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.

Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink

Inspired by the demand of improving the riding comfort and meeting the lightweight design of the vehicle, an inerter-based X-structure nonlinear energy sink(IXNES) is proposed and applied in the half-vehicle system to enhance the dynamic performance. The X-structure is used as a mechanism to realize the nonlinear stiffness characteristic of the NES, which can realize the flexibility, adjustability, high efficiency, and easy operation of nonlinear stiffness, and is convenient to apply in the vehicle suspension, and the inerter is applied to replacing the mass of the NES based on the mass amplification characteristic. The dynamic model of the half-vehicle system coupled with the IX-NES is established with the Lagrange theory, and the harmonic balance method(HBM) and the pseudo-arc-length method(PALM) are used to obtain the dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and random excitation is evaluated by six performance indices, and compared with that of the original half-vehicle system to show the benefits of the IX-NES. Furthermore, the structural parameters of the IX-NES are optimized with the genetic algorithm. The results show that for road harmonic and random excitation, using the IX-NES can greatly reduce the resonance peaks and root mean square(RMS) values of the front and rear suspension deflections and the front and rear dynamic tire loads, while the resonance peaks and RMS values of the vehicle body vertical and pitching accelerations are slightly larger.When the structural parameters of the IX-NES are optimized, the vehicle body vertical and pitching accelerations of the half-vehicle system could reduce by 2.41% and 1.16%,respectively, and the other dynamic performance indices are within the reasonable ranges.Thus, the IX-NES combines the advantages of the inerter, X-structure, and NES, which improves the dynamic performance of the half-vehicle system and provides an effective option for vibration attenuation in the vehicle engineering.

A vertical track nonlinear energy sink

Eliminating the effects of gravity and designing nonlinear energy sinks(NESs)that suppress vibration in the vertical direction is a challenging task with numerous damping requirements.In this paper,the dynamic design of a vertical track nonlinear energy sink(VTNES)with zero linear stiffness in the vertical direction is proposed and realized for the first time.The motion differential equations of the VTNES coupled with a linear oscillator(LO)are established.With the strong nonlinearity considered of the VTNES,the steady-state response of the system is analyzed with the harmonic balance method(HBM),and the accuracy of the HBM is verified numerically.On this basis,the VTNES prototype is manufactured,and its nonlinear stiffness is identified.The damping effect and dynamic characteristics of the VTNES are studied theoretically and experimentally.The results show that the VTNES has better damping effects when strong modulation responses(SMRs)occur.Moreover,even for small-amplitude vibration,the VTNES also has a good vibration suppression effect.To sum up,in order to suppress the vertical vibration,an NES is designed and developed,which can suppress the vertical vibration within certain ranges of the resonance frequency and the vibration intensity.

A viscoelastic nonlinear energy sink with an electromagnetic energy harvester:Narrow-band random response

Nonlinear energy sink is a passive energy absorption device that surpasses linear dampers, and has gained significant attention in various fields of vibration suppression. This is owing to its capacity to offer high vibration attenuation and robustness across a wide frequency spectrum. Energy harvester is a device employed to convert kinetic energy into usable electric energy. In this paper, we propose an electromagnetic energy harvester enhanced viscoelastic nonlinear energy sink(VNES) to achieve passive vibration suppression and energy harvesting simultaneously. A critical departure from prior studies is the investigation of the stochastic P-bifurcation of the electromechanically coupled VNES system under narrowband random excitation. Initially, approximate analytical solutions are derived using a combination of a multiple-scale method and a perturbation approach. The substantial agreement between theoretical analysis solutions and numerical solutions obtained from Monte Carlo simulation underscores the method's high degree of validity. Furthermore, the effects of system parameters on system responses are carefully examined. Additionally, we demonstrate that stochastic P-bifurcation can be induced by system parameters, which is further verified by the steady-state density functions of displacement. Lastly,we analyze the impacts of various parameters on the mean square current and the mean output power, which are crucial for selecting suitable parameters to enhance the energy harvesting performance.

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink （NES）, which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric sys- tem is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the tran- sient vibration, and a 1：1 transient resonance capture occurs between two subsystems. The investigation demonstrates that the integrated NES-piezoelectric mechanism can re- duce vibration and harvest some vibration energy.

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink(NES)are investigated.The linear system is excited by a harmonic and random base excitation,consisting of a mass block,a linear spring,and a linear viscous damper.The NES is composed of a mass block,a linear viscous damper,and a spring with ideal cubic nonlinear stiffness.Based on the generalized harmonic function method,the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system.The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions.The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities,the transmissibility transition probability density,and the percentage of the energy absorption transition probability density of the linear oscillator.The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio.The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters,which will affect the stability of the system.

