Design Of Nonlinear Energy Sink Research Articles

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.

An Energy Transfer-Based Bifurcation Detection Method for Nonlinear Rotating Systems: Enables Accurate Capture of Period-Doubling Bifurcation and Instability

Rotor systems are widely used in industrial power generation and propulsion. Once the nonlinear contact stiffness and oil film force are taken into account, the dynamics and stability of rotor systems become quite complex, often accompanied by super-harmonic and chaotic motions. Furthermore, conventional methods face limitations in real-time detection of the bifurcations and complex nonlinear motions. This research investigates the bifurcations and stability induced by nonlinear factors in a rotor-bearing system from an energy perspective. Dynamic equations of a rotor-bearing system considering cubic term stiffness are established, the steady responses are obtained by the fourth-order Runge–Kutta method. The relationship between the bifurcations and energy transfers is analyzed numerically, the proposed stability criterion is validated by comparing the Lyapunov exponents. The bistable phenomenon of period-3[Formula: see text] ([Formula: see text]) motion is discussed in terms of numerical results and experiments which corresponds to the asymmetric jumps of the generalized energy. It is found that bifurcations and unstable motions of the nonlinear system can be captured accurately by detecting the energy transfers, the proposed generalized energy curve exhibits more detailed information than the conventional speed-up curve. These findings provide a new perspective on studying bifurcations and stability of rotating systems, which can be further applied in the condition monitoring, stability prediction as well as the design of nonlinear energy sink, representing significant progress in converting theory into engineering applications for rotor systems.

Power Spectrum Analysis and Optimization Design of Nonlinear Energy Sink Under Random Excitation

Power Spectrum Analysis and Optimization Design of Nonlinear Energy Sink Under Random Excitation

Characteristic analysis and design of nonlinear energy sink with cubic damping considering frequency detuning

Characteristic analysis and design of nonlinear energy sink with cubic damping considering frequency detuning

Data-driven optimization for flutter suppression by using an aeroelastic nonlinear energy sink

Aeroelastic systems are at risk of flutter instabilities which can lead to structural failure. Recently, an innovative design of nonlinear energy sink (NES) has been introduced to suppress flutter instabilities by adding a NES to the flap control surface as a nonlinear energy absorber resulting in a flap-NES. Optimal choice of flap-NES parameters, however, requires a comprehensive characterization of the nonlinear response of the system in the design space. Performing this nonlinear analysis using traditional approaches demands massive theoretical and computational efforts. This work is a foundational study of flap-NES-based flutter control of a typical pitch–plunge section and focuses on obtaining flap-NES parameters using a data-driven optimization algorithm. The optimization is based on a genetic algorithm combined with a recently introduced data-driven bifurcation forecasting method that allows constructing the bifurcation diagram of the system dynamics using limited time series data. Results of this study show that an optimal design of the flap-NES system results in an increased linear flutter speed, reduced post-flutter limit cycle oscillation amplitudes, and improved nature of the bifurcation diagram from subcritical to supercritical.

Passive suppression of vortex-induced vibrations using a nonlinear energy sink—Numerical and analytical perspective

This study investigates the suppression mechanism of instabilities induced by fluid–structure interactions (FSI) using passive vibration absorption devices, such as nonlinear energy sink (NES). The present FSI framework comprises a low-order phenomenological model, wherein the wake effect is modeled using the classical Van der Pol oscillator. The structure is represented as a cylindrical bluff body with degree-of-freedom along the cross-flow direction. The response of the NES-augmented structure exhibits specific relaxation type oscillations, referred to as strongly modulated response (SMR), passively suppressing the high amplitude vortex-induced vibrations (VIV). The underlying mechanism of SMR is studied using an analytical approach based on the Complexification-Averaging (CXA) technique. Using the CXA technique, the slow flow for the coupled FSI system with the NES attachment is modeled effectively, revealing nonlinear beating regimes and initiation of the targeted energy transfer (TET) mechanism. Subsequently, a transient resonance capture, implying a significant energy transfer from the structure to the NES, results in effective VIV suppression. The occurrence of SMRs is explained by analyzing the global dynamics using the slow invariant manifold (SIM) derived from the slow flow of the coupled system. The resultant SIM topology reveals a jump phenomenon between the stable branches, wherein the flow jumps from a lower stable branch to a higher stable branch through SMR. The novelty of this study lies in identifying the occurrence of SMRs as the mechanism of energy transfer and uses the CXA technique to explain the global dynamics by modeling the SIM for the 3-DOF coupled FSI framework with the NES attachment. Furthermore, the optimal operational parameter ranges for an efficient NES design are identified through a parametric study using the slow-flow model.

