Bistable Nonlinear Energy Sink Research Articles

Vibration control and stroke evaluation of bi-directional bistable nonlinear energy sinks applied in monopile offshore wind turbines during emergency shutdown

Monopile offshore wind turbines (OWTs) in complex wind and wave environments can generate more excessive vibrations in the fore-aft (FA) and side-to-side (SS) directions when emergency shutdowns occur, and therefore damping techniques to alleviate such vibrations are essential. Due to the potential frequency detuning (reduced damping effectiveness) of traditional tuned mass dampers (TMDs) and stroke issues (such as large strokes of TMDs and limited maximum strokes of unidirectional nonlinear energy sinks (NESs)) in existing absorbers, this paper proposes a bi-directional bistable nonlinear energy sink (BBNES) to mitigate the vibration of the OWT in the FA and SS directions during the emergency shutdown. First, the proposed device and its operation mechanism are elaborated, and an optimization method for the device is introduced. Then, the dynamic analysis model of the BBNES is developed for vibration control of the OWT and incorporated into a fully coupled numerical simulation tool with high fidelity, FAST v8. Subsequently, the responses of the OWT without and with the proposed BBNES and the bi-directional tuned mass damper (BTMD) are exhaustively investigated under diverse conditions (including mass ratios, wind-wave loadings, emergency shutdown times, wind-wave misalignments, and 1st mode natural frequencies of the OWT) to reveal their performances and compare them. The research results show that under most conditions, the BBNES and BTMD have a similar damping performance in the FA direction, whereas the BBNES has a slightly lower damping performance in the SS direction than the BTMD. In addition, except for the wind velocity of 8 m/s at the hub and the wind-wave misalignment of 90°, the FA stroke of the BBNES with a small mass ratio (i.e., 0.01∼0.035) is significantly smaller than that of the BTMD with the same mass ratio by more than 1.1 m, and even up to about 4 m. The SS stroke of the BBNES is slightly greater than that of the BTMD, and in most cases, the difference between both is less than 0.52 m. Therefore, the BBNES is superior to the BTMD in this regard. When the 1st mode natural frequency of the OWT decreases, the BTMD can lose its tuning efficacy and makes the tower more susceptible to resonance caused by 1p and wave loadings, while the BBNES is not affected by the 1st mode natural frequency variation of the OWT, demonstrating its stronger robustness.

A customizable cam-typed bistable nonlinear energy sink

A novel cam-typed bistable nonlinear energy sink (CBNES) is first proposed in this paper. The CBNES achieves a customized design of the ideal configuration of BNES by introducing a cam-roller-spring negative stiffness mechanism (CRS-NSM). The design criteria for continuous and smooth bistable cam profiles are studied, and the extreme values of dimensionless stiffness and pre-compression are predicted. Furthermore, the periodic and quasi-periodic dynamics of the system are studied by using the complexification-averaging (CA-X) method. By combining Slow Invariant Manifold (SIM) and phase trajectory, the energy dissipations of different response types of the CBNES are predicted. The SMR and chaotic response have the best and lowest targeted energy transfer (TET) efficiency, respectively. The saddle-node (S-N) and Holf bifurcation characteristics of the periodic fixed points are analyzed to predict the possibility of SMR occurrence. The analysis of the amplitude frequency curve with the variation of system parameters indicates that weak negative stiffness and intermediate cubic stiffness are more beneficial to vibration suppression. The highlight is that the excitation thresholds of SMR are predicted by using analytical and numerical methods, and the influences of system parameters on the thresholds are analyzed. The deviation between the analytical and numerical results will decrease with increasing damping. Finally, the correctness of the analytical results is verified through a series of fixed-frequency experiments. The proposed CBNES provides a valuable potential solution for designing efficient and robust mechanical BNES physical implementations.

