Type Of Nonlinear Energy Sink Research Articles

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.

Performance evaluation of a nonlinear energy sink with quasi-zero stiffness property for vertical vibration control

The advantages of nonlinear energy sink (NES) have been proven to effectively reduce vibrations in the horizontal direction. The application of NES devices to suppress vertical vibration is still at an early stage. In this study, a new type of NES that works in the vertical direction, where disc springs and viscous dampers are utilized to connect an additional mass with the primary structure, is proposed. The NES device can provide a cubic restoring force characterized by the quasi-zero stiffness (QZS) property. Initially, the equations of motion of the primary structure supplemented with NES were established. Then, the force and displacement transmissibility curves were obtained via the steady-state analysis for the NES-controlled, tuned mass damper (TMD)-controlled, and uncontrolled systems. Analytical results revealed that the targeted energy transfer (TET) property of the NES can absorb the kinetic energy within the operating range without amplifying the response in the lower and higher frequency ranges. In contrast, TMD is more efficient within the operating range. Finally, a practical large-span floor structure was adopted to compare the operating performance of NES and TMD. External vibration includes track-induced vibration, vertical earthquake, and human-induced vibration. Numerical results show that the NES performs better than traditional TMD in controlling the vertical response. Moreover, the addition of a NES device will not potentially amplify the response on some occasions.

A review of the mechanical inerter: historical context, physical realisations and nonlinear applications

In this paper, a review of the nonlinear aspects of the mechanical inerter will be presented. The historical context goes back to the development of isolators and absorbers in the first half of the twentieth century. Both mechanical and fluid-based nonlinear inerter devices were developed in the mid- and late twentieth century. However, interest in the inerter really accelerated in the early 2000s following the work of Smith [87], who coined the term ‘inerter’ in the context of a force–current analogy between electrical and mechanical networks. Following the historical context, both fluid and mechanical inerter devices will be reviewed. Then, the application of nonlinear inerter-based isolators and absorbers is discussed. These include different types of nonlinear energy sinks, nonlinear inerter isolators and geometrically nonlinear inerter devices, many relying on concepts such as quasi-zero-stiffness springs. Finally, rocking structures with inerters attached are considered, before conclusions and some future directions for research are presented.

Comparison of a modified vibro-impact nonlinear energy sink with other kinds of NESs

Vibration mitigation is essential to many dynamical and engineering structures that are subjected to destructive vibration amplitudes induced by impulsive loading, seismic excitation, blasts, flutter, collisions, fluid–structure interaction and so on. Unprotected structures by vibration absorbers could be exposed to failure which lead to enormous losses in human lives, major equipment and economy. Employing the nonlinear targeted energy transfer (TET) concept in nonlinear vibration absorbers which are later called as nonlinear energy sinks has ignited a very rapid research interest since 2001. Up-to-date, considerable growth in the NESs field has taken place. Accordingly, various types of NESs have been introduced for vibration mitigation in variety of dynamical and structural engineering systems. The types of introduced NESs included, but not limited to, stiffness-based, rotating and the vibro-impact NESs. Among these common types of NESs, the most effective and efficient one is the single-sided vibro-impact (SSVI) nonlinear energy sink (NES). However, most of investigations has implemented a coefficient of restitution of 0.7 which closely corresponds to a steel-to-steel impact. Therefore, this paper is aimed to further improve the SSVI NES by including the coefficient of restitution in the performance optimization. Accordingly, significant improvement in the SSVI NES performance is obtained when the coefficient of restitution is found to be near 0.45. In addition, performance comparison between the enhanced SSVIe NES with several existing types of NESs is performed here where a nine-story large-scale structure is employed for this numerical comparison. Accordingly, the performance of the enhanced SSVIe NES of nearly 0.45 coefficient of restitution is found to be more robust to the initial impulsive energy levels and to its physical parameters variation than other kinds of existing NESs.