The Parameter Design of Nonlinear Energy Sink Installed on the Jacket Pipe by Using the Nonlinear Dynamical Theory

The aim of this paper is to investigate the vibration suppression effect of a nonlinear energy sink (NES) on the wind-vortex-induced vibration of deep-water jacket pipes. Based on nonlinear dynamical theories, the coupled dynamic equation of a deep-water jacket pipe with NES was established, and the nonlinear response characteristics and motion stability of the system were studied by using the multi-scale mixed harmonic balance method and Routh–Hurwitz criterion. The paper also analyzed the influence of the nonlinear stiffness and damping parameters of an NES on the dynamic response of the pipe. It is concluded that when the nonlinear stiffness of an NES increases to a certain extent, the motion response of the pipe appeared as a saddle-node and Hopf bifurcation, and the vibration amplitude of the pipe is greatly suppressed. For a system with nonlinear motion, NES damping mainly affects the range of the unstable region. For the system without nonlinear motion, the increases in NES damping will reduce the amplitude near the resonance region. Selecting proper parameters of an NES nonlinear stiffness and damping can effectively suppress the vortex-induced vibration of pipes.

A Nonlinear Energy Sink Design to Attenuate the Torsional Oscillations of Lightly Loaded Gear Pairs

Nonlinear energy sinks (NES) have recently attracted significant interest for the suppression of unwanted vibrations in a variety of mechanical systems. The key advantage in employing this (vibration absorber) approach is the broadband nature of the interactions with a primary system for which vibration energy dissipation is required. Thus, the effectiveness of the NES is decoupled from the need of tuning to specific frequencies. Nevertheless, NES for rotational fluctuations of powertrains have received limited attention in the literature. In this work, a design for a rotational NES to mitigate speed fluctuations in gear trains is presented and tested experimentally. The development of the proposed system is underpinned by previous optimisation studies conducted by the authors, where a disk was utilised as an inerter NES. A set of beams couple the inerter with the wheel gear of a spur gear pair with a nonlinear restoring torque, which is designed to approach the desired essential nonlinearity within realistic practical tolerances. Static and dynamic identification is conducted to confirm the desired characteristics. Despite uncertainties in the prototype testing, the approach is found to reduce the speed fluctuations on the gear pair output shaft, with appropriate predictability established for the model and the design procedure.

Passive fluid-induced vibration control of viscoelastic cylinder using nonlinear energy sink

This study focuses on the performance of the nonlinear energy sink (NES) in passive controlling the cantilever cylinder vibrations subjected to the external fluid flow. The nonlinear differential equations of motion are obtained by considering the large strain-displacement relation and viscoelastic behavior. Wake oscillation in fluid-structure interaction is modeled based on the Van der Pol wake oscillator model with is the classic acceleration coupling between the cross-flow motion and wake. Based on the Von Karman strain-displacement relation, and Euler-Bernoulli beam theory, the nonlinear vibration equations which are coupled with attached NES motion are obtained using Newton's second law, and discretized by applying the Galerkin method. The fluid flow velocity and nonlinear stiffness, damping, and mass of the NES are studied to determine their effects on the vibration response of the system. The present study comprehensively evaluates the effects of adding a NES on the lock-in phenomenon and maximum oscillating amplitudes of a cantilever cylinder, and guides to determine the best design of NES for significant fluid-induced vibration mitigation.