Effect of magnetic-spring bi-stable nonlinear energy sink on vibration and damage reduction of concrete double-column piers: Experimental and numerical analysis

Concrete structures suffer from crack damage under heavy vibrations, caused by seismic loads. Passive vibration control devices can be used to reduce the damage. The most common device is the tuned-mass-damper (TMD), which is tuned to match the natural frequency of the primary structure. However, under prolonged vibration load, the natural frequency of the concrete structure decreases, reducing the TMD's effectiveness in mitigating vibrations and damage, as it can only target a fixed natural frequency. Therefore, this study will propose and implement the nonlinear energy sink (NES), which is a vibration control device that can adapt to changing frequency, resulting in a larger effective bandwidth than the TMD. As a concrete structure, the cast-in-place double-column piers is seismically loaded with a shaking table with and without NES to observe the vibration and damage-mitigating properties of the NES. More specifically, a magnetic bi-stable NES (MBNES) with a viscous fluid damper (VFD) is designed and built. The bi-stable restoring force allows for a larger bandwidth than conventional NESs, and the magnets and VFD allow for easy manufacturability. An optimization method is proposed to obtain optimal parameters, and the restoring force and damping of the experimentally designed MBNES are verified using the restoring force surface method. The proposed design, optimization and identification procedure are generic and can be applied to any (concrete) civil structure. Shaking table tests are used to verify the robust performance of MBNES under continuous changes in the natural frequency of concrete double-column piers. The experimental results show that the MBNES can effectively mitigate vibrations of the pier and, consequently, reduce the damage of the pier, slow down the decrease of the stiffness of the pier, reduce the curvature and shear deformation of the pier. Numerical analysis results show that MBNES can absorb the energy of the primary structure in a wide frequency bandwidth and has excellent robust performance compared to conventional devices.

A novel vari-potential bistable nonlinear energy sink for improved vibration suppression: numerical and experimental study

A novel vari-potential bistable nonlinear energy sink for improved vibration suppression: numerical and experimental study

Tailored nonlinear stiffness and geometric damping: Applied to a bistable vibration absorber

A novel device is proposed to obtain arbitrary restoring force characteristics and nonlinear geometric damping. It consists of linear springs and dampers that are compressed along a track. The obtained nonlinear damping and stiffness law depend on the track’s shape. The device is then applied to obtain a nonlinear energy sink (NES) to damp the vibrations of a host system. Both the case of transient vibrations, induced by shock loads, and sustained vibrations, induced by harmonic loads, are studied. For arbitrary stiffness and damping, slow flow dynamics and slow invariant manifolds (SIMs) are derived by applying harmonic balancing and multiple timescales techniques. Under transient vibrations, two performance measures are derived from the SIM, the relative residual energy and the pumping time, and are found for generic nonlinear spring force and nonlinear geometric damping. For sustained vibrations, a load-dependent frequency response (FR) is derived from the SIMs. This FR predicts the occurrence of the efficient strongly modulated responses but also the occurrence of the unfavorable detached responses called isolas, where the NES fails to mitigate and even amplifies vibrations.This research investigates the performance of a conventional cubic NES and a bistable NES (BNES) with nonlinear damping obtained from the proposed device. Especially the BNES with nonlinear damping shows attractive properties, with a high degree of robustness over a wide energy range and a low vibration threshold under transient loading. Under harmonic loads, the nonlinear damping helps reduce the effect of isolas. A novel tuning methodology is proposed to avoid isolas for a range of load magnitudes. The new device opens up a whole range of possibilities regarding energy dissipation through nonlinear damping.

Study on excitation threshold of strong modulation response and vibration suppression performance of bistable nonlinear energy sink

The dynamics and vibration reduction performance of bistable nonlinear energy sink (BNES) are studied in this paper. First, the negative stiffness of BNES is realized by geometric nonlinearity, and the dynamics model of the system is established. The slow flow equation of the system under 1:1 main resonance is analyzed based on the complexification-averaging (CX-A) method, and the boundary conditions of saddle node bifurcation and Hopf bifurcation are analyzed. Second, the slow invariant manifold (SIM) of the BNES is studied based on multiscale analysis, and the excitation threshold of strongly modulated response (SMR) is analyzed; the analysis results are verified by the numerical method. The results show that the analytical solution is highly consistent with the numerical solution, and the error is less than 1%. Finally, the influence of structural parameters on the vibration reduction performance is analyzed and optimized. The vibration reduction performance of BNES and CNES is compared, and the results show that the BNES has better vibration reduction performance in the full frequency band.

