Nonlinear Dynamic Vibration Absorber Research Articles

Vibration suppression of a platform by a fractional type electromagnetic damper and inerter-based nonlinear energy sink

The theory of linear and nonlinear dynamic vibration absorbers is a well-established topic for many years. However, many recent contributions paid attention to the nonlinear vibration absorbers and different practical realizations of corresponding devices. Here, we propose a mechanical system constituted of the inerter-based nonlinear energy sink attached to the main body that is resting on an elastic foundation and is grounded through the fractional type electromagnetic damper. The two-degree-of-freedom system is described via two coupled differential equations with one of them having a fractional-order derivative term and the other one containing cubic stiffness nonlinearity. The incremental harmonic balance (IHB) method is employed to solve the equations and studies the strongly nonlinear periodic responses of the system. Applied approximated solution methodology is validated by the numerical Newmark method adapted to deal with the system of nonlinear fractional-order differential equations. The appropriate and necessary number of harmonics used in the IHB solution is commented and validated. This study can be a first step in understanding the dynamics and giving directions for the future design of vibration-isolating platforms based on inerter-based nonlinear vibration absorbers and electromagnetic dampers.

Energy analysis of a nonlinear gas-spring dynamic vibration absorber subjected to seismic excitations

Nonlinear control methods and devices have been widely used in seismic vibration reduction of engineering structures. A nonlinear gas-spring dynamic vibration absorber (NGSDVA) has been recently proposed by the authors and demonstrates a wideband vibration suppression capability across various excitation amplitudes. In this study, an energy analysis method for a multi-story structure with NGSDVA attached under seismic excitation is proposed through experimental and numerical simulation analysis. The energy distribution of the controlled structure and the energy transmission process between the main structure and the damping system are analyzed. It is found that the intermodal energy transfer phenomenon occurs in the five-story steel frame structure during the energy transmission process, while the first-order modal energy is converted to high-order modal energy simultaneously. A series of energy-based parametric studies are further conducted, and the consistency of the parameter influence rules under four different seismic waves is proved, indicating the advantages of energy evaluation indicators for optimizing the design of this nonlinear damper with amplitude-frequency characteristics.

Torsional vibration attenuation of a closed-loop engine crankshaft system via the tuned mass damper and nonlinear energy sink under multiple operating conditions

In recent years, nonlinear energy sink (NES), as a nonlinear dynamic vibration absorber (NDVA), has been widely studied due to its high robustness and broadband vibration attenuation effectiveness, compared with the traditional linear dynamic vibration absorber (LDVA). In the area of crankshaft torsional vibration reduction, the external excitation of a closed-loop crankshaft model changes with the variation of speed, which puts forward higher requirements for wide-band torsional vibration attenuation. This study attempts to explore the feasibility of NES replacing the traditional linear tuned mass damper (TMD) for engine crankshafts in possible practical engineering application by studying a four-cylinders diesel engine crankshaft. Firstly, a multi-inertias nonlinear closed-loop self-excited coupled oscillation model (M-NCSCO) of crankshaft is established, and the correctness of the model is verified through comparison with those from experiments. Based on this, the crankshaft is coupled with optimal TMD (O-TMD), general NES (G-NES), and optimal NES (O-NES), respectively. An improved Newmark–β method is proposed to solve the nonlinear dynamic model numerically. The effects of NES and TMD on the vibration attenuation behavior of the crankshaft are studied under different engine operating conditions (including power, injection timing, single cylinder flameout, and load). The results show that the vibration attenuation efficiency and robustness of G-NES are 7.90% and 3.47% higher than that of O-TMD when considering the above four typical working conditions comprehensively. After further optimization of G-NES, the vibration reduction efficiency of O-NES is improved by 3.1% compared with G-NES.

Study on the Effect of Anti-galloping Device with Cubic Stiffness and Particle Damping

The galloping of iced conductors is a common disaster of overhead conductors. Most traditional anti-galloping devices lack a nonlinear dynamic vibration absorber; hence, they have a limited anti-galloping effect. In this study, we designed, optimized, and tested an electric power fitting and an anti-galloping device with cubic stiffness and particle damping for ultra-high-voltage (UHV) transmission lines. We built a nonlinear dynamic model of the coupling galloping system comprising split conductors and anti-galloping devices. The harmonic balance method obtained the steady-state analytical solutions and corresponding averaged equations. The test spans in the laboratory were used to design the test program and equipment. We verified the accuracy of the nonlinear dynamic model and the harvesting effect of the anti-galloping device with cubic stiffness and particle damping. The theoretical and experimental results were highly consistent, and in the range of (0, 2] Hz, the anti-galloping device reduced the galloping amplitude. Therefore, cubic stiffness and particle damping can effectively improve the anti-galloping ability of UHV transmission lines, prolonging their service period.