Mass design of nonlinear energy sinks

Nonlinear energy sink (NES) is attracting more attention because of its promising in the control of engineering structure vibration. This paper thoroughly reviews the selection of NES mass ratios in existing studies and finds the big difference. So there is still a lack of a unified and profound understanding of the mass design of the NES. To achieve decent vibration mitigation and reduce costs, the mass design of the NES is essential. This paper pioneers the optimal mass design of NESs. The non-dominated sorting differential evolution algorithm and parameter sensitivity analysis are adopted. The relations between the optimal mass and the vibration mitigation effects are discussed in different damping and harmonic excitation strength. The results show that different from the monostable NES, the bistable NES with a small mass ratio (no more than 0.7%) and small damping can reduce 30% of the resonance peak of the primary system in most situations. However, both these two NESs with large damping need larger mass ratios to achieve decent vibration mitigation. Smaller damping of the primary system will contribute to wider effective ranges of the mass ratio of the two NESs, while larger excitation will contribute to those of the monostable NES. To ensure the vibration mitigation effects in small mass ratio, the monostable and bistable NESs with small damping need large and small cubic stiffness, respectively. Besides, the bistable NES with small damping prefers small negative linear stiffness. In summary, this paper presents a detailed study of the mass design of the nonlinear energy sink. It will help researchers and engineers find the suitable mass and design NES in the vibration reduction of engineering structures.

Basic Constraints for Design Optimization of Cubic and Bistable Nonlinear Energy Sink

Abstract This work mainly concentrates on the optimization of cubic and bistable nonlinear energy sink (NES) to find the maximum efficiency point under harmonic excitation. The conservative system is considered to reveal the inner property of the damping system. With the application of the multiple scales method and the complex variables method, the threshold of excitation and different response regimes are distinguished under the assumption of 1:1 resonance. The maximum efficiency point of cubic and bistable NES occurs when strongly modulated response disappears. The factors that affect the optimal efficiency limit are explored. The result indicates that the maximum absorption efficiency level is mainly determined by the damping parameters. Compared with the cubic case, the bistable case involves more complex regimes in terms of chaos oscillation. The influence of damping parameters on the chaos threshold is discussed to adopt different energy levels. With the help of analytical predictions, the proper nonlinear stiffness is determined for certain harmonic excitation. This study offers some fundamental insights into the optimal design of cubic and bistable NES.

Robust design optimization of nonlinear energy sink under random system parameters

Generally, in designing nonlinear energy sink (NES), only uncertainties in the ground motion parameters are considered and the unconditional expected mean of the performance metric is minimized. However, such an approach has two major limitations. First, ignoring the uncertainties in the system parameters can result in an inefficient design of the NES. Second, only minimizing the unconditional mean of the performance metric may result in large variance of the response because of the uncertainties in the system parameters. To address these issues, we focus on robust design optimization (RDO) of NES under uncertain system and hazard parameters. The RDO is solved as a bi-objective optimization problem where the mean and the standard deviation of the performance metric are simultaneously minimized. This bi-objective optimization problem has been converted into a single objective problem by using the weighted sum method. However, solving an RDO problem can be computationally expensive. We thus used a novel machine learning technique, referred to as the hybrid polynomial correlated function expansion (H-PCFE), for solving the RDO problem in an efficient manner. Moreover, we adopt an adaptive framework where H-PCFE models trained at previous iterations are reused and hence, the computational cost is less. We illustrate that H-PCFE is computationally efficient and accurate as compared to other similar methods available in the literature. A numerical study showcasing the importance of incorporating the uncertain system parameters into the optimization procedure is shown. Using the same example, we also illustrate the importance of solving an RDO problem for NES design. Overall, considering the uncertainties in the parameters have resulted in a more efficient design. Determining NES parameters by solving an RDO problem results in a less sensitive design.

Optimal design of nonlinear energy sinks for mitigation of seismic response on structural systems

This paper proposes an approach for the optimal design of nonlinear energy sinks (NES) installed in structures subjected to stochastic excitation. The response of these nonlinear systems subjected to stationary or non-stationary stochastic excitations has been characterized by the time-history of its covariance matrix. However, time-invariant equivalent linearization methods of NES equipped structures will not always converge due to its essential nonlinearity. A solution strategy is proposed using equivalent linearization at each time step of the governing matrix differential equation, obtained through a sequence of Lyapunov equations. The adequacy of this method for optimization problems is evaluated by comparison with Monte Carlo simulations of two representative NES examples. Moreover, the influence of the Gaussian assumption of the equivalent system response is studied in these examples. An optimization formulation to design systems equipped with NES devices is proposed, in which the performance function is defined in terms of the maximum variance over the time-history. This result is obtained by using the proposed method with a Gaussian assumption of the equivalent linear system. To illustrate the proposed methodology, parametric optimization of an NES installed at the top of a shear building structure is performed.