Targeted energy transfer analysis of a nonlinear oscillator coupled with bistable nonlinear energy sink based on nonlinear normal modes

The nonlinear energy sink (NES), which has been proven to conduct quick and passive targeted energy transfer (TET), has been implemented in several structures to reduce vibration. For an NES to perform efficiently via targeted energy transfer (TET), the vibration levels must surpass a well-defined threshold; otherwise, the NES will perform inefficiently. The bistable NES (BNES) produces a nonlinear force with a negative linear and a positive nonlinear stiffness component. This investigation examines the energy flow characteristics of a bistable nonlinear energy sink coupled with a nonlinear oscillator (NO). Where frequency–energy graphs (FEPs) demonstrated the nonlinear normal modes (NNMs) and dynamic behaviour of the resultant NO-BNES system. At low energy levels, the emergence of many symmetrical and asymmetrical in-phase and out-of-phase backbone branches is emphasized. The superimposed wavelet frequency spectra of the NO-BNES response on the FEP have validated the robustness of the TET mechanism, where the contribution of the asymmetrical NNM backbones in TET can be viewed with clarity. Comparing the BNES and cubic NES by superimposing the wavelet frequency spectra on FEPs and energy dissipation efficiency reveals that the BNES performs better in TET.

A bi-stable device for simultaneous vibration absorption and energy harvesting using bi-stable piezoelectric composite laminate

A bi-stable device is presented for simultaneous vibration absorption and energy harvesting by introducing the piezoelectric element into the bi-stable nonlinear energy sink (BNES), which is called the bi-stable piezoelectric absorber (BPZA). BPZA only consists of the cantilever bi-stable piezoelectric composite laminate (BPCL) and tip masses. This BPZA is a lightweight, simple and reliable structure since it does not need any external devices to maintain bistability. A finite element model (FEM) and an equivalent theoretical model are developed to model a harmonically excited linear oscillator coupled with BPZA. The Runge-Kutta method is used to solve the theoretical model numerically. The effects of the excitation amplitude, the tip mass of BPZA and the load resistance are considered on the vibration suppression efficiency and energy harvesting of BPZA. The results show adjusting these parameters can improve the vibration suppression efficiency and energy harvesting of BPZA. In addition, the experimental prototype is prepared and verifies the rightness of the finite element model and theoretical model. The BPZA achieves the goal of higher power density at lower acceleration and simultaneously has a good vibration absorption effect. Maximum power of 15.8mW is generated at an excitation frequency of 22 Hz and acceleration of 0.5 g.

Interpretable sparse identification of a bistable nonlinear energy sink

Bistable nonlinear energy sinks have received great interest due to their efficient broad-band targeted energy transfer over a wide range of input energy levels. The precise identification of bistable nonlinear stiffness force is of significance to predict and enhance the system performance of the vibration energy absorption. However, the nonlinear stiffness force in nonlinear energy sink structures with local bistability is difficult to measure and identify because of snap-through characteristics. Inspired by physics-informed data-driven regression in machine learning, an interpretable sparse identification method is proposed to determine the stiffness force of a bistable nonlinear energy sink. The restoring force surface is constructed on bistable nonlinear energy sink equations and the nonlinear stiffness force trajectory is intercepted by assuming two quasi-zero velocity planes. Furthermore, the candidate functions in the sparse regression algorithm can be physically informed by conducting the least-squares parameter fitting of the intercepted nonlinear stiffness force trajectories. Numerical investigations demonstrate that the proposed method not only gives physics information but also improves the accuracy by 0.48%, 3.26% and 22.21% under the noise level of 30 dB, 20 dB, and 10 dB, respectively. Moreover, the reconstructed dynamic response has a good agreement with the theory. Experimental measurements are performed on a magnetically coupled bistable nonlinear energy sink. Results show that the accuracy improves by 4.52% and 11.76% compared to restoring force surface and Hilbert transform-based methods, respectively.

