Vibro-impact Nonlinear Energy Sink Research Articles

Design and optimization of a two-degrees-of-freedom single-sided vibro-impact nonlinear energy sink for transient vibration suppression of a thin plate

To rapidly suppress the transient vibration response of a thin plate, a two-degrees-of-freedom single-sided vibro-impact nonlinear energy sink (TSSVI NES) is proposed in this paper. Based on the Kirchhoff hypothesis, the coupled equations of motion between the plate and the TSSVI NES are established. The system is modeled by the Galerkin technique and numerically solved using the fourth order Runge-Kutta method. To obtain the optimal parameters of the TSSVI NES, a particle swarm optimization method is adopted. The system response with the TSSVI NES is compared with that of the cubic nonlinear energy sink (CNES) and the single-sided vibro-impact nonlinear energy sink (SSVI NES), showing that the vibration suppression ability of the TSSVI NES is better. The mechanism of rapid response suppression of the TSSVI NES is demonstrated by way of simulations. A parametric study is also conducted to determine the effects of damping, the coefficient of restitution, mass, stiffness, and installation position of TSSVI NES on the efficacy of the vibration control device. The numerical results demonstrate that the performance of the TSSVI NES is robust to the damping, coefficient of restitution, and installation position, but sensitive to mass difference and stiffness difference. Finally, the effect of the TSSVI NES is examined when the plate is excited by seismic loads, demonstrating a good response suppression performance.

The influence of various optimization procedures on the dynamics and efficiency of nonlinear energy sink with synergistic effect consideration

The vibro-impact system under consideration consists of a primary structure, which is a linear oscillator (LO) and a vibro-impact damper coupled with it. The damper is a vibro-impact nonlinear energy sink (VI NES). The dynamics of this system and damper efficiency in attenuation vibrations of the primary structure are studied using numerical simulation. The paper examines the problem of choosing optimal damper parameters that provide the best mitigation of the primary structure energy. The optimization procedure was carried out in several stages. The multiple parameters optimization manifested a synergistic effect. This made it possible to select the most effective VI NES design. The chosen damper design provided the best energy reduction. Thanks to it, the irregular regimes of the system movement turned into the periodic ones. The damper hits both the primary structure directly and an obstacle rigidly connected to the primary structure.

An Analytical Investigation on the Vibration Suppression Performance of the Single-sided Vibro-impact Nonlinear Energy Sink

An Analytical Investigation on the Vibration Suppression Performance of the Single-sided Vibro-impact Nonlinear Energy Sink

Selection of the optimal design for a vibro-impact nonlinear energy sink

The efficiency of a vibro-impact nonlinear energy sink (VI NES), that is, a vibro-impact damper, is largely determined by its design. The optimal damper design can be found through optimization procedures. However, the result of their work is ambiguous, their various options show different values of the optimal damper parameters. A thorough analysis of the obtained parameters values allow you to select the best option according to a certain criterion. While carrying out this analysis, we observe many interesting phenomena, namely, the synergistic effect of multiple parameters, rich complex dynamics of the VI NES, the presence of direct impacts between the damper and the main body, the dependence of the total energy on the exciting force parameters.The analysis also allows us to formulate the limitations of the VI NES. All these problems are reflected in this article.

Exploring effective TET through a vibro-impact nonlinear energy sink over broad parameter regimes

In recent times, the vibro-impact nonlinear energy sink (VINES) has emerged as a promising passive mechanism for vibration mitigation in engineering systems. The VINES system consists of a ball traveling within a cavity of an externally excited linear oscillator (LO). The ball impacts either end of the cavity, transferring energy from the LO to the ball and mitigating excess oscillations of the LO. Earlier studies of VINES analyzed scenarios with the mass of the ball to be small relative to the LO, with low forcing amplitude near the resonant frequency of the LO. Improvements in targeted energy transfer (TET), observed for an increased mass of the ball, motivate an investigation of VINES for larger mass ratios, using a recently developed semi-analytical map-based approach that provides the exact solution without the limitations of previous analyses. Complementary analytical and numerical approaches treat larger mass ratios and higher amplitudes of the external harmonic excitation for forcing frequencies away from the natural frequency of the LO, identifying parameter regimes for efficient and inefficient performance based on standard measures of energy transfer. The analysis identifies multiple regions for the desired behavior with two alternating impacts per forcing period and provides relevant stability conditions. Numerical results indicate chattering behavior in regimes where energy transfer is minimal, yielding performance that appears similar to resonance. This phenomenon can be directly related to the passive nature of the VINES design, where the natural frequency of the VINES system decreases as the mass of the ball, and thus that of the system, increases. Then the peak response of the LO is shifted away from its resonant frequency, allowing excellent energy transfer to be realized there.