Nonlinear energy sink and Eurocode 8: An optimal design approach based on elastic response spectra

In this paper, the authors propose novel empirical formulae for the optimal design of Nonlinear Energy Sinks (NESs) to control seismic induced vibrations in structures. While large part of the existing literature on NES for seismic applications is based on deterministic analyses of the structural response to recorded ground motions, herein the effectiveness of the device is studied in a stochastic framework. In fact, the seismic excitation has been modeled using a response spectra consistent power spectral density function, taking into account design spectra prescribed into Eurocode 8. Statistics of the structural response have been determined by Monte Carlo Simulations, performing nonlinear time-domain analyses to investigate the dependence of the optimal NES parameters on the main characteristics of the primary system and on the seismic load amplitude. The outcomes of these analyses have been translated into empirical expressions allowing for computing the optimal NES stiffness and damping. Since these are closed-form relationships depending on the main structure and the response spectra parameters, their use allows for an immediate estimate of the NES optimal design configuration, avoiding demanding numerical analyses and making their implementation suitable for practical engineering purposes. The accuracy of the design formulae has been tested by comparison with numerical optimisations for a set of possible configurations of the main structure and for varying intensity of the external excitation. Although the proposed relationships have been extrapolated from single degree of freedom system responses, applications to multi degree of freedom structures is quite straightforward, as shown through two case studies involving the analysis of a 2D multi-storey structure and a 3D multi-bay frame controlled by two orthogonal NESs.

Performance of non-smooth nonlinear energy sink with descending stiffness

The traditional nonlinear energy sink (NES), i.e., a smooth and cubic NES, can cause stable higher branch of response of primary systems with increasing excitation forcing. For this reason, the traditional NES is only effective in a certain excitation range. A kind of non-smooth NES with descending stiffness is proposed for expanding this effective range. The non-smooth NES has a higher cubic nonlinear stiffness in the initial range, and the stiffness is reduced as its amplitude exceeds the initial range. The governing equation of motion for a linear primary oscillator attached to the non-smooth NES is obtained in the case of harmonic excitation. The complexification-averaging method is used to obtain the steady-state equation of the system. A least square-based program with the help of a Runge–Kutta-based program is used to analyze the dynamic behaviors of the system. The results demonstrate that the non-smooth NES can eliminate the stable higher branch, therefore expanding the effective excitation range, until the excitation amplitude increases to a very high level. The influences of the piecewise boundary and the stiffness of the secondary stage of the non-smooth NES on the vibration absorption performance are investigated, and the drawbacks of this NES design are discussed. Finally, a structural design based on the theoretical results of the non-smooth NES is proposed, which is composed of permanent magnets, a smooth and discontinuous oscillator and linear springs.

Rotary-impact nonlinear energy sink for shock mitigation: analytical and numerical investigations

The nonlinear energy sink (NES) is a lightweight, strongly nonlinear dynamical attachment coupled to a (typically linear) large-scale primary structure for passive vibration mitigation. There are two nonlinear mechanisms governing the dynamics of the coupled system: irreversible targeted energy transfer (TET) from the primary structure to the NES, where energy is confined and locally dissipated, and NES-induced nonlinear energy scattering between the structural modes of the primary structure. In the literature, different NES designs have been investigated to optimize their nonlinear effects on the primary structures. One such design is the rotary NES consisting of a small mass inertially coupled to the primary structure through a rigid arm; another is the vibro-impact NES with non-smooth nonlinearities and inelastic collisions with the primary structure. These types have been found to achieve strong and rapid TET and are less sensitive to energy fluctuations. In this work, a hybrid NES design is proposed based on the synergetic synthesis of the rotary and impact-based NESs in a single rotary-impact NES (RINES). The RINES incorporates a fixed rigid barrier attached (typically) to the top floor of the primary structure to inflict impacts between its rotating mass and the top floor. An analytical study to evaluate its capacity to engage in resonance capture with a primary structure is presented first, followed by numerical investigations of cases when the RINES is attached to the top floors of small- and large-scale linear primary structures under impulsive excitation. The non-smooth nonlinearities induced through the consecutive impacts resulted in effective broadband shock mitigation at highly energetic response regimes, whereas the nonlinear inertial coupling enables similar beneficial mitigation capacity at lower-energetic response regimes. Hence, the combined effect of non-smooth and inertial nonlinearities enables effective passive mitigation capacity for a broad range of applied impulsive energies.