Theoretical and experimental study of a novel triple-magnet magnetic dynamic vibration absorber with tunable stiffness

PurposeThe existing Nonlinear Dynamic Vibration Absorbers (NLDVAs) have the disadvantages of complex structure, high cost, high installation space requirements and difficulty in miniaturization. And most of the NLDVAs have not been applied to reality. To address the above issues, a novel Triple-magnet Magnetic Dynamic Vibration Absorber (TMDVA) with tunable stiffness, only composed of triple cylindrical permanent magnets and an acrylic tube, is designed, modeled and tested in this paper.Design/methodology/approach(1) A novel TMDVA is designed. (2) Theoretical and experimental methods. (3) Equivalent dynamics model.FindingsIt is found that adjusting the magnet distance can effectively optimize the vibration reduction effect of the TMDVA under different resonance conditions. When the resonance frequency of the cantilever changes, the magnet distance of the TMDVA with a high vibration reduction effect shows an approximately linear relationship with the resonance frequency of the cantilever which is convenient for the design optimization of the TMDVA.Originality/valueBoth the simulation and experimental results prove that the TMDVA can effectively reduce the vibration of the cantilever even if the resonance frequency of the cantilever changes, which shows the strong robustness of the TMDVA. Given all that, the TMDVA has potential application value in the passive vibration reduction of engineering structures.

Research on dynamic characteristics of a novel triple-magnet magnetic suspension dynamic vibration absorber

A novel Triple-magnet Magnetic Suspension Dynamic Vibration Absorber is designed and modeled in this paper. The equivalent dynamic model of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber vibration reduction system is established. Meanwhile, the calculation model of the nonlinear magnetic suspension force is derived. Based on the force model, it is found that the nonlinear stiffness feature can be adjusted by changing the magnet distance of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber. Then the dynamic equations of the vibration reduction system are solved by using the Complex Variable Average method. And the correctness of the derivation procedure is verified through the Runge–Kutta method. From the numerical solutions, bifurcation phenomena occur in the system responses when the excitation amplitude is larger than a certain value. Adjusting the magnet distance and the damping coefficient of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber can delay or avoid bifurcation behaviors. When the excitation amplitude varies over a wide range, the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber with a larger magnet distance and damping coefficient shows better vibration reduction performance. This study provides a theoretical basis for the practical application of the Triple-magnet Magnetic Suspension Dynamic Vibration Absorber and new ideas for controlling the bifurcation of traditional nonlinear dynamic vibration absorbers.

Nonlinear gas-spring DVA for seismic response control: Experiment and numerical simulation

A gas-spring with adjustable nonlinear capacity is introduced into a conventional linear dynamic vibration absorber (DVA), thus forming a nonlinear gas-spring dynamic vibration absorber for structural seismic response control, which is a nonlinear energy sink with a fundamental tuning function. The mechanical properties of the symmetrical combined gas-spring system are studied first by theoretical analysis and model tests. A series of shaking table tests are designed and conducted to systematically investigate the control effect and nonlinear damping mechanism of the gas-spring DVA for a 5-story structure. A numerical model of the nonlinear gas-spring DVA attached to the structure is established and validated by the experimental results. The experimental results show that the proposed nonlinear gas-spring DVA can effectively mitigate the structural dynamic responses and has a wide damping bandwidth with good stability. The presented system has amplitude-frequency characteristics, and the sensitivity of its control performance to amplitude is significantly reduced by introducing a fundamental tuning mechanism. The nonlinear DVA vibrates in a broadband mode and is capable of resonating with the structure at multiple frequencies so that the nonlinear restoring force of the gas-spring DVA redistributes the structure’s vibration energy from its low-order modes to high-order modes. Compared with the optimum tuning DVA, the reasonably designed nonlinear gas-spring DVA has a similar control effect and shorter working stroke, possessing the advantage of flexible parameter configuration capabilities. Moreover, the experimental and numerical simulation results are in good agreement, indicating that the proposed numerical model is accurate in predicting the behaviors of the nonlinear gas-spring DVA.