The synergistic effect of the multiple parameters of vibro-impact nonlinear energy sink

This article studies the dynamics and efficiency of a vibro-impact damper (single-sided vibro-impact nonlinear energy sink—SSVI NES) depending on the exciting force parameters. The damper is coupled with a linear oscillator—the primary structure. It is shown that the damper is quite effective in a wide range of the exciting force amplitude and in the range of its frequency, which are higher than the resonant frequency; damper efficiency in these regions is fairly stable. The dynamics of the vibro-impact system “primary structure—SSVI NES” is rich and complex, which, however, does not impair the damper efficiency. In complex oscillatory regimes, the damper makes bilateral impacts: it hits both an obstacle and directly against the primary structure, which actually turns a single-sided NES into a double‐sided one. The optimization procedure and the choice of optimal damper parameters play a very important role in damper design. Optimizing multiple damper parameters instead of three shows a synergistic effect and provides better results.

Influence of stiffness parameters on vibro-impact damper dynamics

The article studies the dynamic behavior of a low-mass vibro-impact damper, considered as a device for passive vibration control. Its design scheme corresponds to the scheme of single-sided vibro-impact nonlinear energy sink (SSVI NES), which is supposed to be used for effective vibrations attenuation under different transient loads, namely, impulsive, broadband, wind. Its dynamics and effectiveness strongly depend both on the damper own parameters and the external load parameters. We consider the response regimes and the damper efficiency for two options of its optimized parameters under periodic loading. The influence of the elasticity characteristics of the colliding surfaces on the damper effectiveness is also analyzed. We show that the modes with rich complex dynamics are implemented in a system with a heavier damper with low stiffness. Despite this, it is more effective, especially with a softer impact.

Maps unlock the full dynamics of targeted energy transfer via a vibro-impact nonlinear energy sink

We consider a model of a vibro-impact nonlinear energy sink (VI-NES), where a ball moves within a cavity of an externally forced mass, impacting either end of the cavity. These impacts result in energy transfer from the mass to the ball, thus limiting the oscillations of the larger system. We develop a semi-analytical map-based approach, recently used for an inclined impact pair model, in the setting where there is energy transfer between the mass and the ball. With this approach we analytically derive exact expressions for the full dynamics of the VI-NES system without restricting the range of parameters, in contrast to other recent work in which an approximate reduced model is valid only for small mass of the ball, small amplitude, and a limited frequency range. We develop the bifurcation analysis for the full VI-NES system, based on exact maps between the states at successive impacts. This analysis yields parameter ranges for complex periodic responses and stability analyses for O(1) mass of the ball, forcing frequencies that are not the same as the natural frequency, and large amplitude forcing. The approach affords the flexibility to analytically study the dynamics of different periodic solutions and their stability, including a variety of impact sequences in the full two degree-of-freedom model of VI-NES. Comparisons of quantities that characterize the energy transfer point to the significance of different types of periodic behavior, which may occur for different parameter combinations. Our semi-analytical results also provide the impact phase, which plays an important role in the efficiency of the energy transfer.

Experimental validation of impact energy scattering as concept for mitigating resonant vibrations.

The Vibro-Impact Nonlinear Energy Sink (or impact damper) is well-known for its ability to engage into transient resonance captures with arbitrary frequencies and thus has inherent broad-band effectiveness. Its working principle relies on (recurrent) energy localization and local dissipation within the contact region. Dissipative (inelastic) collisions are inevitably associated with damage and challenging to predict. Recently, it has been shown theoretically that the device is effective even for purely elastic collisions when the energy is (almost) irreversibly transferred from the critical low-frequency modes to high frequencies.In that case, the device is more properly termed Impact Energy Scatterer (IES). In the present work, we experimentally validate, for the first time, the working principle of the IES. To this end, we design a test rig consisting of a cantilevered beam, hosting a spherical impactor inside a cavity at its tip. The resonant vibrations of the lowest-frequency bending mode are reduced by a factor of 10-20. Given that the IES weighs less than 1% of the host structure, this corresponds to a paramount vibration mitigation capability. We achieve excellent agreement between the measurements and the numerical predictions obtained by modeling the impacts as perfectly elastic. We also demonstrate that the dissipation in the contact region is negligible, while a substantial amount of energy is scattered to higher frequencies, validating the theoretically proposed working principle.