Limit cycle oscillation suppression of 2-DOF airfoil using nonlinear energy sink

This paper presents a novel mechanical attachment, i.e., nonlinear energy sink （NES）, for suppressing the limit cycle oscillation （LCO） of an airfoil. The dynamic responses of a two-degree-of-freedom （2-DOF） airfoil coupled with an NES are studied with the harmonic balance method. Different structure parameters of the NES, i.e., mass ratio between the NES and airfoil, NES offset, NES damping, and nonlinear stiffness in the NES, are chosen for studying the effect of the LCO suppression on an aeroelastic system with a supercritical Hopf bifurcation or subcritical Hopf bifurcation, respectively. The results show that the structural parameters of the NES have different influence on the supercritical Hopf bifurcation system and the subcritical Hopf bifurcation system.

Vibration absorption of parallel-coupled nonlinear energy sink under shock and harmonic excitations

Nonlinear energy sink(NES)can passively absorb broadband energy from primary oscillators.Proper multiple NESs connected in parallel exhibit superior performance to single-degree-of-freedom(SDOF)NESs.In this work,a linear coupling spring is installed between two parallel NESs so as to expand the application scope of such vibration absorbers.The vibration absorption of the parallel and parallel-coupled NESs and the system response induced by the coupling spring are studied.The results show that the responses of the system exhibit a significant difference when the heavier cubic oscillators in the NESs have lower stiffness and the lighter cubic oscillators have higher stiffness.Moreover,the efficiency of the parallel-coupled NES is higher for medium shocks but lower for small and large shocks than that of the parallel NESs.The parallel-coupled NES also shows superior performance for medium harmonic excitations until higher response branches are induced.The performance of the parallel-coupled NES and the SDOF NES is compared.It is found that,regardless of the chosen SDOF NES parameters,the performance of the parallel-coupled NES is similar or superior to that of the SDOF NES in the entire force range.

Resonance response of fluid-conveying pipe with asymmetric elastic supports coupled to lever-type nonlinear energy sink

This paper studies the vibration absorber for a fluid-conveying pipe,where the lever-type nonlinear energy sink(LNES)and spring supports are coupled to the asymmetric ends of the system.The pseudo-arc-length method integrated with the harmonic balance method is used to investigate the steady-state responses analytically.Meanwhile,the numerical solution of the fluid-conveying pipe is calculated with the Runge-Kutta method.Moreover,a special response,called the collapsible closed detached response(CCDR),is first observed when the vibration response of mechanical structures is studied.Then,the relationship between the CCDR and the main structure primary response(PR)is obtained.In addition,the closed detached response(CDR)is also observed to research the resonance response of the fluid-conveying pipe.The appearance of either the CCDR or the CDR does affect the resonance attenuation.Furthermore,the mentioned two phenomena underline that the trend of vibration responses under external excitation goes continuous and gradual.Besides,the main advantage of the LNES is presented by contrasting the LNES with the nonlinear energy sink(NES)coupled to the same pipe system.It is found that the LNES can reduce the resonance response amplitude by 91.33%.

Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

Due to the increasing use of passive absorbers to control unwanted vibrations,many studies have been done on energy absorbers ideally,but the lack of studies of real environmental conditions on these absorbers is felt.The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink(NES).In this paper,the Burgers model is assumed for the viscoelasticity in an NES,and a linear oscillator system is considered for investigating the instabilities and bifurcations.The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods.The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches,and by increasing the stiffness parameters of the viscoelasticity,the conditions of these branches occur in larger ranges of the external force amplitudes,and also reduce the frequency range of the branches.In addition,increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

Vertical vibration control using nonlinear energy sink with inertial amplifier

To reduce additional mass, this work proposes a nonlinear energy sink(NES)with an inertial amplifier(NES-IA) to control the vertical vibration of the objects under harmonic and shock excitations. Moreover, this paper constructs pure nonlinear stiffness without neglecting the gravity effect of the oscillator. Both analytical and numerical methods are used to evaluate the performance of the NES-IA. The research findings indicate that even if the actual mass is 1% of the main oscillator, the NES-IA with proper inertia angles and mass distribution ratios can still effectively attenuate the steady-state and transient responses of the main oscillator. Nonlinear stiffness and damping also have important effects. Due to strongly nonlinear factors, the coupled system may exhibit higher branch responses under harmonic excitation. In shock excitation environment, the NES-IA with a large dynamic mass can trigger energy capture of both main resonance and high-frequency resonance. Furthermore, the comparison with the traditional NES also confirms the advantages of the NES-IA in overcoming mass dependence.

Fractional nonlinear energy sinks

The cubic or third-power(TP)nonlinear energy sink(NES)has been proven to be an effective method for vibration suppression,owing to the occurrence of targeted energy transfer(TET).However,TET is unable to be triggered by the low initial energy input,and thus the TP NES would get failed under low-amplitude vibration.To resolve this issue,a new type of NES with fractional nonlinearity,e.g.,one-third-power(OTP)nonlinearity,is proposed.The dynamic behaviors of a linear oscillator(LO)with an OTP NES are investigated numerically,and then both the TET feature and the vibration attenuation performance are evaluated.Moreover,an analogy circuit is established,and the circuit simulations are carried out to verify the design concept of the OTP NES.It is found that the threshold for TET of the OTP NES is two orders of magnitude smaller than that of the TP NES.The parametric analysis shows that a heavier mass or a lower stiffness coefficient of the NES is beneficial to the occurrence of TET in the OTP NES system.Additionally,significant energy transfer is usually accompanied with efficient energy dissipation.Consequently,the OTP NES can realize TET under low initial input energy,which should be a promising approach for micro-vibration suppression.

Vibration Absorption Efficiency and Higher Branches Elimination of Variable-Stiffness Nonlinear Energy Sink

Vibration absorption efficiency of a variable⁃stiffness nonlinear energy sink(NES)was investigated when the main oscillator was subjected to harmonic and impulse excitations.The slow flow equations of the coupled system were derived by using the complexification⁃averaging method,and the nonlinear equations which describe the steady⁃state response were obtained.As the harmonic excitation force increased,the system which comprises constant⁃stiffness NES generated higher branch responses,greatly reducing the vibration absorption efficiency.The influence of nonlinear stiffness on the responses of the system was investigated.Results show that,with the increase of harmonic exciting force,a reduction of NES stiffness can eliminate the higher branch responses and even the frequency band of strongly modulated responses.The vibration absorption efficiency of variable⁃stiffness NES attached to the linear oscillator for different amplitudes of impulse excitation was investigated.Results show that the proper reduction of nonlinear stiffness under increasing impulse excitation can greatly increase the vibration absorption efficiency of NES,and the variable⁃stiffness design can effectively mitigate the negative influences of the increase of the excitation amplitude on the efficiency of constant⁃stiffness NES.

Comparison of the performance and dynamics of the asymmetric single-sided and symmetric double-sided vibro-impact nonlinear energy sinks with optimized designs

The operation of symmetric double-sided and asymmetric single-sided vibro-impact nonlinear energy sinks(DSVI NES and SSVI NES)is considered in this study.The methodology of optimization procedures is described.It is emphasized that the execution of optimization procedures is ambiguous,allows for a great deal of arbitrariness,and requires experience and intuition on the part of the implementer.There are a lot of damper parameter sets providing similar attenuation of the primary structure(PS)vibrations.It is shown that the efficiency of such mitigation for both VI NES types with optimized parameters is similar.However,their dynamic behavior differs significantly.The system with the attached DSVI NES exhibits calm dynamics with periodic motion and symmetrical bilateral impacts on both obstacles.The system with attached SSVI NES exhibits rich complex dynamics when the exciting force frequency is varied.Periodic modes of different periodicity with different numbers of asymmetric impacts per cycle on the PS directly and on the obstacle alternate with various irregular regimes,namely,chaotic mode,intermittency,and crisis-induced intermittency.The regions of bilateral impacts are narrow and located near resonance;they are narrower for a system with an attached DSVI NES.In a system with an attached SSVI NES,there are wider areas of asymmetric unilateral impacts.

Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks

Nonlinear vibration absorbers have been widely used for vibration suppression of elastic structures,but they were usually placed within the structures.However,designing such a vibration damping device within an engineering structure is possibly difficult.In this paper,an inertial nonlinear energy sinks(NES)is mounted on the boundaries of the elastic beam to suppress its vibration.Although this vibration suppression approach is more in line with engineering requirements,it introduces nonlinear oscillators at boundaries.This brings certain difficulties to the structural vibration analysis and the optimal absorber design.An approximate analytical approach for the steady-state response is developed in this work and verified by numerical solutions.The comparison with the uncontrolled system demonstrates the high-efficiency vibration suppression of the inertial NES installed on the boundary.Besides,the optimization of the NES parameters is performed.Resonance amplitude of the elastic structure can be reduced by 98%with the optimized NES.In summary,this paper proposes a novel approach to suppress the bending vibration of elastic structures through boundary NESs.The vibration reduction effect is very significant,and it is more feasible to implement.Therefore,this work is helpful to study the vibration of elastic structures with nonlinear boundaries and to promote the application of nonlinear vibration absorbers.

Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink

This paper draws attention to the issue of the vibration absorption of nonlinear mechani- cal system coupled to nonlinear energy sink （NES） under the impact of the narrow band stochastic excitation. Firstly, based on the complex-averaging method and frequency detuning methodology, response regimes of oscillators have been researched under the linear impact of coupling a nonlinear attachment with less relativistic mass and an external sinusoidal forcing, of which results turn out that the quasi-periodicity response regime of system which occurs when the external excitation amplitude exceeds the critical values will be the precondition of the targeted energy transfer. Secondly, basing on the path integration method, vibration suppression of NES has been researched when it is affected by a main oscillator with a narrow band stochastic force in the form of trigono- metric functions, of which results show that response regimes are affected by the amplitude of stochastic excitation and the disturbance strength. Finally, all these conclusions have been approved by the numerical verification and coincided with the theoretical analysis; meanwhile, after the com- paring analysis with the optimal linear absorber, it turns out that the NES which is affected by the narrow band stochastic force could also suppress the vibration of system with a better effect.

A ground-limited nonlinear energy sink

The nonlinear energy sink(NES)is outstanding in vibration control for the well-known character of energy targeted transmitting and resonance automatically capturing.To enhance the practicability,this paper proposes a ground-limited NES.The novel design can be encapsulated in a certain box.However,as the vibration region of NES is limited,the control efficiency of it must be considered seriously.Hence,the ground-limited NES is discussed via the analytical method,the simulation method,and especially the experiment in forced vibration.All parameters involved in this study are obtained through the parameter identification based on the experimental platform.The piecewise nonlinearity is fitted into the continuous nonlinearity by the hyperbolic tangent function.Then the harmonic balance method(HBM)is used during the analytical processing to promote the accuracy of the solution.The direct numerical method produces results to verify the analytical method together with the experimental records.The discussion on the control parameters shows that a proper limiting spring can effectively reduce the vibration of the NES while the cost of the control efficiency is small.In a word,this work provides a simple and reliable approach for restricting the NES,which is beneficial to the design of the NES and broadens the application of the NES in engineering.

Forced vibration control of an axially moving beam with an attached nonlinear energy sink

This paper investigates a highly efficient and promising control method for forced vibration control of an axially moving beam with an attached nonlinear energy sink（NES）.Because of the axial velocity,external force and external excitation frequency,the beam undergoes a high-amplitude vibration.The Galerkin method is applied to discretize the dynamic equations of the beam–NES system.The steady-state responses of the beams with an attached NES and with nothing attached are acquired by numerical simulation.Furthermore,the fast Fourier transform（FFT）is applied to get the amplitude–frequency responses.From the perspective of frequency domain analysis,it is explained that the NES has little effect on the natural frequency of the beam.Results confirm that NES has a great potential to control the excessive vibration.

Suppressing nonlinear aeroelastic response of laminated composite panels in supersonic airflows using a nonlinear energy sink

This paper proposes using a Nonlinear Energy Sink(NES) to suppress the nonlinear aeroelastic response of laminated composite panels in supersonic airflows. Relevant aeroelastic equations are established using Hamilton’s principle and a finite element approach, drawing upon Von Karman’s large deflection theory and first order piston theory. The idea of the NES suppression region is proposed and the effects of NES parameters on the NES suppression region are studied in detail. The results show that the nonlinear aeroelastic responses of the panel can be completely suppressed by the Transient Resonance Capture(TRC);the appropriate NES parameter values can increase the critical dynamic pressure for flutter and suppress the nonlinear aeroelastic response effectively. Increasing the mass ratio of the NES can improve the NES suppression region;the nonlinear stiffness coefficient and damping of the NES within a specific range can suppress the nonlinear aeroelastic response. The most effective installation position for a NES is in a specific region behind the center-line of the panel in the direction of the airflow.

Enhanced vibration suppression and energy harvesting in fluid-conveying pipes

A novel vibration absorber is designed to suppress vibrations in fluidconveying pipes subject to varying fluid speeds.The proposed absorber combines the fundamental principles of nonlinear energy sinks(NESs)and nonlinear energy harvesters(NEHs).The governing equation is derived,and a second-order discrete system is used to assess the performance of the developed device.The results demonstrate that the proposed absorber achieves significantly enhanced energy dissipation efficiency,reaching up to 95%,over a wider frequency range.Additionally,it successfully harvests additional electric energy.This research establishes a promising avenue for the development of new nonlinear devices aimed at suppressing fluid-conveying pipe vibrations across a broad frequency spectrum.