Nonlinear energy transfer from an engine crankshaft to an essentially nonlinear attachment

This study proposes an application of lightweight vibration control strategy known as nonlinear energy sink (NES) to mitigate the undesired vibrations in engine crankshaft systems. Linear vibration absorbers have long been used to suppress undesired vibrations. These devices can be tuned to reduce vibrations at a single frequency while adding extra inertia to the powertrain system. On the contrary, the NES is a lightweight vibration energy absorber. The presence of essential nonlinearity in the NES design provides the means for realization of irreversible targeted energy transfer (TET) from the primary system to the NES and attenuation of energy over a wide range of frequencies. This study introduces the conditions critical to achieve TET through its mathematical analysis and understanding the dynamical mechanisms governing this phenomenon in a strongly nonlinear transient dynamical system.

On the energy transfer mechanism of the single-sided vibro-impact nonlinear energy sink

In this paper, the vibration energy transfer mechanism of the single-sided vibro-impact (SSVI) nonlinear energy sink (NES) is studied. The concept of impact mode is proposed where the device velocities are decomposed into an energy free impact mode (EFIM) and an energy dissipation impact mode (EDIM). The impact modes are applied to the analysis of a single-degree-of-freedom (SDOF) vibration system with a SSVI NES. This analysis shows that the energy in the system can be redistributed between the different impact modes and that energy transferred from the EFIM to the EDIM is beneficial, because portions of the energy in the EDIM will be dissipated by impact, while the energy in the EFIM will not. More importantly, the mechanism of the SSVI NES to realize the local dissipation of energy is revealed. Furthermore, in order to better evaluate the energy dissipation performance of the SSVI NES, a new evaluation criterion called the vibro-impact vibration reduction (VVR) factor is proposed. Then, the relationship between the VVR factor and the energy free impact mode coefficient is investigated using the Hilbert transform. Finally, the effect of the SSVI NES parameters on the energy dissipation performance of the SSVI NES with various initial conditions is discussed, and a satisfactory region for the SSVI NES design, which is identified via numerical simulation, is proposed.

Tuned Nonlinear Energy Sink With Conical Spring: Design Theory and Sensitivity Analysis

This paper is devoted to the study of a nonlinear energy sink (NES) intended to attenuate vibration induced in a harmonically forced linear oscillator (LO) and working under the principle of targeted energy transfer (TET). The purpose motivated by practical considerations is to establish a design criterion that first ensures that the NES absorber is activated and second provides the optimally tuned nonlinear stiffness for efficient TET under a given primary system specification. Then a novel NES design yielding cubic stiffness without a linear part is exploited. To this end, two conical springs are specially sized to provide the nonlinearity. To eliminate the linear stiffness, the concept of a negative stiffness mechanism is implemented by two cylindrical compression springs. A small-sized NES system is then developed. To validate the concept, a sensitivity analysis is performed with respect to the adjustment differences of the springs and an experiment on the whole system embedded on an electrodynamic shaker is studied. The results show that this type of NES can not only output the expected nonlinear characteristics, but can also be tuned to work robustly over a range of excitation, thus making it practical for the application of passive vibration control.

Activation characteristic of a vibro-impact energy sink and its application to chatter control in turning

The ultimate goal of this paper is to propose a procedure for the optimal design of a Vibro-Impact (VI) Nonlinear Energy Sink (NES) to control the vibration of any possible linear or nonlinear main systems. To this end, the activation characteristic of VI NES at a range of displacement amplitude of a main system is generalized from linear systems to nonlinear systems. It is theoretically proved and experimentally observed that this activation characteristic is almost independent of frequency, which provides direct proof for the effectiveness of VI NES in a broad frequency bandwidth. In terms of vibration control, this feature is very attractive and builds a bridge between linear and nonlinear systems. Then it is applied for the design of VI NES attached to nonlinear systems. In this way, the design of VI NES for a nonlinear system is simplified to the optimal design for a linear system, which is designed to be similar to this target nonlinear system. Because the latter can be analytically calculated, the proposed method is feasible from a quantitative perspective. Finally, this activation characteristic and a proposed design method are applied to control chatter in a turning process, and results prove its feasibility.