Dynamics of primary structure coupled with single-sided vibro-impact nonlinear energy sink

In this paper, we consider a two-mass 2-DOF vibro-impact system, consisting of a linear oscillator, called the primary structure, and an impact damper attached to it. A damper with a small mass hits a wall rigidly connected to the primary structure. This scheme corresponds to the scheme of single-sided vibro-impact nonlinear energy sink – SSVI NES. It is shown that even a light damper can reduce the amplitude and velocity of the primary structure oscillatory movement, that is, decrease its energy. Further optimization of damper parameters should improve this effect. The impact simulation using Hertz’s nonlinear contact force makes it possible to take into account the mechanical characteristics of all colliding surfaces in more detail. The introduction of the initial distance between the primary structure and the damper into the calculation scheme makes it possible to take into account the impact between bodies and see when this impact is absent.

Optimization for vibro-impact nonlinear energy sink under random excitation

As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available for the design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effort to address this gap. Specifically, the approximate analytical solution of the system stochastic response is obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Taking advantages of this approximate solution, the variance of the system is defined and easily minimized to calculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlate with direct numeric simulations.

Choice of the Model for Vibro-impact Nonlinear Energy Sink

The nonlinear energy sink (NES) is defined as a single-degree-of-freedom structural element with relatively small mass and weak dissipation, attached to a primary structure via essentially nonlinear coupling. It is a passive energy dissipation device designed to rapidly absorb vibration energy (due to shock, blast, earthquakes, etc.) from a primary structure and locally dissipate it. The article contains a mini-review of the works on NESs. Design schemes for single-sided and double-sided vibro-impact NESs (SSVI and DSVI NESs) are proposed on the basis of conceptual and design NES schemes that exist in the world scientific literature. The motion equations and the impact rule are given. The quasistatic Hertz contact law is adopted as the impact rule. Various representations of the impulsive loading on the primary structure are discussed. These are excitations by initial velocities only, periodic excitation, a shock in the half-sine form, single-sided periodic impulses of a rectangular shape,wind, seismic and broadband excitation. The Tables of some numerical parameters that can be accepted for VI NES are given. Using the presented data, the authors intend to investigate both the efficiency of SSVI and DSVI NESs under different types of impulsive load, and their dynamical behavior with the changing in their parameters.

Finite contact duration modeling of a Vibro-Impact Nonlinear Energy Sink to protect a civil engineering frame structure against seismic events

This paper reassesses carefully the effects and consequences of instantaneous contact mechanics versus finite contact duration modeling of Vibro-Impact Nonlinear Energy Sinks (VI NES). The device is composed of a container enclosing an inelastic sphere, interacting via a nonlinear viscoelastic dissipative force with the inner walls of the container. The VI NES is considered in a practical context, the control of the vibrations of a civil engineering frame structure under seismic input. It is connected by a rigid link to the structure: the particle bounces within the container when it vibrates, exploring dynamical regimes ranging from periodic collisions to chaos while dissipating energy. Our VI NES is designed in order to mitigate vibrations of a ten-story frame structure under two historic earthquake signals, in order to rule out specific effects. The dynamics of the system, obtained from both finite and instantaneous contact models, are compared and discussed. The main result reveals a significant effect of the contact duration on the estimation of the dissipated energy, even for very brief collisions. Instantaneous contact model indeed provides incommensurate values in terms of acceleration during the impacts, leading to a higher sensitivity to Initial Conditions (IC) revealed by large fluctuations of the mechanical response. In turn, any finite duration contact models is proved to be less sensitive to IC, and thus more precise. Our findings demonstrate that both finite and instantaneous models converge in fact to the same value, in average, but the finite duration models require much less realizations to converge to the mean value. In practice, the finite contact duration low pass filters the mechanical responses of the VI NES, avoiding the system to fall into nonphysical chaotic states experienced by the instantaneous model.

