Targeted Energy Transfer Research Articles

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.

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.

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.

Targeted Energy Transfer Dynamics and Chemical Reactions.

Ultrafast reaction processes take place when resonant features of nonlinear model systems are taken into account. In the targeted energy or electron transfer dimer model this is accomplished through the implementation of nonlinear oscillators with opposing types of nonlinearities, one attractive while the second repulsive. In the present work, we show that this resonant behavior survives if we take into account the vibrational degrees of freedom as well. After giving a summary of the basic formalism of chemical reactions we show that resonant electron transfer can be assisted by vibrations. We find the condition for this efficient transfer and show that in the case of additional interaction with noise, a distinct non-Arrhenius behavior develops that is markedly different from the usual Kramers-like activated transfer.

Stochastic optimization of targeted energy transfer with time-dependent cubic nonlinearity

The stochastic optimization of a nonlinear energy sink (NES) with a time-dependent stiffness is considered. The NES is linearly coupled to a main system. The optimization aims to find the stiffness properties of the NES that minimize the expected value of the velocity of the main system while accounting for the statistical distributions of the excitation amplitude and frequency. It is shown that the system’s responses are highly sensitive to uncertainty and can even exhibit a discontinuous behavior. This represents a major hurdle for the optimization, which is already hampered by the potentially large computational cost associated with the time integrations. To tackle the high-sensitivity to uncertainties and reduce the computational burden, a dedicated surrogate-based stochastic optimization algorithm is used. Specifically, the approach uses Kriging surrogates built from the unsupervised identification of clusters resulting from response discontinuities. Comparisons between efficiencies of optimal nonlinear absorbers with and without time-dependent stiffness are performed and discussed.

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.

Nonlinear Normal Modes of Vibrating Mechanical Systems: 10 Years of Progress

Abstract This paper contains a review of the theory and applications of nonlinear normal modes, which have been developed during last decade. This review has more than 200 references. It is a continuation of two previous review papers by the same authors. The following theoretical issues of nonlinear normal modes are treated: basic concepts and definitions; application of the normal form theory for nonlinear modes construction; nonlinear modes in finite degrees-of-freedom systems; resonances and bifurcations; reduced-order modeling; nonlinear modes in stochastic dynamical systems; numerical methods; identification of mechanical systems using nonlinear modes. The following applied issues of this theory are treated in this review: experimental measurement of nonlinear modes; nonlinear modes in continuous systems; engineering applications (aerospace engineering, power engineering, piecewise-linear systems and structures with dry friction); nonlinear modes in nanostructures and physical systems; targeted energy transfer and absorption problem.

Double base mismatches mediated catalytic hairpin assembly for enzyme-free single-base mutation detection: integrating signal recognition and amplification in one.

Single nucleotide polymorphism (SNP) biosensors are emerging rapidly for their promising applications in human disease prevention diagnosis, treatment, and prognosis. However, it remains a bottleneck in equipping simple and stable biosensors with the traits of high sensitivity, non-enzyme, and low cost. Double base mismatches mediated chain displacement reactions have attracted fascinating advantages of tailorable thermodynamics stability, non-enzyme, and excellent assembly compliance to involvement in SNP identification. As the base mismatch position and amount in DNA sequence can be artificially adjusted, it provides plenty of selectivity and specificity for exploring perfect biosensors. Herein, abiosensor with double base mismatches mediated catalytic hairpin assembly (CHA) is designed via one base mismatch in the toehold domain and the other base mismatch in the stem sequence of hairpin 1 (H1) by triggering CHA reaction to achieve selective amplification of the mutation target (MT) and fluorescence resonance energy transfer (FRET) effect that is composed of Cy3 and Cy5 terminally attached H1 and hairpin 2 (H2). Depending on the rationally designed base mismatch position and toehold length, the fabricated biosensors show superior SNP detection performance, exhibiting a good linearity with high sensitivity of 6.6 fM detection limitand a broad detection abundance of 1%. The proposed biosensor can be used to detect the KRAS mutation gene in real samples and obtain good recoveries between 106 and 116.99%. Remarkably, these extendible designs of base mismatches can be used for more types of SNP detection, providing flexible adjustment based on base mismatch position and toehold length variations, especially for their thermodynamic model for DNA-strand displacement reactions.

