Nonlinear Energy Sink 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.

Bifurcation curves of a linear system attached with a bistable nonlinear energy sink

Bifurcation curves of a linear system attached with a bistable nonlinear energy sink

New effectual configuration of bistable nonlinear energy sink

The study presents a new configuration of nonlinear energy sinks (NESs) which is adaptable to function as either stable or bistable NES. The proposed NES is based on the spring-loaded inverted pendulum (SLIP) in which a torsional stiffness element couples the SLIP to the linear oscillator (LO). The bistable configuration provides a critically stable position when the SLIP is vertically aligned with respect to the LO motion. At this critical stability position, the SLIP NES incorporates pre-stored potential energy which generates the bistability characteristics resembling that of a stiffness-based bistable NES. The equations of motion of the coupled LO with the SLIP NES are derived based on the Euler–Lagrange method in non-dimensional form. The parameters of the considered SLIP NESs are optimized to achieve an optimum energy absorption from the LO. The proposed B-SLIP NES is also applied to suppress seismic ground motion and forced torsional vibrations. The obtained numerical simulation and analytical response results verify the robustness of the B-SLIP NES in vibration suppression performance compared with the tuned mass damper and the cubic stiffness NES.

Study on Cubic Stiffness Nonlinear Energy Sink Controlling Dynamic Responses of Multi-Degree-of-Freedom Structure by Shake Table Tests

A nonlinear energy sink (NES) has such advantages as controlling broader band responses and better robustness than conventional control devices like tuned mass dampers (TMDs). In this research, a cubic stiffness NES mitigating the dynamic responses of a multi-degree-of-freedom structure under white noise, harmonic and seismic excitations was tested using a shake table, and the influences of the parameters of the NES on vibration mitigation effects were investigated. The test results indicate that the NES has the same vibration mitigation effects on the acceleration responses under the white noise and harmonic excitations as TMDs, even though the mass ratio of the NES is less than that of a TMD. The average control effects of the NES on the acceleration responses of the structure under the effect of 100 seismic waves are better than those of a TMD, which indicates that an NES has better robustness than a TMD.

Theoretical investigation on vibration mitigation in a system with fractional nonlinear energy sinks

Theoretical investigation on vibration mitigation in a system with fractional nonlinear energy sinks

A composite structure device: vibration control and energy harvesting of tool system in aviation thin-walled parts milling process

Abstract The intense vibration generated by the high-speed milling cutter in the processing process not only seriously affects the surface roughness but also may damage important components of the machine tool, resulting in significant economic losses. Therefore, a composite structure of piezoelectric energy-collector (PEC) and nonlinear energy sink (NES) is innovatively constructed by combining theoretical research and numerical analysis to achieve more efficient vibration suppression and energy recovery in milling. Using the Hamilton principle, the electromechanical model of the composite structure is developed. Then, based on the Galerkin truncation to discretized displacement functions, we solve the amplitude-frequency response of the tool structure by using the harmonic balance method. The validity analysis of the proposed method can be verified by rigorous comparison with the results of the Runge-Kutta method. A novel NES-PEC composite structure presented in this work shows excellent vibration suppression capability in the milling process. More importantly, the structure also enables self-powered sensing of the tool system, significantly reducing dependence on external power sources. This innovative design substantially improves the stability and reliability of milling processes and opens up new ways to optimize the energy efficiency of tool systems. In summary, this paper’s modeling and solving methods, vibration reduction techniques, and energy harvesting strategies have laid a solid foundation for applying a high-speed milling cutter system. More relevant literature on applying vibration suppression and energy harvesting devices in milling must be reviewed. This paper fills in the research gap and provides a valuable reference for future tool systems design and optimization.

Vibration Suppression and Energy Harvesting of Nonlinear Energy Sink-Based Piezoelectric System with Combined Damping and Bistability Properties for Nonlinear Oscillator

Nonlinear energy sink (NES) as a new type of dynamic absorber has received widespread attention due to its broadband vibration suppression capability, but it has a certain requirement of energy triggering threshold. In this work, a bistable NES-based piezoelectric system with combined damping (BCPNES) and low threshold requirement is proposed. Electromechanical-coupled equations for the nonlinear oscillator coupled with BCPNES (NO-BCPNES) are established. The vibration suppression and vibration energy harvesting performance for the coupled system are investigated numerically and analytically. The frequency–energy plots of the conservative system are investigated using the complex-variable averaging method and the electromechanical decoupling method. The influence of circuit parameters on the target energy transfer threshold and harvested energy is discussed through the equivalent stiffness and damping of the circuit. The vibration suppression performance and the target energy transfer characteristics are analyzed in terms of the time–history response, the time–frequency response and the slowly varying dynamic flow, respectively. The results show that the electromechanical coupling coefficient affects the skeleton curve of frequency–energy plots in the form of equivalent stiffness. The NO-BCPNES system exhibits higher energy dissipation performance and better targeted energy transfer form under various excitations. From the phase perspective, NES-based piezoelectric system achieves vibration suppression of the main structure through the phase locking phenomenon. The mechanism of the influence of piezoelectric device parameters on the energy harvesting performance of the systems is clarified.