Enhancement of bistable nonlinear energy sink based on particle damper

To outperform the conventional bistable nonlinear energy sink (BNES), a particle damper bistable nonlinear energy sink (PDBNES) for torsional vibration suppression of rotor systems is designed in this paper. The nonlinear stiffness of the PDBNES is achieved by mutually repulsive magnets, while the nonlinear damping is generated using particle damping technology. Then, the dynamic model of the rotor-PDBNES system is established, and the effect of PDBNES parameters on the equivalent damping coefficient is discussed. Next, the optimization strategies for steady-state response and transient response of the rotor-PDBNES system are proposed, and a comparative study is conducted on the PDBNES and conventional BNES. Finally, the experimental test of the rotor-PDBNES system is carried out, which verifies the ability of the PDBNES to suppress the steady-state vibration of the rotor system. The results show that the vibration suppression performance of the PDBNES is better than that of the conventional BNES. For the steady-state response, the vibration suppression rate of the PDBNES is improved by 15.72% in simulations and 23.23% in experiments. In the transient response, the displacement attenuation speed of the PDBNES is increased by 22.73%, and the efficiency of TET is catalyzed.

Variable-potential bistable nonlinear energy sink for enhanced vibration suppression and energy harvesting

A variable-potential bistable nonlinear energy sink coupled electromagnetic harvesters (VBNES-EH) is proposed, that can simultaneously achieve high efficiency, broadband vibration suppression and energy harvesting under ultra-low and ultra-wide input energy level excitation. The performance is enhanced by introducing two horizontal energy harvesters (HEHs) to dynamically reduce the potential barrier height of the bistable nonlinear energy sink (BNES) or called bistable energy harvester (BEH) to form lower excitation thresholds of the chaotic and strong modulated responses. Firstly, the dimensionless mathematical model of the VBNES-EH is proposed and verified by the experiment. The experimental results are qualitatively consistent with the simulation results. The transient dynamics and the corresponding energy dissipation rates of five target energy transfer (TET) mechanisms for the weakly damped system are summarized numerically. The variable-potential energy effect and its benefits for the dual functions of vibration suppression and energy harvesting are analyzed. Afterward, the stiffness of the VBNES-EH and the fixed-potential BNES-EH (FBNES-EH) are optimized, and their energy dissipation rates under impact excitation are compared. The results indicate that the former has better performance under low- and intermediate-level impact excitations. Furthermore, the influence of system parameters on the energy harvesting rate is discussed to guide the optimal design of the performance. Finally, the dynamical evolution of the VBNES-EH and the parameter effects on the dual performance of the system under harmonic sweep excitation are investigated. Numerical results demonstrate that the VBNES-EH can achieve high performance under the different amplitudes of the harmonic excitation through stiffness optimization.

Bistable enhanced passive absorber based on integration of nonlinear energy sink with acoustic black hole beam

The nonlinear energy sink (NES) has a broader frequency bandwidth than the linear tuned-mass-damper (TMD), making it more robust. However, the NES is only efficient in a narrow energy range. The mitigation property of NES may deteriorate when input energy is too small or large. To overcome this shortage, a novel NES named ABH-BNES is proposed in this paper, by combining a bistable nonlinear energy sink (BNES, which has negative linear stiffness, cubic nonlinear stiffness, and linear damping) and acoustic black hole (ABH) beam. The negative linear stiffness and cubic nonlinear stiffness elements can generate a large cross-well motion to improve the performance of vibration mitigation for low input energy. By replacing the attached mass in traditional NES as an ABH beam, multiple high-damping modes can be introduced into the vibration absorber. So that the performance of ABH-BNES is also enhanced for large input energy. First, the Gaussian Expansion Method and Modal Approach are employed to establish the dynamic model of a single-dof linear oscillator coupling with an ABH-BNES. Such a modeling approach is verified by comparing it with the models in the existing literature and established by the finite element method (FEM). The slow invariant flow (SIM) theory and time-domain integration are employed to analyze the novel NES's vibration mitigation mechanism. In addition, a multi-solution boundary related to the existence of targeted energy transfer is derived for optimizing the nonlinear absorber. Then, the energy method is used to verify the superiority of the novel NES by comparing it with TMD, NES, and the Linear ABH absorber. The results show that the ABH-BNES can behave with an excellent mitigation effect and an extensive energy bandwidth when the parameters are appropriately selected. Finally, an experiment is carried out to verify the new NES's superiority and the correctness of the theoretical model.

Magnet based bi-stable nonlinear energy sink for torsional vibration suppression of rotor system

This paper investigates the application of a magnetic bi-stable nonlinear energy sink (MBNES) on torsional vibration suppression of the rotor system. Firstly, the structure of the proposed nonlinear energy sink is introduced, which simultaneously combines a set of positive stiffness connecting rods with the overlapping magnet negative stiffness configurations together to produce the bi-stable characteristic. Furthermore, the analytical expression of the nonlinear torsional stiffness of the MBNES is derived by applying the magnetic charge theorem, and the dynamic model of the rotor-MBNES system is established in turn. Next, the vibration attenuation performances of the MBNES under transient and steady-state excitations are evaluated, respectively, and the parameter affections are studied. Finally, experimental studies are carried out on the coupled system. The results demonstrate that adding MBNES to the main system can obtain 2.22 times dissipating speed in transient response, and the vibration suppression rates of 65.68% in simulation and 54.10% in experiment are achieved in steady-state response.

A bi-stable nonlinear energy sink using the cantilever bi-stable hybrid symmetric laminate

This paper develops a new bi-stable nonlinear energy sink (BNES) only consisting of the cantilever bi-stable hybrid symmetric laminate (BHSL) and tip masses. This BNES has advantages of light weight, simple and reliable structure, since it does not need external devices or magnets to maintain its bi-stable characteristic. A finite element model (FEM) is developed to perform static and dynamic analyses of a harmonically excited linear oscillator coupled with BNES. An equivalent theoretical model is developed to model the coupled system based on the relationship between the restoring force and the displacement of BHSL. The Runge-Kutta method is used to perform direct numerical solutions. Different types of the steady-state response for BNES contain the local and global periodic motions, the local and global strongly modulated responses and chaos, while the primary object exhibits the periodic motion and the strongly modulated response. The effects of the excitation amplitude, the tip mass of BNES, the lay-up design and the length of BHSL are considered on the dynamic responses and vibration suppression efficiency of BNES. The results show adjusting these parameters and lay-up designs can improve the vibration suppression efficiency of BNES. In addition, the experimental prototype is prepared and verifies the rightness of the finite element model and theoretical model.

Experimental study of magnetic bistable nonlinear energy sink for structural seismic control

In previous work, magnetic bistable nonlinear energy sink (MBNES) had been numerically demonstrated as an efficient absorber for seismic mitigation of shear-frame structures. The present paper, for the first time, experimentally investigates the MBNES device, as well as its control performance using both cyclic-load and shake-table tests. Both spatial magnetic force and sliding friction were included in the proposed MBNES model and the device was designed, manufactured, and assembled in the lab. The cyclic-load tests were conducted to validate and calibrate the theoretical model of the MBNES. Subsequently, a series of shake-table tests of a one-story shear frame equipped with the present MBNES device was performed. By a proposed algorithm, the numerical model of the control system was successfully identified based on the response data. A comparison of the experimental and numerical results revealed the accuracy of the identified numerical model. By using the present device, significant suppressions of the seismic responses were observed. The transient internal resonance captures of the MBNES control system can also be observed during the seismic responses. The study experimentally demonstrates the potential of the MBNES device as an efficient absorber for seismic mitigation of structures.

