Nonlinear Energy Sink System Research Articles

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

On formation, annihilation, and evolution of potential wells, and nonlinear phenomena of multi-magnet energy sink system.

This paper investigates the formation, annihilation, and evolution mechanisms of potential energy wells in nonlinear energy sink systems. The nonlinear energy sink system is composed of multiple inner and outer magnets. Two multi-magnet energy sink (MES) architectures are designed: a single-magnet vibrator and a double-magnet vibrator. Multi-stable (bi-, tri-, quad-, penta-, hexa-, and hepta-stable) mechanisms are elaborated by the Poincaré section and bifurcation diagram concerning the magnet length, the link length, and the MES configuration. The results show that the change in the internal structural parameters of the MES system will generate different types of bifurcations (i.e., saddle-node, subcritical, and super pitchfork bifurcations) and phase trajectories and have rich nonlinear response behaviors in the low frequency and wide frequency range, which can be used for damping and vibration reduction of engineering structures, vibration control, and energy source of the microgrid.

Energy Transfer and Dissipation in Combined-Stiffness Nonlinear Energy Sink Systems

Abstract Nonlinear energy sinks (NES) are highly efficient vibration energy absorption and dissipation devices, and play an important vibration-suppression role in many types of structures. In this study, the influence of parameters on the combined stiffness nonlinear energy sink system is revealed from the perspective of energy, in which combined-stiffness terms are composed of piecewise linear stiffness and cubic stiffness. First, the slow-varying derivative of the combined-stiffness nonlinear energy sink system is calculated based on the complexification-averaging and multiscale methods. Second, an approximate expression for the extreme points on the slow-invariant manifold (SIM) of the system is derived by polynomial approximation, and the energy dissipation equation of the combined-stiffness nonlinear energy sink system is derived. The impacts of the stiffness gap, piecewise linear stiffness coefficient, and cubic stiffness coefficient on the system are analyzed by studying the energy transfer efficiency equation. Additionally, the relationship between the damping ratio of the primary structure and the dissipation time is analyzed.

Research on the optimal excitation threshold interval of targeted energy transfer for piezoelectric nonlinear energy sink

In this paper, in order to design a piezoelectric nonlinear energy sink system (NES), a coupling system of elastic plate and piezoelectric nonlinear energy sink is established. The nonlinear stiffness and damping are realized by the shunt circuit of piezoelectric materials. By using the harmonic balance method to analyze the forced vibration characteristics of the coupling system, it is found that within a certain range of harmonic excitation amplitude, the targeted energy transfer (TET) phenomenon occurs in the system. There is a threshold interval for the TET phenomenon of the system, where the TET does not occur when the excitation is less than the lower limit of the threshold. When the excitation exceeds the upper limit of the threshold, the system response appears a new high amplitude branch. The definite solution to the lower limit of the excitation threshold is determined, but when the system parameters are different, the high amplitude branch of the system response will appear above or below the amplitude of the platform. The results of this paper give the solution of the optimal TET excitation threshold interval in these two different cases and are helpful to design a NES for different applications.

Quasi-periodic oscillation characteristics of a nonlinear energy sink system under harmonic excitation

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation.

Mitigating jacket offshore platform vibration under wave loadings utilising nonlinear energy sinks

ABSTRACT The random vibrations of jacket offshore platforms caused by wave loadings can reduce the service life and fatigue failure of the offshore platforms. The nonlinear energy sink (NES) has great application potential because of its lightweight, high robustness and wide frequency band of vibration attenuation. The NES is introduced to mitigate the vibrations of the jacket offshore platform as a passive control device under wave loadings. The dynamic model of jacket platforms is developed with the NES system. The optimal parameters of the NES system are obtained by exhaustive search method. The results show that the NES system can effectively mitigate the responses of the deck level of jacket platforms under different wave states. The NES system could reduce the response under various deck's mass and stiffness of jacket platforms. The present study proves the feasibility of the NES system in the application of vibration control for marine structures.