Dynamics of an electromagnetic vibro-impact nonlinear energy sink, applications in energy harvesting and vibration absorption

Dynamics of an electromagnetic vibro-impact nonlinear energy sink, applications in energy harvesting and vibration absorption

Predictive design of impact absorbers for mitigating resonances of flexible structures using a semi-analytical approach

Analytical conditions are available for the optimum design of impact absorbers (or Vibro-Impact Nonlinear Energy Sinks) for the special case where the host structure is well described as a rigid body. Accordingly, the analysis relies on the assumption that the impacts cause immediate dissipation in the contact region, which is modeled in terms of a coefficient of restitution (Newton’s impact law) that is assumed to be known and fixed. When a flexible host structure is considered instead, the impact absorber not only dissipates energy at the time instances of impact, but, and perhaps more importantly, it inflicts nonlinear energy scattering between structural modes. Hence, it is crucial to account for such nonlinear energy transfers yielding energy redistribution within the modal space of the structure. In the present work, we develop a design approach for flexible host structures. We consider the case of a forced excitation near primary resonance with a well-separated mode. We demonstrate that the time scales of the impact and the resonant vibration can be decoupled. On the long time scale, the dynamics of the host structure can be properly reduced to the fundamental harmonic of the resonant mode. A light impact absorber responds to this enforced motion, and we show that the conventional Slow Invariant Manifold of the dynamics is recovered for the commonly considered regime of two symmetric impacts per period. On the short time scale of the impact dynamics, the contact mechanics and elasto-dynamics must be finely resolved. We show that it is sufficient to run a numerical simulation of a single impact event with representative pre-impact velocity. From this short-time simulation, we derive an effective modal coefficient of restitution and the properties of the contact force pulse, needed to approximate the behavior on the long time scale. We derive a closed-form expression of the periodic resonant response and establish that the design problem can be reduced to four dimensionless parameters. We demonstrate the approach for the numerical example of a cantilevered beam with a spherical impact absorber. We conclude that the proposed semi-analytical procedure enables deep qualitative understanding of the problem and, at the same time, yields a quantitatively accurate prediction of the optimum design.

Importance of gravity and friction on the targeted energy transfer of vibro-impact nonlinear energy sink

The effect of gravity and sliding friction on the dynamics around targeted energy transfer of an inclined vibro-impact nonlinear energy sink (VINES) is addressed. The non-smooth dynamics is first formulated in Signorini’s contact law and treated using a Moreau-Jean scheme adapted with an energy-conserving integration method. Exhaustive discussions are then carried out regarding the vibration damping performance of the VINES, as well as their dependence on the underlying vibro-impact induced response regimes, under both transient and steady-state responses. It is demonstrated that gravity is responsible for reducing the energy barrier required for achieving targeted energy transfer in the transient response, or enlarge the existing bandwidth of the effective strongly modulated response (SMR) regimes, which is an equivalent representation of TET in the steady-state response, to improve considerably the overall damping efficiency. Some adverse effects brought by gravity and friction are also reported, and it is found that, when the incline angle or friction coefficient grows large, the bandwidth of SMR reduces again and leads to a deterioration of efficiency. The results open a door for appropriately taking advantage of the gravity into the VINES design to improve its damping performance.

Potential of a vibro-impact nonlinear energy sink for energy harvesting

The energy harvesting potential of a vibro-impact nonlinear energy sink (VINES) is investigated. Applying Signorini’s contact law, the non-smooth dynamics is first formulated in a measure differential complementarity problem and treated using a Moreau-Jean scheme adapted with an energy-conserving integration method. The resulting scheme thus shows a good energy preservation property, allowing one to calculate the energy flow of the system in high precision. Exhaustive discussions are then carried out regarding the energy harvesting performance of the proposed VINES harvester, as well as their dependence on the underlying vibro-impact induced response regimes, under both transient and steady-state responses. It is demonstrated that the vibro-impact is responsible for achieving targeted energy transfer in the transient response or controlling the regimes in the steady-state response, to improve significantly the harvesting efficiency. Moreover, a properly designed VINES, working with 1–2 impacts per cycle, is capable for effective broadband energy harvesting over a wide amplitude and frequency range. Two specific considerations are also performed to evaluate further the generality and efficacy of the proposed harvester, and it is proved the VINES can provide higher energy density than the classical linear or cubic NES harvesters, and its effectiveness could be robust over a certain low level of noise.