Passivity‐based control of nonlinear active dynamic vibration absorber

AbstractIn this article, a nonlinear active dynamic vibration absorber based on passivity‐based energy shaping control is proposed. Using the proposed method, the vibrations that are excited by force and velocity disturbances simultaneously can be controlled. The control law only uses the relative displacement and velocity of the vibration system, which can be easily measured by sensors. The numerical solutions to the partial differential equations are not required in our proposed method. The main idea of the controller's parameters design is to convert a plant system with a nonlinear dynamic vibration absorber into a desired system with multiple virtual skyhook dampers. We also derive the parameters' selection guidelines for the proposed controller. The global asymptotical stability is guaranteed through passivity‐based control theory, although the parameter design is based on linearization. We verify the effectiveness of the proposed controller by some simulations on a cart‐pendulum system.

A novel triple-magnet magnetic suspension dynamic vibration absorber

The existing Nonlinear Dynamic Vibration Absorbers (NLDVA) have the disadvantages of complex structure, high cost, high installation space requirements, and difficulty in miniaturization. And most of the NLDVAs have not been applied to reality. To address the above issues, a novel Triple-magnet Magnetic Suspension Dynamic Vibration Absorber (TMSDVA), only composed of triple cylindrical permanent magnets and an acrylic tube, is proposed in this paper. Firstly, the equivalent dynamics model of a TMSDVA cantilever system is established. A comparison of the simulation and experimental results serves to indicate that the suspended magnet will be "locked" when the instantaneous total energy of the system is less than a certain threshold. According to that, we modify the dynamics model. Next, the vibration reduction mechanism of the TMSDVA is revealed from the perspective of transient dynamics and energy. The TMSDVA can resonate with primary structures with different natural frequencies, so that the vibration energy can be targeted transferred to the TMSDVA and dissipated by the damping. Whether the acrylic tube has holes affects the damping of the TMSDVA, then the energy transfer between the primary structure and the TMSDVA and the energy dissipation rate of the TMSDVA, and ultimately the vibration reduction effect of the TMSDVA. By comparing the vibration reduction effects of the TMSDVA with holes and the TMSDVA without holes, we find increasing the damping coefficient appropriately can improve the vibration reduction effect of the TMSDVA, reduce the sensitivity of the vibration reduction effect to the excitation amplitude, and further enhance the robustness of the TMSDVA. Taken together, the TMSDVA has potential application value in the gravity direction vibration reduction of engineering structures.

Random vibration analysis of nonlinear structure with pounding tuned mass damper

To mitigate the undesired vibrations of the structure, a cost-effective approach is to set up the nonlinear dynamic vibration absorber (NLDVA) on the structure. As an alternative NLDVA, the Pounding Tuned Mass Damper (PTMD) gathered extensively attention in recent years. However, the random vibration analysis of structure coupled with PTMD still poses a challenge. Besides, there remains an urgent need to construct a more comprehensive recovery coefficient (RC) for the two-stage damping mechanism of PTMD. To fill in this gap, this work involves the nonlinear random vibration of a type of two degree-of-freedom system composing of a main structure (MS) coupled to a PTMD device, in which the collision process of the system is portrayed by a segmented recovery coefficient (RC) model. Specifically, an equivalent system of structure-PTMD is firstly constructed by coordinate transformation. Then, the approximate probability density function (PDF) of equivalent system is performed by combining non-smooth conversion and stochastic averaging method (SAM). Further, the approximate PDF solution of the structure-PTMD can be determined by resorting to Jacobi transformation and verified numerically. Remarkably, the approximate PDF solutions of the system can also be applied to estimate the power spectral density of the system response. Being analytical, the analysis in this work yields results in the closed-form expressions that enable one to acquire new insight into the dynamic features of the structure-PTMD system. Moreover, the proposed scheme will promote the design and application of PTMD in practical projects from a theoretical point of view.

New force transmissibility and optimization for a nonlinear dynamic vibration absorber

New force transmissibility and optimization for a nonlinear dynamic vibration absorber

A Comparison Between the Linear and Nonlinear Dynamic Vibration Absorber for a Timoshenko Beam

Dynamic vibration absorbers (DVAs) play an important role in the energy dissipation of a vibrating system. Undesirable vibrations of structures can be reduced by using the absorbers. This paper investigates the effect of an attached energy sink on the energy dissipation of a simply supported beam subjected to harmonic excitation. The aim is to design an optimal linear energy sink (LES) and a nonlinear energy sink (NES) and then compare them with each other. Each absorber includes a spring, a mass, and a damper. For each absorber, the optimum mass, stiffness, and damping coefficients are obtained in order to minimize the beam’s maximum amplitude at the resonant frequencies. The optimization problem is minimizing the maximum amplitude of the beam subjected to an arbitrary harmonic force excitation. For consideration of the effects of rotary inertia and shear deformation, the Timoshenko beam theory is used. The mathematical model of beam with DVA is verified by using the ANSYS WORKBENCH software. Finally, by considering the uncertainty on the DVA parameters it was observed that the LES is more robust than the NES.