Dynamic Analysis and Piezoelectric Energy Harvesting from a Nonideal Portal Frame System including Nonlinear Energy Sink Effect

This paper investigates, through numerical simulations, the application of piezoelectric materials in energy generation. The mathematical model describes a U-shaped portal frame system, excited by an engine with unbalanced mass and coupled to a nonlinear energy sink (NES), which is used as a passive vibration absorber. The influence of the piezoelectric material parameters used in the energy collection and the dimensioning parameters of the NES system is deeply analyzed in this paper. Numerical simulations are presented considering all combinations of the parameters of the piezoelectric material model and the NES. The system dynamics were analyzed through phase diagrams and the 0–1 test. The estimation of energy collection was carried out by calculating the average power. The numerical results show that a more significant potential for energy generation is obtained for certain combinations of parameters, as well as chaotic behavior in some cases.

The vibration mitigation of jacket offshore platform based on inerter nonlinear energy sink

The application of the traditional passive vibration control system is limited by the demand for large mass. To ameliorate this situation, the inerter nonlinear energy sink (NES) is introduced and applied, as the substitute for the traditional passive vibration control system, to vibration mitigation of jacket offshore platform under random wave loading, since it has the clear advantage of obtaining apparent vibration control effect through low amounts of added mass. For one thing, the equation of jacket offshore platform including inerter NES is developed considering wave loads. For another, the optimal parameters of inerter NES are obtained through Particle Swarm Optimization (PSO) using numerical simulations. Both analytical and numerical results strongly support that the inerter NES contributes greatly to vibration suppression, compared with traditionally tuned mass dampers (TMD). To explore more practical benefits, further comparison between the vibration mitigation of inerter NES and the optimal TMD system, considering different masses and stiffness, is made right after, which verifies the effectiveness and robustness of inerter NES. Based on the above study and results, it proves valid to conclude that the inerter NES system allows practical application of vibration mitigation for marine structures.

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.

Shaking table test study on seismic performance of RC frame structure with NES

A new type of nonlinear vibration absorber NES (Nonlinear Energy Sink) studied in this paper belongs to the structural passive control technology, which consists of a horizontal track and an additional mass block. Acting as a damper absorb and dissipate energy, the NES completes the target energy transfer by generating a horizontal nonlinear restoring force and reduces the response of the main structure. In this paper theoretical analysis of the new NES was analyzed by the expression of the restoring force of the NES and the equation of motion of the additional NES system are deduced. Shaking table test was carried out on the 1:4 scale RC frame structure model installed with the new NES shock absorber, focusing on the research on the energy dissipation and shock absorption effect of the NES shock absorber, and whether it can improve the seismic performance of the RC frame structure damaged in the earthquake. The results show that the NES installed in the RC frame structure has sufficient nonlinear displacement and energy dissipation capacity under the moderate and strong earthquakes, showing a very good energy dissipation and shock absorption effect. The NES can reduce the top story displacement and acceleration response of the main structure under the action of earthquake; the top story displacement and absolute acceleration response are related to the natural frequency of the frame and the spectral characteristics of seismic waves, so that the vibration control effect is affected by the frequency spectrum of seismic waves. In the frequency domain analysis of the frame dynamic response, the nonlinear energy well exhibits the characteristics of broadband control. This type of NES significantly reduces the seismic response of damaged structures, improves the seismic performance of damaged structures under moderate to strong earthquakes, and decreases the risk of potential collapse and construction costs during earthquake aftershocks.

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.

Singularity analysis on vibration reduction of a nonlinear energy sink system

Nonlinear energy sink (NES) can be used to reduce the forced vibration of the primary system. Many different kinds of periodic responses of the linear system coupled with NES have been presented in the literature. In order to reveal all kinds of periodic responses of the NES system on given parameter planes, this study intends to achieve the classification of different kinds of periodic responses of linear oscillator coupled with a NES under harmonic excitation, which is modeled as a 2-degree-of-freedom system. The amplitudes of periodic responses of the nonlinear system are obtained by using the harmonic balance method. Then a general method based on the singularity theory is proposed to reveal all kinds of periodic responses under a given set of parameters. The periodic responses include 10 kinds known responses and 4 kinds of newly-revealed responses. The complete classification of the responses ensure the reliability and the efficiency of a NES.