Hamiltonian dynamics and targeted energy transfer of a grounded bistable nonlinear energy sink

A two-degree-of-freedom nonlinear mechanical system describing a damped linear oscillator weakly coupled to a lightweight grounded bistable nonlinear energy sink is proposed to investigate the targeted energy transfer (TET) under asymmetric local nonlinear potentials. The bifurcations of equilibria are discussed to reflect the bistable and asymmetric characteristics of the system. Through projections of isoenergetic manifolds, the topological features of the Hamiltonian dynamics under 1:1 internal resonance have been investigated, which induces conditions for energy localization and exchange. In the general case, the topological features of the Hamiltonian dynamics related to the nonlinear normal modes (NNMs) are classified by the Poincaré map, the relations between the NNMs and the Hamiltonian dynamics have been interpreted through the frequency energy plots. The results show that introducing the asymmetric characteristics may enhance the TET and realize the complete TET.

Experimental testing and system identification of the sliding bistable nonlinear energy sink implemented to a four-story structure model subjected to earthquake excitation

Bistable nonlinear energy sink system has been explored as an efficient vibration absorber in many areas. This paper aims to experimentally validate the seismic mitigation performance of sliding bistable nonlinear energy sink (SBNES) for multi-story building structures. An SBNES device was designed and placed on top of a four-story building structure model. Earthquake ground motions were applied through a shake table as the base excitation input into the structure model. By matching the time history envelope curves between the experiment and numerical simulation, the structural parameters of the primary structure, as well as the constitutive model of the SBNES, were experimentally determined. The comparisons between mitigated and unmitigated structural responses, including inter-story drift, acceleration, base-shear force and base-overturning moment of the primary structure, show that substantial reduction of structural seismic responses can be achieved by the SBNES device. The 1:1 transient internal resonance is verified as the dominant scheme for highly efficient targeted energy transfer. With respect to variation of peak ground acceleration, a relatively optimal interval distributed near the borderline of intra-well and inter-well regime is proposed for robust SBNES design. The test validates the potential of the SBNES strategy for both acceleration and displacement control of multi-story building structures.

Qualitative analysis of the response regimes and triggering mechanism of bistable NES

The main focus of this study is the development of an adapted complex variable method with respect to the equilibrium point in bistable nonlinear energy sink (NES), which is mainly investigated in the vicinity of 1:1 resonance. A simplified chaos trigger model is established to describe the distance between the stable phase cycle and the pseudo-separatrix. An analytical expression can predict the excitation threshold for chaos occurrence. The relative positions between the chaos trigger threshold line and the slow invariant manifold structure can interpret the distribution of response regimes under growing harmonic excitation. The degeneration of the response regimes can be demonstrated by the qualitative analysis method, which helps to classify the bistable NES. The experiment confirms the analytical result of intra-well oscillation in the frequency domain. The characteristic response regimes of weak, modest, and strong bistable NES are identified by the experimental results.

Estimation of Energy Pumping Time in Bistable Nonlinear Energy Sink and Experimental Validation

Abstract The bistable nonlinear energy sink (NES) shows high efficiency in mitigating vibration through targeted energy transfer (TET). It performs well in low- and high-energy input cases, whereas, for a cubic NES, TET occurs only above a certain energy threshold. In this work, the measure of energy pumping time is extended to a harmonic excitation case by the application of a particular integration assumption. An equivalent point in the slow invariant manifold (SIM) structure can represent the average variation of the amplitudes of linear oscillator (LO) and NES. The marked robustness of this semi-analytical prediction method under parameter perturbation is investigated numerically here. The influence of parameters on the rate at which the amplitude declines is also investigated for both impulsive and harmonic excitation. The pumping time estimation is validated in a low-energy input experimental test.

Micro-amplitude vibration suppression of a bistable nonlinear energy sink constructed by a buckling beam

Micro-amplitude vibration suppression of a bistable nonlinear energy sink constructed by a buckling beam