Two-dimensional nonlinear energy sink for effective passive seismic mitigation

Structures and machines are often exposed to sudden high-amplitude vibrations that may cause local or extended structural failure. This calls for effective and reliable methodologies for vibration mitigation, one of which is the use of linear or nonlinear dynamic vibration absorbers. Current studies in this area have focused mainly on uni-directional vibration absorbers, thus limiting their applicability in practical applications where the excitation is applied in the plane. For example, real-life structures are subjected to a multitude of multi-directional seismic excitations, so uni-directional devices for mitigating such effects would have limited effectiveness. Accordingly, in this work we propose a two-dimensional nonlinear passive absorber, which we term two-dimensional nonlinear energy sink (2D-NES), and investigate its efficacy to robustly suppress seismic excitations in arbitrary directions on the plane. First, a numerical optimization process is formulated to optimize the 2D-NES for the especially severe Kobe seismic excitation through a set of quantitative measures related to the seismic response of the primary structure. Then, its robustness is confirmed by applying two additional historic earthquakes with different frequency and energy contents. The results demonstrate that the optimized 2D-NES is capable of effectively and rapidly suppressing seismic, multi directional excitations. This work is one of the first studies of 2D nonlinear vibration absorbers capable of robust passive mitigation of seismic loads applied in arbitrary planar directions. This design can be suitable for broad applications ranging from the nano/micro- to the macro-scale.

A Novel Dynamic Absorber with Variable Frequency and Damping

Smoothness and discontinuous (SD) oscillator is a nonlinear oscillator with the variable frequency, whose frequency can be varied with the smoothing parameter. However, how to adjust the smoothing parameter has not been solved in the actual device. In this paper, the shape memory alloy (SMA) is introduced into the SD oscillator to form the SMA-SD oscillator to adjust the smoothing parameters. Combining the SMA-SD oscillator with MRF, a nonlinear dynamic vibration absorber (DVA) with variable frequency and damping is designed. The structure and control principle of the designed DVA is studied to achieve the two variable characteristics simultaneously by adjusting the current intensity. Numerical results on a two-degree-of-freedom coupled system show that the proposed DVA can adapt to different working conditions only by adjusting the current intensity.

On-Line Modal Parameter Identification Applied to Linear and Nonlinear Vibration Absorbers

A solution of the vibration attention problem on a flexible structure from a dynamic vibration absorption perspective is experimentally and numerically studied in this article. Linear and nonlinear dynamic vibration absorbers are properly implemented on a primary structure of n degrees of freedom through a modal decomposition analysis and using the tuning condition when the primary system has one single degree of freedom. A time-domain algebraic identification scheme for on-line modal parameter estimation of flexible structures is presented. A fast frequency estimation of harmonic excitation force is also obtained. A Hilbert transform analysis of the frequency response function for the case of nonlinear dynamic vibration absorption is introduced. In this way, influence of this particular passive nonlinear control device on system dynamic response can be determined. The proposed approach is validated on an harmonically perturbed building-like structure, which is discretized in a finite number of degrees of freedom. The flexible structure is subjected to resonant operational conditions, and coupled to a pendulum vibration absorber configured as a tuned mass damper as well as an autoparametric system.

Nonlinear vibration absorbers applied on footbridges

This paper deals with the performance of linear and nonlinear dynamic vibration absorbers (DVAs) to suppress footbridges vertical vibrations. The walking pedestrian vertical force is modeled as a moving time-dependent force and mass. The partial differential equations govern the dynamics of the system; such equations are reduced to a set of ordinary differential equations by means of the Bubnov–Galerkin method with an accurate multimode expansion of the displacement field. The optimal vibration absorber parameters are determined using two objective functions: maximum footbridge deflection and the transferred energy from the footbridge to the DVA. The most suitable nonlinear DVA is proposed for the investigated footbridge. The results show that the DVAs with quadratic nonlinearity are the most performant DVAs.