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.

Targeted Energy Transfer Evaluation for Nonlinear Vibrations of Elastic Medium-Finite Length Beam System Using Nonlinear Energy Sink Theory

The elastic medium can usually reduce the vibration of supporting structure, and the impact of the interaction on the vibration characteristics of the structure is similar to the characteristic of nonlinear energy sink. At present, the dynamic research of beam on elastic foundation considering soil motion has been paid more and more attention. According to the modified Winkler model, the finite-depth elastic medium can be considered to the nonlinear energy sink mass, and the vibration energy dissipation capacity and parameter optimization of the elastic medium supporting finite-length beam under half sine pulse are studied. The Galerkin truncation is applied to the discretization of the governing equations. The numerical solution of the beam coupling system with simple support on the elastic medium is obtained by applying the fourth-order Runge–Kutta method. Based on this, the input energy ratio of the elastic medium dissipation is investigated. Furthermore, through the analysis and optimization of targeted energy transfer and dissipation, the dissipation effect of the finite range elastic medium on the vibration energy of its supporting beam is revealed, and the optimal parameter range of the elastic medium is proved. The results show that after adjusting the elastic medium parameters by technical means, the nonlinear energy sink can absorb most of the vibration energy of the beam quickly and effectively, and the optimal energy dissipation ratio can reach 95.16[Formula: see text]. The quantitative evaluation of the energy dissipation in elastic medium within soil–structure interaction effect is realized.

Exploiting multi-stiffness combination inspired absorbers for simultaneous energy harvesting and vibration mitigation

In scenarios where wide-amplitude shock excitation is encountered, a routine bistable configuration struggles to achieve satisfactory energy transfer, and a sensible combination of multiple nonlinear oscillators with different stiffness mechanisms can be exploited to achieve optimal vibration mitigation performance. In this paper, a nonlinear energy conversion and multi-stiffness combination inspired dynamic vibration absorber (NECMC-DVA) is proposed with a magnetic-spring tunable nonlinear stiffness element as the substructure. Parametric studies are performed for different modes of magnet-spring tunable nonlinear stiffness unit arrays considering transient impulses and harmonic excitation. The NECMC-DVA device, which comprises bistable oscillators, cubic stiffness oscillators, and hybrid stiffness oscillators, is also experimentally demonstrated for its synergistic performance in vibration mitigation and energy harvesting. The performance of the NECMC-DVA is measured under transient impulses and harmonic excitations. It has been found that the NECMC-DVA, which consists of a bistable oscillator, a cubic stiffness oscillator, a hybrid stiffness oscillator, energy-capture elements, and motor sequences, achieves high-efficiency nonlinear energy transfer and significant shock robustness in wide-amplitude impulsive scenarios. The NECMC-DVA with hybrid energy sinks demonstrates more remarkable targeted energy transfer and energy conversion performance than its pure bistable oscillator counterpart. Furthermore, the NECMC-DVA prototype can achieve adaptive vibration control modulation and energy conversion management through motion control boards by monitoring ambient excitation signals. Therefore, the NECMC-DVA enables integrated active and passive mitigation and energy harvesting to simultaneously accommodate multi-source indeterminate vibration and shock environments.

Irrational Nonlinearity Enhances the Targeted Energy Transfer in a Rotary Nonlinear Energy Sink

Abstract Efficient passive vibration absorption can prevent the failure of systems without requiring sensors or energy sources. Nonlinear energy sinks (NES) have gained popularity as passive vibration absorbers due to their targeted energy transfer (TET) mechanisms that extract and dissipate vibrational energy over broad frequency ranges. In this work, the vibration suppression performance of a novel bistable rotary nonlinear energy sink (BRNES) is studied numerically in the cases of impulse and harmonic excitation. The BRNES consists of a secondary mass that connects to the primary system by a rigid arm and spring that pivot at each connection point. The spring produces an irrational nonlinear restoring force that introduces bistability and favorable oscillatory TET mechanisms. The BRNES outperforms the traditional rotary NES and, in some cases, even the bistable NES. Moreover, unlike most NESs restricted to rectilinear motion, the BRNES is efficient at multiple orientations, thus demonstrating its potential to passively suppress vibrations in any in-plane direction over broad excitation magnitude and frequency ranges.

An Enhanced Nonlinear Energy Sink for Hybrid Bifurcation Passive Mitigation and Energy Harvesting From Aeroelastic Galloping Phenomena

Abstract Galloping is a self-excited vibration problem that structures immersed in fluid flow can experience. Due to its essential nonlinear phenomena, the structure exhibits limit cycle oscillations (LCOs), which, at high levels, can lead to failure of the systems. This work proposes an investigation of electromagnetic-enhanced nonlinear energy sinks (NES-EH) for the hybrid mitigation of aeroelastic LCOs and energy harvesting. The study focuses on a prismatic bluff body with a linear suspension immersed in the airflow, using classical steady nonlinear modeling for aerodynamic loads. The conventional NES approach is adopted, employing cubic stiffness and linear damping. Additionally, a linear electromagnetic transducer is included in the assembly for the energy harvesting process. By combining the method of multiple scales with the Harmonic Balance Method, analytical solutions are derived to characterize the system's dynamics under the influence of the device. The different response domains and their respective boundaries induced by the NES-EH are characterized based on the bifurcation diagrams. Furthermore, a slow invariant manifold (SIM) characterization is presented for each induced response domain, and its significant features are discussed. Parametric studies are carried out based on bifurcation analyses to assess the effect of NES-EH parameters on the galloping system dynamics, which allows for designing the absorber parameters. The electrical resistance is optimized to maximize the harvested power. The optimal design of NES-EH is then compared with classical energy harvesting solutions for the galloping problem. Additionally, a thorough analysis of the Target Energy Transfer phenomenon is performed.

The transverse dynamic behavior study of a beam system coupled through a local nonlinear coupling layer

In engineering, some complex systems can be reduced to the beam system connected by serval coupling elements. To explore the potential application of local coupling nonlinearity on the transverse dynamic behavior of beams, this work establishes the physical model of a beam system coupled by a local nonlinear coupling layer. On the basis of ensuring the validity of the results, studies the effect of the nonlinear coupling layer on the transverse forced vibration of the beam system. Exploring the characters and reason for complex responses of the beam system coupled through a local nonlinear coupling layer. After discussing the numerical results, it can be found that the beam system presents complex responses within some parameters of the local nonlinear coupling layer, including amplitude jumping, quasi-periodic state, and targeted energy transfer, in which the change of the nonlinear restoring force is the reason for the appearance or disappearance of complex responses. For single-frequency responses, complex responses of the beam system can be motivated by changing the parameters of the local nonlinear coupling layer. With the simultaneous variation of the nonlinear stiffness and viscous damping, responses of the beam system contain both amplitude-sensitive regions and amplitude-jumping regions, in which the amplitude-sensitive region provides an effective parameter range for controlling the vibration by adjusting the local nonlinear coupling layer. On the whole, a suitable combination of nonlinear stiffness and viscous damping of the local nonlinear coupling layer can effectively reduce the vibration at the boundaries of the beam system.

Vibration Suppression Study of Parallel Combined Damping Nonlinear Energy Sink on Piecewise Linear Systems

The Nonlinear Energy Sink (NES) is a passive control device capable of achieving targeted energy transfer and effectively suppressing system vibrations. This paper conducts dynamic modeling and vibration suppression analysis of parallel combined damping nonlinear energy sinks in piecewise linear systems. Initially, the system's amplitude-frequency response curve is obtained using the harmonic balance method, validated by the Runge-Kutta method for accuracy. Subsequently, an analysis is performed on the vibration reduction capabilities of the parallel combined damping nonlinear energy sink and the influence of parameters on its vibration suppression effectiveness. Finally, the study investigates changes in the main system's maximum response amplitude with varying damping under different stiffness conditions and determines optimal parameter values based on trend analysis. Research findings indicate that the vibration reduction performance of the parallel combined damping nonlinear energy sink surpasses that of a single connected damping nonlinear energy sink. Furthermore, after parameter optimization, the main system achieves superior vibration reduction effects.