A new semi-analytical approach for quasi-periodic vibrations of nonlinear systems

This paper presents a new semi-analytical approach, namely the enhanced time-domain minimum residual method to solve the semi-analytical quasi-periodic solution for nonlinear system. This approach does not require multiple numerical integration and can be applied to strongly nonlinear systems. The approach is mainly three-fold. Firstly, the semi-analytical solution of the nonlinear quasi-periodic system is expanded into a set of trigonometric series with unknown coefficients, i.e., x(t)≈∑k=1N[bkcos(ωkt)+cksin(ωkt)]. Then, the problem of solving quasi-periodic solution can be expressed as: determining the coefficients of the trigonometric series so that the residual objective function R=Mx¨+Cx˙+Kx+N(x¨,x˙,x,t)−F(t) is minimum over a period, i.e., mina∈A∫0TR(a,t)TR(a,t)dt. Finally, the nonlinear minimum optimization problem is solved iteratively through the enhanced response sensitivity approach. Moreover, the “adaptive zero-setting curve” is introduced to accelerate the convergence. Two numerical examples, a van der Pol-Duffing system and a nonlinear energy sink system are adopted to verify the feasibility of the proposed approach.

Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping, and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

Modeling and harmonic analysis of energy extracting performance of a piezoelectric nonlinear energy sink system with AC and DC interface circuits

Nonlinear energy sink (NES) has been successfully integrated with vibration energy harvesters to enhance energy extracting performance in a broadband manner. This article intends to evaluate a piezoelectric energy harvester based on the NES technique and coupled to a pure resistive load (EHNES-AC) and a standard rectifying energy extracting circuit (EHNES-DC) under harmonic excitation. A new approach for the analysis of the EHNES-DC system is proposed by simplifying the DC circuit on the basis of the equivalent impedance method (EIM). The theoretical solutions and analyses of the EHNES-AC system, the EHNES-DC system with an original DC circuit based on Shockley diode model and the EHNES-DC system with a simplified DC circuit based on EIM are then derived by the harmonic balance method (HBM). On the other hand, the holistic circuit simulation is performed by employing the equivalent circuit model (ECM) to validate those approximate theoretical analyses. With the assistance of the proposed models and simulation tool, the effect of the load resistance on the efficiencies of the EHNES-AC and EHNES-DC systems is parametrically studied. Experiments are also conducted and verify the main conclusions given by theoretical and numerical studies.

Vibration Control of Conveying Fluid Pipe Based on Inerter Enhanced Nonlinear Energy Sink

Many fundamental studies have indicated that the vibration of conveying fluid pipe is more severe and complex at high subcritical fluid velocity. The control of vibration in this case, however, still remains a challenge for the general vibration absorbers. In this work, the inerter enhanced nonlinear energy sink (NES) is used to solve the severe vibration problem. The partial differential equation form model of the conveying fluid pipe-inerter enhanced NES system is derived and converted to an ordinary differential equation with an easy solution. Global stability of the conveying fluid pipe-inerter enhanced NES system is proved under the Lyapunov stability theory framework and functional analysis technique, to explain the effectiveness of the inerter enhanced NES. The influence of parameters on the conveying fluid pipe is discussed through a sensitivity analysis. The parameters of the proposed controller are optimized based on the energy functional. Finally, numerical examples are provided to verify the control effectiveness and the theoretical results, and also to show the advantages of inerter enhanced NES by comparing with the general NES.