Experimental characterization and performance of dynamic vibration absorber with tunable piecewise-linear stiffness

Dynamic vibration absorber (DVA) is one of the ways to control the level of vibration. Among many mechanisms and control strategies of the DVA, passively tuned DVA emerges as one of the most effective absorbers due to its simple mechanism. However, the performance of the passive tuned DVA suffers from narrow suppression bandwidth. This paper introduces a nonlinear dynamic vibration absorber (NDVA) with an adjustable piecewise-linear stiffness mechanism which has a characteristic almost similar to hardening stiffness to broaden the vibration suppression bandwidth. The mechanism is made of a cantilever beam constrained by two vertically and horizontally adjustable limit blocks on either side of the beam’s equilibrium position. The static and dynamic properties of the proposed NDVA were first investigated for different positions of the limit blocks. Then the performance of the NDVA was compared with the linear DVA in terms of the vibration suppression bandwidth, separation of resonance frequencies and the ability to cope with mistuning. Overall, the NDVA seems to outperform the linear DVA, and it is more forgiving in the case of mistuning.

Design and Analysis of a Geometrically Nonlinear Dynamic Vibration Absorber

AbstractThe design and optimization of a nonlinear dynamic vibration absorber based on a snap-through truss geometry is investigated. The effect of absorber's parameters on primary system (PS) vibration amplitude reduction and frequency range of operation is analyzed. Within parametric analyses of the absorber, a methodology was proposed to tune the absorber's stiffness. Results show that the nonlinear vibration absorber may be substantially more effective than its linear counterpart both in terms of vibration amplitude reduction and absorption frequency range. Possible difficulties and/or limitations caused by the nonlinearity induced by the absorber are analyzed and, for the studied case, do not diminish the advantages of the nonlinear absorber (NLAbs). The effect of absorber's damping on the vibration reduction performance was also analyzed indicating that the NLAbs outperforms its linear counterpart even for higher damping levels.

DYNAMIC MODELING AND STABILITY ANALYSIS OF A NONLINEAR SYSTEM WITH PRIMARY RESONANCE

In recent years, there has been growing interest in the study of nonlinear phenomena. This is due to the modernization of structures related to the need of using lighter, more resistant and flexible materials. Thus, this work aims to study the behavior of a mechanical system with two degrees of freedom with nonlinear characteristics in primary resonance. The structure consists of the main system connected to a secondary system to act as a Nonlinear Dynamic Vibration Absorber, which partially or fully absorbs the vibrational energy of the system. The numerical solutions of the problem are obtained using the Runge-Kutta methods of the 4th order and approximate analytical solutions are obtained using the Multiple Scales Method. Then, the approximation error between the two solutions is analyzed.
 Using the aforementioned perturbation method, the responses for the ordinary differential equations of the first order can be determined, which describe the modulation amplitudes and phases. Thus, the solution in steady state and the stability are studied using the frequency response. Furthermore, the behavior of the main system and the absorber are investigated through numerical simulations, such as responses in the time domain, phase planes and Poincaré map; which shows that the system displays periodic, quasi-periodic and chaotic movements. The dynamic behavior of the system is analyzed using the Lyapunov exponent and the bifurcation diagram is presented to better summarize all the possible behaviors as the force amplitude varies. In general, the main characteristics of a dynamic system that experiences the chaotic response will be identified.

Impulsive vibration mitigation through a nonlinear tuned vibration absorber

The dynamics of a nonlinear passive vibration absorber conceived to mitigate vibrations of a nonlinear host structure is considered in this paper. The system under study is composed of a primary system, consisting of an undamped nonlinear oscillator of Duffing type, and a nonlinear dynamic vibration absorber, denominated nonlinear tuned vibration absorber (NLTVA). The NLTVA consists of a small mass, attached to the host structure through a linear damper, a linear and a cubic spring. The host structure is subject to free vibrations and the performance of the NLTVA is evaluated with respect to the minimal time required to dissipate a specific amount of the mechanical energy of the system. In order to characterize the dynamics of the system, a combination of numerical and analytical techniques is implemented. In particular, on the basis of the first-order reduced model, slow invariant manifolds of the transient dynamics are identified, which enable to estimate the absorber performance. Results illustrate that two different dynamical paths exist and the system can undergo either of them, depending on the initial conditions and on the value of the absorber nonlinear stiffness coefficient. One path leads to a very fast vibration mitigation, and therefore to a favorable behavior, while the other one causes a very slow energy dissipation.