A complete set of design rules for a vibro-impact NES based on a multiple scales approximation of a nonlinear mode

The aim of the paper is to formulate a complete set of design rules for a vibro-impact nonlinear energy sink (VI NES). Hereto, analytical and numerical methods to extract the backbone curve of vibro-impact systems are presented. The adopted approach exploits the multiple scales method and is applied to a linear oscillator coupled with a VI NES. The dynamics of the system are explored and the system’s response under harmonic forcing in the vicinity of resonance is analyzed and approximated. The presented method allows for the derivation of a closed-form approximation of a nonlinear mode. The relation between the steady state response and the input parameters is established. The resonance frequency of the examined nonlinear system for different excitation levels is estimated and the corresponding backbone curve is identified. The theoretical predictions are confirmed through a comparison with the standard resonant decay method combined with a phase-locked loop. Finally, the closed-form approximations are used to derive a complete set of design rules for a vibro-impact nonlinear energy sink.

On the analysis of a passive vibration absorber for submerged beams under hydrodynamic forces: An optimal design

This paper investigates the passive vibration control of immersed beams under sinusoidal hydrodynamic forces using a vibro-impact nonlinear energy sink (VI-NES). This type of absorber has a lower activation threshold compared to other nonlinear isolators. It is comprised of a clearance containing an impact element. Neither spring nor damper is required, and the restitution coefficient is the only source of damping. The equation of motion of the coupled system is analytically solved utilizing the multiple scales method and is verified via a numerical solution. The strongly modulated response (SMR), chaotic response, regimes with two impacts per cycle (symmetric and asymmetric) and more than two impacts per cycle have been observed in the nonlinear dynamic behavior of the coupled system which is associated with the location of the fixed points on the slow invariant manifold (SIM). The optimal design of the absorber is also investigated for the impulsive excitation case. Here, it is aimed to decrease the amount of time that takes the absorber to mitigate 95 percent of the primary system’s initial energy. The absorber location, restitution coefficient, clearance length, and mass ratio between the impact element and the beam are treated as design parameters. Furthermore, the influence of the design parameters on the SIM and the transient dynamic behavior of the system is also studied. The results show that the optimally designed absorber can mitigate the initial energy of the structure in a short time. It is observed that the strongly modulated response and the regime with two impacts per cycle (symmetric) are the most optimal responses. Also, comparing the performance of the mentioned absorber to the cubic NES yields satisfying results.

Vibration suppression and modal energy transfers in a linear beam with attached vibro-impact nonlinear energy sinks

We present a comprehensive study of nonlinear resonant modal energy scattering and passive vibration suppression in a linear cantilever beam with vibro-impact nonlinear energy sinks (VI NESs) attached to it. It is well-known that vibro-impacts are a strong source of non-smooth nonlinearity, resulting in rapid and intense multi-scale energy scattering from low-to-high frequencies in the modal space of the beam. We present a direct correlation between such low-to-high frequency nonlinear energy scattering induced by vibro-impacts and vibration suppression of the beam vibrations under both sweep- and constant-frequency harmonic excitations. In particular, we study the intensity of the collisions between the tip of the beam and the particles of the VI NESs by means of an event-driven method based on an explicit variable time step integration scheme, and relate the dynamics of the integrated beam-VI-NES system to the induced resonant energy scattering from low beam modes to higher ones. On this basis, the effects of the mass ratio and clearance between the absorber and the beam on the resonant energy scattering are presented. Our aim is to perform predictive design of the VI NESs for effective and robust vibration mitigation of the beam response. To this end we perform optimization studies on the mass ratio and clearance between the absorber and beam for the case of single and multiple VI NESs and identify regions of optimal suppression. Besides, since the single VI NES is only effective in a limited frequency and amplitude range – as its dynamics is energy-dependent – using multiple VI NESs with optimized parameters can extend the frequency range of effective vibration suppression, rendering the resulting vibration mitigation more robust to variations of the applied excitations.