Nonlinear Energy Sinks With Piecewise-Linear Nonlinearities

Abstract An efficient nonlinear energy sink (NES) is developed here by employing a symmetric piecewise nonlinear coupling force. The proposed piecewise NES has a symmetric clearance about its equilibrium position in which zero stiffness is assumed. However, at the boundaries of the symmetric clearance, the NES is coupled to the linear structure by either linear or nonlinear stiffness elements. The damping is assumed to be continuous linear viscous damping during the oscillation of the NES mass inside and outside the clearance zone. This design is further modified by incorporating a negative coupling stiffness within the clearance zone. Therefore, the performance of the proposed piecewise NESs in rapid vibration suppression is numerically investigated with two-degree-of-freedom spring-mass system and compared with existing NESs in the literature. Accordingly, significant improvement in vibration suppression has been achieved by the proposed piecewise NES compared with other types of existing NESs. Moreover, the numerical simulation results have shown more robustness in the piecewise NES performance for a wide range of stiffness and damping variations than the linear absorber and other types of NESs in the literature.

An inertial nonlinear energy sink

The demand for large mass limits the engineering application of traditional nonlinear energy sinks. In this paper, a novel type of nonlinear energy sink is proposed to overcome this drawback. The mass in the traditional nonlinear energy sink is replaced by an inerter. A substantial reduction in the mass of nonlinear energy sinks has been achieved. At the same time, the effect of vibration suppression is improved. Introducing the inertance without the mass, the equation of motion for the inertial nonlinear energy sink is established. By applying the harmonic balance method, the nonlinear forced vibration response of the system is predicted. The analytical results are supported by numerical simulations. By comparing with the traditional nonlinear energy sink, the benefits of using inertial nonlinear energy sink are explored. For examples, the additional mass required to achieve the same vibration suppression effect is smaller. The same additional mass enables better vibration suppression. Moreover, the optimum mass ratio is searched by the maximum amplitude trajectory. Furthermore, amplitude-frequency responses are generated for different parameters. The numerical results demonstrate that the inertial design could enhance the vibration suppression performance. In general, this work shows that the inertial design can significantly reduce the additional mass. Therefore, this study promotes the practical application of the NES.

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.

Numerical and experimental investigations of a rotating nonlinear energy sink

In this work, passive nonlinear targeted energy transfer (TET) is addressed by numerically and experimentally investigating a lightweight rotating nonlinear energy sink (NES) which is coupled to a primary two-degree-of-freedom linear oscillator through an essentially nonlinear (i.e., non-linearizable) inertial nonlinearity. It is found that the rotating NES passively absorbs and rapidly dissipates a considerable portion of impulse energy initially induced in the primary oscillator. The parameters of the rotating NES are optimized numerically for optimal performance under intermediate and strong loads. The fundamental mechanism for effective TET to the NES is the excitation of its rotational nonlinear mode, since its oscillatory mode dissipates far less energy. This involves a highly energetic and intense resonance capture of the transient nonlinear dynamics at the lowest modal frequency of the primary system; this is studied in detail by constructing an appropriate frequency–energy plot. A series of experimental tests is then performed to validate the theoretical predictions. Based on the obtained numerical and experimental results, the performance of the rotating NES is found to be comparable to other current translational NES designs; however, the proposed rotating device is less complicated and more compact than current types of NESs.

Forced System with Vibro-impact Energy Sink: Chaotic Strongly Modulated Responses

The paper treats forced response of primary linear oscillator with vibro-impact energy sink. This system exhibits some features of dynamics, which resemble forced systems with other types of nonlinear energy sinks, such as steady-state and strongly modulated responses. However, the differences are crucial: in the system with vibro-impact sink the strongly modulated response consists of randomly distributed periods of resonant and non-resonant motion. This salient feature allows us to identify this type of dynamic behavior as chaotic strongly modulated response (CSMR). It is demonstrated, that the CSMR exists due to special structure of a slow invariant manifold (SIM), which is derived with the help of a multiple-scale analysis of the system. In the considered system, this manifold has only one stable and one unstable branch. This feature defines new class of universality for the nonlinear energy sinks. In the system with the vibro-impact sink, such responses are observed even for very low level of the external forcing. This feature makes such system viable for possible energy harvesting applications.