Dual-power nonlinear energy sink for targeted energy transfer in ultra-wide range of impulsive energy

Recently, the NES with one third power (OTP) nonlinearity was proposed to attenuate micro-vibrations under low-level initial impulsive energy. However, the targeted energy transfer (TET) region for effective vibration mitigation is narrow. This paper develops a new type of NES with dual-power (DP) nonlinearity by combining the third power (TP) nonlinearity and the OTP one in parallel. Firstly, the dynamic behaviors of the DP NES are investigated, and significant vibration mitigation is observed in two discontinuous TET regions that are separately induced by the OTP and TP nonlinearities. Furthermore, the parameter analysis is conducted to find out a feasible avenue to merge such two discontinuous TET regions. It demonstrates that there exist optimal parameters to achieve a wide and continuous TET region. Finally, the design optimization of the DP NES is carried out with the aid of the genetic algorithm, and the optimal parameters enable the DP NES to trigger TET in an ultra-wide and continuous range of initial impulsive energy. Consequently, the proposed DP NES should be an effective solution to substantially broaden the TET region and attenuate vibration in an ultra-wide range of initial impulsive energy.

Dynamic analysis of a plate system coupled through several nonlinear spring-mass couplers

Nowadays, plates have been widely used in various engineering fields, where nonlinear additional equipment is designed to control the vibration of plates. However, the current studies mainly concentrate on the single-plate system with nonlinear additional equipment. Seldom studies use nonlinear couplers to connect the plate system, making the working mechanism of nonlinear couplers on the vibration responses of the plate system unclear, limiting the application of nonlinear couplers on vibration control of the plate system. To explore the potential application of nonlinear couplers, this work introduces nonlinear spring-mass couplers to connect the plate system, where the transverse vibration analysis model of the plate system coupled through nonlinear couplers is established. The Galerkin truncation method (GTM) is used to predict vibration responses of the plate system coupled through nonlinear couplers. After ensuring the validation of numerical results, forced vibration responses of the plate system coupled by nonlinear couplers are investigated. According to numerical results, responses in the vibration of the plate system are influenced by nonlinear couplers greatly. Choosing suitable parameters for nonlinear couplers plays an important role in the vibration control of the plate system. Under a certain parameter range of nonlinear couplers, responses in vibration present complex characters. Under complex responses, the target energy transfer is present in the vibration responses of the plate system.

Vibration mitigation and energy harvesting of vibro–impact dielectric elastomer oscillators

Dielectric elastomers (DEs), as a type of intelligent materials, have the characteristics of light weight, high energy density, high conversion efficiency, and damping effect, and thus can achieve the potential dual–use value of concurrent vibration mitigation (VM) and energy harvesting (EH) by combining with mechanical structures. This paper investigates the vibro–impact dielectric elastomer oscillator (VI DEO) and the proposed rolling VI DEO (RVI DEO) to achieve or enhance the potential dual–use value of DE oscillators. First, the schematics of the VI DEO and the RVI DEO are elaborated in detail. Then, the two dynamics analysis models of the linear oscillator (LO)–VI DEO and LO–RVI DEO systems are developed. On this basis, the VM and EH performances of the two DE oscillators under transient and harmonic excitations are numerically studied. It is demonstrated that the two DE oscillators have the most effective VM performance when the LO–VI DEO and LO–RVI DEO systems behave most efficiently in the 1:1 resonance vibro–impact regime with targeted energy transfer (TET). Hence, to achieve this response regime, the influences of the parameters such as the ball's mass, impact distance, pre–stretched ratio and friction coefficient of the two DE oscillators on their VM and EH performances are investigated one by one. The research results show that the most effective VM can only be achieved by adjusting the ball's mass, and the largest output power is generated in the resonance region. Hence, we further perform multi–parameter optimization to find the two DE oscillators with the best performance. Based on the multi–parameter optimization results, the performances of the two optimal oscillators are evaluated under mid–energy level harmonic and variable–frequency excitations with different amplitudes, and it is proved that both optimal DE oscillators not only have good performances, but also the RVI DEO has a better robustness.

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.