the control law are obtained and compared to the case of constant friction and the case of no control. The study indicates that the active control algorithm shows a good vibration reduction efficiency and a wide vibration reduction bandwidth.

Experimental investigation on amplified multilayer viscoelastic damper and vibration mitigation evaluation subjected to wind loads

Methods to improve the damping efficiency of dampers have been extensively studied. This study proposes a multilayer viscoelastic damper with an amplified deformation device (MAVE), which combines a traditional viscoelastic damper (VE) with a lever amplification device. The proposed device utilizes multiple viscoelastic damping layers and a lever system to amplify the inter-story displacement, thereby increasing the damping force and enhancing energy dissipation capability. A mechanical model of MAVE was established, and model tests were performed to compare MAVE and VE. The test results demonstrate that MAVE can effectively amplify the deformation of the damper. The damping force of MAVE increased by 5.23 times, while the stiffness increased by 5.59 times, resulting in a 3.11 times increase in energy dissipation capacity. Furthermore, the deviations in the amplification factor and the comparisons between experimental and theoretical results were discussed. The experimental and theoretical deviations were within 10%. Finally, a numerical simulation was performed on a super-tall structure to demonstrate the vibration control capabilities of the MAVE system. By comparing the response of the structure and the energy consumption of the dampers, the vibration reduction efficiency of MAVE under wind loads was confirmed. The peak acceleration at the top floor was reduced by 51%, and the standard deviation (STD) acceleration was reduced by 37%. The peak displacement at the top floor was reduced by 80%, and the STD displacement of the same floor was reduced by 76%. MAVE effectively enhanced the comfort level of super-tall structures.

A tristable nonlinear energy sink to suppress strong excitation vibration

As well known, the vibration reduction efficiency of the nonlinear energy sink (NES) is poor under strong excitation. In this paper, a tristable NES (TNES) is proposed. The TNES can degenerate into bistable and mono-stable NES by adjusting the geometric parameters of the springs. The governing equations of a linear oscillator coupled with the TNES under harmonic excitation are derived. The approximate analytical solution of the coupled system is obtained by using the harmonic balance method and verified numerically. The vibration suppression efficiency of TNES and NES is compared. The dynamic behavior of TNES under strong excitation is demonstrated. The results show that the nonlinear restoring force is softened due to the wide distribution of the three stable points of TNES. Therefore, compared with NES, the proposed TNES can suppress stronger excitation vibration. In addition, the low side barrier depth is conducive to TNES to perform chaotic inter-well oscillation, which can effectively suppress the strong excitation vibration and obtain good vibration reduction performance. As a result, the proposed TNES can eliminate the detached resonance curve and enlarge the effective range of the NES. Under relatively weak excitation, the vibration suppression efficiency of TNES is slightly lower than that of NES, although the TNES is also relatively significant. Therefore, this paper reveals the vibration suppression mechanism of TNES, and provides a way to effectively solve the problem of low vibration reduction efficiency of NES under strong excitation.

Influence of Damping Particles on the Vibration of Spur Gear Transmission Using Numerical Modelization

The article numerically simulates the vibration reduction of a spur gear transmission by using damping particles placed in technological holes designed on the gear itself. The vibration of the gear transmission is reduced based on friction and inelastic collision which eliminates the vibrational energy by the loss during the motion of the damping particles within the technological holes. The kinematic processing of the gear system is analyzed using Adams software. The displacement acceleration data at the survey site is obtained from the Adams instrument which is valuable for evaluating the vibration level of the gear transmission. The interaction between the damping particles as well as the interaction between the particles with the gear model is simulated using EDEM software based on the discrete element method. The vibration of the gear transmission is assessed by the acceleration of the driven gear’s center of mass. The results show that the center of mass acceleration is remarkably reduced when particles are used at the rotation speed of 500 rpm and of 700 rpm. However, at the rotation speed of 1000 rpm, the vibration reduction is not much. This can be explained by the high speed and high inertia which cause the damping particles to rotate along with the gear, resulting in almost no collision between damping particles. The study also assesses the vibration reduction efficiency of the gear transmission according to the number of damping particles in each cavity and found that the number of particles accounting for 45.5% to 47.2% of the fill volume would reduce vibration most effectively. The three-millimeter diameter damper particles provide the most effective damping effect, at second place are the particles in four-millimeter diameter, and the least effective are those with two-millimeter diameter.

Research on Vibration Control of Paired Inclined Nozzles Dynamic Coupled Tubes

The barrel vibrates violently, which will lead to a serious drop in shooting accuracy. To solve this issue, a barrel vibration control method of the paired oblique nozzle dynamic couple is proposed. A pair of inclined nozzle devices are designed on the barrel to fully use the gunpowder gas energy in the chamber during the shooting process. A dynamic couple is generated to balance the turning moment of the barrel weapon. Simultaneously, the recoil force is reduced by exporting the gunpowder gas in the chamber. Therefore, the vibration of the barrel is reduced. Firstly, the internal ballistic two-phase flow model including the gas transient flow model in the vibration control device is modelled based on the internal ballistic theory of two-phase flow. Secondly, the numerical simulation of the weapon launching process is carried out. Thirdly, the rigid-flexible coupling firing dynamics modelling and simulation research is conducted on a 30mm chain gun equipped with a paired oblique nozzle dynamic couple vibration control device. At last, the effects of the device on the continuous firing vibration control of barrel weapons are analyzed. The results show that the vibration reduction efficiency of the inclined nozzle is better than that of the vertical nozzle and the horizontal nozzle. When the angle of the inclined nozzle is 30°, the barrel shows the highest vibration reduction efficiency. The vibration reduction efficiency of each vibration characteristic is 39.2%, 17.1%, 44.8%, and 48.9%, respectively.

A tristable nonlinear energy sink

The tristable characteristics are mostly used in the field of energy harvesting and vibration isolator, but are rarely devoted to in the field of vibration absorption. In this paper, a tristable nonlinear energy sink (TNES) model is proposed for vibration absorption. The TNES is constructed by fixing a magnet in the middle of the clamping pre-pressure beam, and setting a magnet on both sides of the fixed magnet. By adjusting the magnet position, the proposed TNES can be transformed into bistable NES (BNES) and monostable NES (MNES). The TNES is coupled with the linear oscillator (LO), and the differential equation of motion of the coupled system is obtained with the Hamiltonian principle. The approximate analytical method and the numerical method are mutually verified. The vibration reduction efficiency of the TNES under harmonic excitation is presented. The influence of the parameters of the TNES on the dynamics and vibration reduction efficiency is studied. The optimal parameters of the TNES are obtained by the particle swarm optimization (PSO) algorithm. Compared with the corresponding bistable NES and monostable NES, it shows that the tristable NES has obvious advantages in vibration suppression efficiency. The effects of the TNES barrier depths and the excitation amplitude on the vibration reduction efficiency are revealed. The TNES can dissipate energy through chaotic inter-well oscillation between three stable positions, and achieve the purpose of effectively suppressing vibration.

Splitting of waves in rotor-in-rotor nonlocal metamaterials by internal rotor coupling

Mechanical metamaterials can be used to control wave propagation because they are flexibly adjustable. In this paper, a one-dimensional rotor-in-rotor metamaterial with internal rotor coupling is proposed. This metamaterial introduces a new connection between lattices into a rotor-in-rotor system to produce a nonlocal metamaterial. Meanwhile, a zero-frequency bandgap with negative mass can be obtained. The vibration reduction efficiency of bandgaps is analysed based on the recursive method and numerically verified. Furthermore, wave splitting is found in the rotor-in-rotor metamaterial due to strong equivalent nonlocal interactions. Its dispersion relation shows a “dual wavevector” phenomenon: there are frequency ranges where a positive slope and a negative slope coexist. Numerical simulations using finite cell analysis are performed to validate the wave splitting by calculating the phase velocity and group velocity. The finding of wave splitting in the dual wavevector region is expected to provide new insights to control wave propagation.

A Combined Viscous-Steel Damping System (CVSDS) for Longitudinal Vibration Mitigation of A long-span Railway Suspension Bridge

ABSTRACT To mitigate longitudinal vibration of long-span railway suspension bridges, a Combined Viscous-Steel Damping System (CVSDS) is put forward in this paper. In the CVSDS, the viscous damper is expected to work under train braking and frequent earthquakes, while the steel damper can resist rare earthquakes. Moreover, a fuse-lock device is proposed to work as the switch between the aforementioned two dampers. The working mechanism of the CVSDS was introduced. The locking function was verified by static test, and the vibration reduction efficiency of the proposed system was validated through numerical method. The results show that the combined system is efficient.