Dynamics of forced system with vibro-impact energy sink

The paper treats forced response of primary linear oscillator with vibro-impact energy sink. This system exhibits some features of dynamics, which resemble forced systems with other types of nonlinear energy sinks, such as steady-state and strongly modulated responses. However, the differences are crucial: in the system with vibro-impact sink the strongly modulated response consists of randomly distributed periods of resonant and non-resonant motion. This salient feature allows us to identify this type of dynamic behavior as chaotic strongly modulated response (CSMR). It is demonstrated, that the CSMR exists due to special structure of a slow invariant manifold (SIM); the latter is derived in a course of a multiple-scale analysis of the system. In the considered system, this manifold has only one stable and one unstable branch. This feature defines new class of universality for the nonlinear energy sinks. Very different physical system with topologically similar SIM – the oscillator with rotational energy sink – also exhibits CSMRs. In the system with the vibro-impact sink, such responses are observed even for very low level of the external forcing. This feature makes such system viable for possible energy harvesting applications.

Track Nonlinear Energy Sink for Rapid Response Reduction in Building Structures

AbstractA new type of nonlinear energy sink (NES), termed a track NES, is proposed in this paper. The shape of the track over which the auxiliary mass moves determines the character of the nonlinear restoring force for the NES. After deriving the equations of motion for the track NES, numerical optimization is carried out for the system implemented in a two-degree-of-freedom primary structure. The optimization results are in the track shape of a fourth-order polynomial. The performance of the track NES is compared with an equivalent tuned mass damper (TMD) and the Type I NES, which utilizes a cubic restoring force. The results of this comparison show that the attenuation observed with the track NES is competitive with the Type I NES and is more robust against changes in the underlying structure than the TMD. Moreover, the track NES is more scalable and offers greater flexibility in prescribing the associated nonlinear restoring force.

Analytical formulas for the energy, velocity and displacement decays of purely nonlinear damped oscillators

Accurate formulas for obtaining the energy, velocity and displacement decay envelopes in purely nonlinear damped oscillators are presented here. These purely nonlinear oscillators have no linear stiffness components, and the new formulas derived in this paper are found to be highly accurate in determining the decay envelopes, regardless of the system’s physical parameters and its initial condition. The mechanism of these new formulas for obtaining the decay envelopes of the nonlinear oscillators is found to be exactly the same as the mechanism of the well-known amplitude decay formulas used for the linear oscillator. Finding such formulas is significant to many scientific applications of these nonlinear oscillators, such as the passive targeted energy transfer through the stiffness-based nonlinear energy sinks (NESs). In these types of NESs, these formulas can be easily applied for system identification and dynamic analysis. In addition, they are expected to have a significant application in different scientific fields for such oscillators.

Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments

We consider the response of a linear structural system when coupled to an attachment containing strong or even essential nonlinearities. For this system, the attachment, designated as a nonlinear energy sink, is designed as a nonlinear vibration absorber, serving to dissipate energy from the structural system. Moreover, the attachment not only leads to a reduction in the total energy of the system, but also nonlinearly couples together the vibration modes of the linear structural system. When the structure is impulsively loaded, the nonlinear energy sink serves to both dissipate and redistribute energy, thus enhancing the observed structural dissipation. The effect of the nonlinear attachment on the linear primary system can be quantified in terms of equivalent measures for the damping and frequency of each mode, derived through consideration of the instantaneous energy balance in each mode. The influence of the nonlinear energy sink on the structural response is illustrated with an impulsively forced two-degree-of-freedom primary system, representing a two-story structure, with different types of nonlinear energy sink attached to the top floor. We perform optimization studies in order to design the nonlinear energy sink for optimal shock mitigation of the primary system. The proposed methodology is based only on measured time series without resorting to frequency analysis. As such, it is valid for strongly nonlinear systems as well as for systems with nonsmooth nonlinearities, and is suited to both simulated and experimental results. Finally, an experimental validation of the enhanced dissipation introduced by the nonlinear energy sink is provided, and the experimental response is compared against numerical simulation of the corresponding analytical model to illustrate the effectiveness of the nonlinear energy sink design. Thus, we analytically predict and experimentally verify the efficacy of the nonlinear energy sink to significantly reduce the response of the two degree-of-freedom system subject to shock excitation.