Effect of Electromechanical Coupling on Dynamic Characteristics of a Piezoelectric Nonlinear Energy Sink System

Integrating a piezoelectric nonlinear energy sink (NES) to a host structure has recently been used to realize simultaneous vibration control and energy harvesting. This paper investigates a piezoelectric NES system connected with a resistive load, revealing the influence of the electromechanical coupling on the nonlinear dynamic phenomena and the consequent energy harvesting performance under impulsive and harmonic excitations. For impulsive excitation, the periodic orbits of the electromechanical system are analysed based on the complexification-averaging method and validated by the wavelet transform of the damped response from numerical simulations. For harmonic excitation, the steady-state response of the displacement and power output can be obtained by the utilization of the Newton-enabled harmonic balance method (NHBM) and numerical simulations. The frequency–energy plot shows the evolution of the backbone branches due to the equivalent electrical stiffness induced by the piezoelectric transducer. Furthermore, for the steady-state response, the influence of the electromechanical coupling on the vibration suppression performance, the harvested power as well as the operational bandwidth are illustrated. In addition to the direct effect on the energy conversion efficiency, the results indicate that the increase of electromechanical coupling will eventually deactivate energy localization phenomenon in the NES for both impulsive and harmonic excitation, which will also affect the energy harvesting performance.

Reliability-based optimization of nonlinear energy sink with negative stiffness and sliding friction

This paper presents implementation of a reliability-based design optimization (RBDO) for Nonlinear Energy Sink (NES) system. The RBDO is implemented with consideration of uncertainties in structural system's parameters and ground acceleration. Negative stiffness based NES and sliding friction are utilized to enhance passive targeted energy transfer from the primary structure to the proposed control device. For a one-story steel moment resistant frame, shake table tests were carried out to show effectiveness of the NES, and the results are used to validate numerical models. Sensitivity analysis is carried out to demonstrate the performance envelops of the proposed control strategy for different stiffness ratios and peak ground acceleration values. Reliable performance of the proposed controller, through tuning parameters of the proposed NES, are determined through the RBDO framework. To reduce computational time, polynomial-chaos-based Kriging surrogate model is used in the RBDO analysis. The numerical results demonstrate efficiency of finding optimal design parameters of the proposed NES system under uncertainties with reasonable computational effort.

Stochastic reduced-order models for stable nonlinear ordinary differential equations

Two methods based on stochastic reduced-order models (SROM) are proposed to solve stochastic stable nonlinear ordinary differential equations. One general method available for the probabilistic characterization of the response of nonlinear systems subjected to random excitation is Monte Carlo (MC), wherein the response of the nonlinear system must be calculated for a large number of samples of the input, which can be very computationally demanding. Random vibration theory is also inadequate for calculating response statistics for both linear systems under non-Gaussian inputs and nonlinear systems subjected to any kind of excitation. The two methods proposed are based on SROM, i.e., stochastic models with a finite number of optimally selected samples. The first method uses a SROM model for the random input. The second method is based on a surrogate model for the response of the nonlinear system defined on a Voronoi tessellation of the input samples. The newly proposed methods are applied for stable nonlinear ordinary differential equations, with deterministic coefficients and stochastic input, that are used in engineering applications: single-degree-of-freedom Duffing and Bouc–Wen systems, and a two-degree-of-freedom nonlinear energy sink system. The numerical results suggest that SROMs are able to estimate statistics of the stochastic responses for these systems efficiently and accurately, results validated by the benchmark MC results.

Aeroelastic suppression of an airfoil with control surface using nonlinear energy sink

Aeroelasticity exists in airfoil with control surface freeplay, which may induce instability in an incompressible flow. In this paper, a nonlinear energy sink (NES) is used to suppress the aeroelasticity of an airfoil with a control surface. The freeplay and cubic nonlinearity in pitch are taken into account. The harmonic balance method is used to analytically determine the limit cycle oscillations (LCOs) amplitudes of the airfoil–NES system. Linear and nonlinear flutter speeds are detected from the airfoil with control surface freeplay. When NES is attached, both the linear flutter speed of airfoil without freeplay and the nonlinear flutter speed of airfoil with a freeplay are increased. Moreover, the LCO amplitude of airfoil is decreased due to NES. Then, the influences of NES parameters on the increase in flutter boundary of airfoil are carefully studied.