Aeroelasticity of an aircraft wing with nonlinear energy sink

In this paper, the effectiveness of nonlinear energy sinks on enhancing aeroelastic stability and post-instability response of aircraft wings is investigated. The wing has two degrees of freedom in bending and torsion, and is modelled using an extended Euler-Bernoulli beam theory with hardening nonlinearity. A Nonlinear Energy Sink (NES) absorber is embedded inside the wing distributed along the wing span. The wing attached unsteady aerodynamic loads are simulated using the Wagner's indicial lift model. The structural dynamics of the wing are derived using Extended Hamilton's Principle and it is discretised using Galerkin's method. The NES mass is connected to the wing spar through a linear damper and nonlinear spring with a cubic stiffness nonlinearity. The coupled aeroelastic equations are then transformed to state space. Then, integrated numerically to resolve the bending and torsional response of the wing to study the impact of spanwise and chordwise positions of the embedded NES on flutter suppression and instability response enhancement. The results demonstrate that the NES is most efficient and is most sensitive to changes in the stiffness when placed at the wingtip. For a given chordwise location, it is found that there is a range of flow speeds over which the NES is most effective and reducing the chordwise offset lowers the speed of the peak efficiency range and moves it closer to the flutter speed. In addition, increasing the stiffness coefficient of the NES improves the efficiency of the device in the immediate post-flutter region. Two near optimum NES devices are proposed with a mass ratios of 1% (located at the wingtip) and 2.5% (located at 75% span). Both of these improve the flutter speed by 5%, and reduce the post-flutter response by 64.5% and 59.2%, respectively.

Research on energy transfer and vibration suppression of nonlinear energy sink with nonlinear damping

The nonlinear energy sink is a nonlinear shock absorber that provides targeted energy transfer and plays a crucial role in structural vibration suppression. In this paper, the energy transfer and dynamic characteristics of nonlinear damping nonlinear energy sink systems are analyzed. Firstly, the theoretical model of the nonlinear damping NES system is described, and secondly, the equations of the system in the free state are derived by using the complex variable average method and the multi-scale method to obtain the energy transfer efficiency equation of the system. Through the study of the slow invariant manifold and energy transfer efficiency of the system, the influence of each system parameter on the energy transfer efficiency is analyzed. Then the equations of the system under harmonic excitation are processed in the same method to obtain the boundary equations of the system, through which the saddle-node bifurcation diagram of the system is plotted to study the influence of each system parameter on the saddle-node bifurcation characteristics of the system. Finally, the slow-varying equation of the system under harmonic excitation is derived, and the influence of each system parameter on the frequency detuning parameter interval of the strongly modulated response is obtained using the phase trajectory and a one-dimensional mapping diagram of the system, and the time-mileage diagram and Poincare section are used to prove the damping effect of the strongly modulated response.

Robust Targeted Energy Transfer with Asymmetric Nonlinear Energy Sinks Under Random Excitations

This study introduces an Asymmetric Nonlinear Energy Sink (ANES) to enhance robust Targeted Energy Transfer (TET) in vibration control. Traditional cubic Nonlinear Energy Sinks (NES) often struggle with varying excitation levels in random vibrations. The ANES integrates a cubic NES, extra inertia, and asymmetric stiffness components like a tension-only rope, two linear springs, and a viscous damper. The rope adds asymmetric stiffness by only applying tension force. This setup effectively absorbs vibrational energy across different levels of excitation, facilitating energy transfer from low-damped to high-damped modes. Numerical simulations demonstrate the ANES’s superior performance compared to traditional NES, supported by modal energy redistribution, Nonlinear Normal Modes (NNM) analysis, and Frequency-Energy Plots (FEP). These findings suggest that this type of ANES is a promising advancement for practical NES applications in vibration control.

Theoretical and experimental analysis of a nonlinear vibro-acoustic energy sink

This study is concerned with the experimental and theoretical analysis of a vibroacoustic nonlinear system devoted to absorption application. Based on the nonlinear energy sink principle, the dynamics of the system is reduced to two coupled degrees of freedom, one of which exhibits nonlinear behavior due to a large displacement mechanism. The set-up allows for precisely characterizing the nonlinear function of the mechanical system, first uncoupled and then coupled with an acoustic and linear resonator. Continuation procedures are performed experimentally and numerically, respectively using a phase-locked loop (PLL) and the asymptotic numerical method implemented in the MANLAB software package. The comparison between theoretical predictions and experimental results obtained on the uncoupled system allows for a parameter identification of the nonlinear resonator. Measurements on the coupled system highlight the energy pumping phenomenon, which can be predicted from numerical predictions in which identified parameters are introduced. The procedure aims at proposing analytical models for achieving efficient level attenuation, and providing design guidelines for sound reduction at high levels in confined spaces.

Analysis of the influence of nonlinear energy sink parameters applicable to helicopter main reduction systems

Abstract 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.

Multi-objective optimization research on nonlinear energy sink system of finite-length beam on elastic medium

Multi-objective optimization research on nonlinear energy sink system of finite-length beam on elastic medium

Gust response alleviation of the aircraft wing aeroelastic systems in supersonic flows using nonlinear energy sink

In order to reduce the gust response level of the aircraft wing aeroelastic systems in supersonic flows, the nonlinear energy sink (NES) is introduced into the aeroelastic system, and the effect of the nonlinear energy sink on the aeroelastic gust response is studied. The gust response dynamic model without and with NES is established by Lagrange equation, considering the cubic nonlinear characteristics of both plunge and pitch stiffness. The piston theory model as well as the '1-cos' model are employed to describe the unsteady aerodynamic load and the gust velocity, respectively. Besides, the comparison study of the gust response amplitude and energy characteristics of the wing aeroelastic systems with and without NES are analyzed. For systems with NES, the amplitude of gust dynamic response decreases rapidly, while vibration can be transmitted to the NES mechanism and causing its vibration. From an energy perspective, about 72.15 % of the original vibration energy has been transferred into NES, and further consumed through its damping. The influence of NES parameters, such as frequency ratio, mass ratio, damping ratio, and installation position on gust response, is discussed. Numerical simulations demonstrate that: as the frequency ratio, damping ratio and mass ratio increase, the dynamic response amplitude of the aeroelastic system decays faster, and the energy transferred from the wing system also increases. In addition, an optimal relative distance for the installation of NES can be found with best gust alleviation effect. The influence of nonlinear energy sink on the targeted transfer of vibration energy in aeroelastic systems are analyzed under different working conditions. The NES shows great gust alleviation effect and good robustness under different flight speeds, gust intensities, and gust lengths.

Vibration suppression in SDOF systems coupled to a nonlinear energy sink under colored noise

This study analyzes the stochastic vibration suppression and optimization of the single-degree-of-freedom (SDOF) system equipped with the cubic stiffness nonlinear energy sink (NES) under colored noise excitation. Two theoretical methods are proposed: an integrated method (denoted as EL-ELM) that combines evolutionary Lyapunov theory with the equivalent linearization method, and the other is an empirical formula. Using EL-ELM, the coupled nonlinear system is simplified to an equivalent linear stochastic system, allowing for a theoretical analysis of the impact of NES structural parameters on suppression performance and the precise determination of optimal parameter configurations for the best suppression effects. Subsequently, based on the results from the EL-ELM and the response data, an empirical formula has been developed that clearly describes the comprehensive laws governing the optimal NES parameters as they vary with vibration system parameters and stochastic excitation. Through error analysis and comparison of the two methods, it is found that the empirical formula significantly outperforms EL-ELM in terms of accuracy and computational cost, but it is contingent on solid prior knowledge. This study explores the influence of NES structural parameters on the system’s dynamic response and energy, further validating the effectiveness of the proposed methods in identifying optimal structural parameters. The phenomenon of targeted energy transfer (TET) under different NES structural parameters is also explained. The methodologies introduced in this study have strengthened the theory of vibration suppression. Specifically, the empirical formula excels in accuracy and computational efficiency by effectively using prior knowledge. The EL-ELM method, owing to its theoretical insights, is vital for analyzing complex stochastic nonlinear models. Combining these approaches offers guidance for advancing vibration control in theoretical and practical domains.

High-dimensional nonlinear flutter suppression of variable thickness porous sandwich conical shells based on nonlinear energy sink

Nonlinear energy sink (NES) is widely applied in engineering field due to the advantages of light weight, high robustness, unidirectional energy transfer, rapid and broadband vibration isolation. In this paper, nonlinear energy sink is utilized to suppress vibration of the variable thickness porous sandwich conical shells for the first time, and the high-dimensional nonlinear flutter suppression characteristics of the system of simply supported variable stiffness truncated porous sandwich conical shell coupled NES under aerodynamic force and thermal stress are investigated. By applying the first-order shear deformation theory (FSDT), Hamilton's principle and Galerkin technique, the high-dimensional nonlinear ordinary differential flutter suppression equations of the system appended with NES are established. The accuracy of the theoretical approach is ensured by the comparison of frequency results, while the NES dissipated kinetic energy ratio and the comparison of NES performance with other suppression systems are presented to prove the effectiveness of NES on nonlinear flutter suppression. The time history diagrams and limit cycle oscillation (LCO) amplitude curves, which reflect the high-dimensional nonlinear flutter suppression effect of NES, are obtained by employing the Runge-Kutta method. The effects of aerodynamic pressure, the parameters and positions of single NES, and the positions of parallel NES and series NES on the high-dimensional nonlinear flutter suppression characteristics of the system attached with NES are discussed in depth. Finally, the optimal high-dimensional nonlinear flutter suppression scheme is arrived.

Multimodal vortex-induced vibration mitigation and design approach of bistable nonlinear energy sink inerter on bridge structure

Large-scale structures, e.g., long-span bridge structures, are prone to induce multi-modal vibrations due to their densely spaced low modal frequencies. Due to the limited frequency bandwidth of linear dynamic absorbers, they are incapable of effectively mitigating vibrations across multiple modes. To this end, the bistable nonlinear energy sink inerter (BNESI) is used to mitigate the multimodal vortex-induced vibration (VIV) of the beam structure. The highly nonlinear equilibrium differential equations of the beam-BNESI system are numerically solved, and the simulated annealing (SA) algorithm is employed to determine the optimal VIV reduction ratio and BNESI parameters. In comparison to the cubic-type nonlinear energy sink inerter (CNESI), BNESI is found to possess more stable equilibrium positions, smaller stiffness coefficients, and higher VIV mitigation efficiency. The selection of design modes has been found to influence the efficiency of multimodal VIV mitigation, with the use of the intermediate modal order as the design mode resulting in the highest efficiency for multimodal VIV mitigation. The performance-based multimodal VIV mitigation design can be realized with three parameters, i.e., inertance ratio, damping coefficient, and stiffness coefficient. Moreover, the performance-based multimodal VIV mitigation approach and models proposed in this study demonstrate a high level of precision.

Torsional vibration suppression of a gear-rotor system using an inerter magnet nonlinear energy sink

The novel inerter magnet nonlinear energy sink (IMNES) utilizes chiral compression-torsion coupling effects to achieve mass augmentation, effectively mitigating torsional vibrations in a gear-rotor system with gear meshing clearance. The positive stiffness generated by the piecewise linear beam combines with the negative stiffness produced by the permanent magnet pair, resulting in the establishment of the IMNES’s nonlinear stiffness. Subsequently, a dynamic model of the IMNES-gear-rotor system is developed. Optimal parameters for the IMNES are determined through analysis of vibrational response surfaces under both transient and steady-state conditions. The numerical calculation of torsional vibration in the IMNES-gear rotor system is conducted across various gear meshing clearances. The results demonstrate that across different gear mesh clearances, the IMNES effectively attenuates torsional vibrations in the gear-rotor system. Under transient excitation, implementation of the IMNES leads to an 87% reduction rate in displacement within the gear-rotor system. In terms of steady-state excitation, simulations show a significant enhancement with a 65% increase in vibration suppression percentage.

Multi-mode vibration suppression of a cantilever beam carrying unbalance rotor using bi-stable nonlinear energy sink

Multi-mode vibration suppression of a cantilever beam carrying unbalance rotor using bi-stable nonlinear energy sink

Research on rapid stabilization of aero-engine casings subjected to shock loads using nonlinear energy sink

In this study, we study the application of nonlinear energy sinks (NES) for targeted vibration energy transfer and absorption in aero-engine casings subjected to shock loads. A simplified single-degree-of-freedom model with an attached NES is characterized to understand the influence of control parameters such as damping and nonlinear stiffness on the NES. Using the complexification-averaging (CX-A) technique, we analyze the main dynamic characteristics of the vibration system, revealing nonlinear normal modes (NNM) and the energy localization phenomenon that enables targeted energy transfer. Then we establish a thin-walled casing model with an NES and calculate its vibration energy transfer under shock load. The results of this study are as follows: (1) NNMs are related to initial energy, with energy localization leading to targeted vibration energy transfer and dissipation; (2) NES operates optimally within a specific energy domain, exceeding this domain reduces its effectiveness, which is primarily influenced by the NES’s nonlinear stiffness; (3) Optimizing the NES’s nonlinear stiffness on the thin-walled casing achieves targeted shock energy transfer and dissipation, significantly reducing the casing’s vibration amplitude (from 0.008 m to 0.003 m, a 62.5% reduction) and stabilization time (from 0.007s to 0.002s, a 71% reduction). The study’s results are instructive for achieving rapid stabilization of aero-engine casings under shock excitation, providing insights into the mechanism of NES and the impact of damping and nonlinear stiffness on its performance. This research guides the optimized design of NES for thin-walled casings to effectively dissipate shock-induced vibrations.