Effective Stiffening and Damping Enhancement of Structures With Strongly Nonlinear Local Attachments

We study the stiffening and damping effects that local essentially nonlinear attachments can have on the dynamics of a primary linear structure. These local attachments can be designed to act as nonlinear energy sinks (NESs) of shock-induced energy by engaging in isolated resonance captures or resonance capture cascades with structural modes. After the introduction of the NESs, the effective stiffness and damping properties of the structure are characterized through appropriate measures, developed within this work, which are based on the energy contained within the modes of the primary structure. Three types of NESs are introduced in this work, and their effects on the stiffness and damping properties of the linear structure are studied via (local) instantaneous and (global) weighted-averaged effective stiffness and damping measures. Three different applications are considered and show that these attachments can drastically increase the effective damping properties of a two-degrees-of-freedom system and, to a lesser degree, the stiffening properties as well. An interesting finding reported herein is that the essentially nonlinear attachments can introduce significant nonlinear coupling between distinct structural modes, thus paving the way for nonlinear energy redistribution between structural modes. This feature, coupled with the well-established capacity of NESs to passively absorb and locally dissipate shock energy, can be used to create effective passive mitigation designs of structures under impulsive loads.

Dynamics of an Eccentric Rotational Nonlinear Energy Sink

The paper introduces a novel type of nonlinear energy sink, designed as a simple rotating eccentric mass, which can rotate with any frequency and; therefore, inertially couple and resonate with any mode of the primary system. We report on theoretical and experimental investigations of targeted energy transfer in this system.

Passive targeted energy transfers and strong modal interactions in the dynamics of a thin plate with strongly nonlinear attachments

We study targeted energy transfers (TETs) and nonlinear modal interactions attachments occurring in the dynamics of a thin cantilever plate on an elastic foundation with strongly nonlinear lightweight attachments of different configurations in a more complicated system towards industrial applications. We examine two types of shock excitations that excite a subset of plate modes, and systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena occurring between the plate and the attachments. The following attachment configurations are considered: (i) a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) attachment—termed nonlinear energy sink (NES); (ii) a set of two SDOF NESs attached at different points of the plate; and (iii) a single multi-degree-of-freedom (MDOF) NES with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and locations of the NESs, in order to optimize passive TETs from the plate modes to the attachments, and we showed that the optimal position for the NES attachments are at the antinodes of the linear modes of the plate. The parametric study of the damping coefficient of the SDOF NES showed that TETs decreasing with lower values of the coefficient and moreover we showed that the threshold of maximum energy level of the system with strong TETs occured in discrete models is by far beyond the limits of the engineering design of the continua. We examine in detail the underlying dynamical mechanisms influencing TETs by means of empirical mode decomposition (EMD) in combination with wavelet transforms. This integrated approach enables us to systematically study the strong modal interactions occurring between the essentially nonlinear NESs and different plate modes, and to detect the dominant resonance captures between the plate modes and the NESs that cause the observed TETs. Moreover, we perform comparative studies of the performance of different types of NESs and of the linear tuned mass dampers (TMDs) attached to the plate instead of the NESs. Finally, the efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed.