Linear Dynamic Vibration Absorber Research Articles

Parameter optimization of a two-stage quasi-zero-stiffness system with linear dynamic vibration absorber

Parameter optimization of a two-stage quasi-zero-stiffness system with linear dynamic vibration absorber

On the dynamic characteristics of using track nonlinear energy sinks for structural vibration control

Nonlinear energy sinks (NESs) have emerged as a promising solution to overcome the narrow effective bandwidth of linear dynamic vibration absorbers such as the tuned mass damper (TMD). In particular, track NESs are increasingly attracting attention as they are capable of generating nonlinear restoring forces by the movement of an additional mass on the curved tracks. The present study aims to investigate and explore the versatile characteristics of track NESs in structural vibration control. To this end, three different track profiles are considered, namely the profiles designed by a quartic term only, by combined positive quadratic and quartic terms, and by combined negative quadratic and positive quartic terms. Their profiles and damping coefficients are analytically derived in closed form. The frequency response functions of standalone track NESs are constructed using the Harmonic Balance Method and compared with those obtained by the 4th-order Runge-Kutta method, and the dynamic responses, including the displacements, the phase planes, the nonlinear stiffness forces, and the vibrational frequencies, of the track NESs are presented and discussed under different excitation amplitudes and frequencies. The effectiveness and robustness of using track NESs for structural vibration control are also systematically investigated and compared with TMD under harmonic and white-noise ground excitations. Results show that the closed-form solutions of optimal profile and damping coefficients are sufficiently accurate for lightly damped structures, and the frequency response functions of track NESs can be accurately estimated using the Harmonic Balance Method for low and moderate excitations, although their dynamic responses are sensitive to the excitation amplitudes and frequencies. Furthermore, in comparison to TMD, the track NESs are superior in terms of decreased stiffness and smaller working strokes. In general, the present study demonstrates the potential of using track NESs as an effective and robust alternative for structural vibration control.

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.

A combined vibration isolation system with quasi-zero stiffness and dynamic vibration absorber

The vibration control performance of a combined vibration isolation (CVI) system consists of a quasi-zero stiffness (QZS) system and a linear dynamic vibration absorber (DVA) is investigated. Firstly, the dynamic equation is established and the amplitude-frequency response of the CVI system is deduced by the harmonic balance method, and the analytical result is verified by numerical simulation. Secondly, the mechanism of CVI system is revealed from the perspectives of vibration amplitude, energy, and force transmission: The vibration isolation performance of the QZS system can be improved by reducing the vibration amplitude. Thirdly, the control performance of the CVI system is analyzed in terms of the effects of the stiffness, damping, mass ratio of DVA, and the damping of the primary system, as well as the robustness of the system. The findings lead to the development of an explicit tuning rule for the DVA attached to the QZS system. Lastly, a comparison of control performance with other three models is conducted. The results demonstrate that the CVI system can effectively suppress the vibration amplitude and broaden the isolation frequency band. The mechanism and tuning rule for the CVI system presented in this paper provides a useful reference for improving the control performance of the QZS system.

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.

Permanent magnet based nonlinear energy sink for torsional vibration suppression of rotor systems

A permanent magnet nonlinear energy sink (PMNES) featuring a combination of negative stiffness and positive stiffness is proposed to suppress the torsional vibrations of the rotor system. The specific structure and working principles of the PMNES are introduced. Then, the dynamic model of the rotor-PMNES system is established, and the vibration attenuation ability of the proposed PMNES is numerically studied. And then, the vibration reduction performance of the PMNES and linear dynamic vibration absorber (LDVA) is compared. Finally, experimental studies on the rotor system are carried out. The results show that the rotor system with the PMNES obtains 2.31 times dissipating speed than the rotor system without the PMNES in transient responses, and the suppression rate of PMNES on the rotor can reach 65.37% in steady-state responses.

Application of non-smooth NES in vibration suppression of rotor-blade systems

The non-smooth nonlinear energy sink (NSNES) is used to suppress the vibration of the rotor-blade system. Firstly, the structure and working principle of the NSNES for rotor-blade system are introduced. Then, the dynamics model of the rotor-blade-NSNES system is established by Lagrangian method. And then, numerical simulations are applied to evaluate the vibration suppression ability of the NSNES on rotor and blade. The results show that the suppression rates of NSNES on the rotor and the blade can reach 81% and 74% in steady state resonance under given parameters, respectively; and for transient vibration of blade, a 1.85 times dissipating speed is obtained in rotor-blade system with NSNES than that without NSNES. In particular, NSNES has better vibration suppression capability than linear dynamic vibration absorber (LDVA) when both have the same vibration absorption mass.

On the numerical simulations of amplitude-adaptive impact dampers

Two impact dampers are analysed and compared with respect to their effectiveness for vibration reduction. Estimations of nonlinear system behaviour are derived using only well-known solutions for a linear dynamic vibration absorber. Critical parameter values separating domains with qualitatively different system behaviours are found. Using numerical simulations, the estimations are verified and the influence of each system parameter on the vibration amplitudes is investigated individually. Each of these systems exhibits advantages in the suppression of particular resonances, because they react either to the absolute or relative motion within the system.

Dynamical stability of cantilevered pipe conveying fluid in the presence of linear dynamic vibration absorber

When the velocity of fluid flow in a cantilevered pipe is successively increased, the system may become unstable and flutter instability would occur at a critical flow velocity. This paper is concerned with exploring the dynamical stability of a cantilevered fluid-conveying pipe with an additional linear dynamic vibration absorber (DVA) attachment. It is endeavoured to show that the stability of the pipe may be considerably enhanced due to the presence of DVA. The quasi-analytical results show that the energy transferred from the flowing fluid to the pipe may be partially transferred to the additional mass. In most cases, thus, the critical flow velocity at which the pipe becomes unstable would become larger, meanwhile the flutter instability of the DVA is not easy to achieve. In such a fluid-structure interaction system, it is also found that flutter instability may first occur in the mode of the DVA. The effects of damping coefficient, weight, location and spring stiffness of the DVA on the critical flow velocities and nonlinear oscillations of the system have also been analyzed.

Performance of a Non Linear Dynamic Vibration Absorbers

AbstractThe most common method of vibration control is the use of the dynamic absorbers. Two types of absorbers can be found: Linear and nonlinear. The use of linear absorbers allows reducing vibration but only at the resonance frequency, whereas nonlinear absorbers attenuate vibration on a wide band of frequency. In this paper, a nonlinear two degrees of freedom (DOF) model is developed. A cubic nonlinearity induced by a gap is considered. The objective of the paper is to characterize nonlinear vibration of the system by applying explicit formulation (EF). An experimental study is performed to validate the numerical results. The jump phenomenon is the principal nonlinear dynamic phenomenon observed on both numerical and experimental investigations.

Sequential design of two orthogonal dynamic vibration absorbers in a pendulum based on stability maximization

A dynamic vibration absorber moving in the tangential or in the normal direction of a pendulum’s orbit can reduce the free vibration of the pendulum. This article discusses the problem of a pendulum structure attached with two dynamic vibration absorbers moving orthogonally at the same time. The analytical optimization is proposed to be done in two steps, in which the parameters of the linear dynamic vibration absorber moving in tangential direction and the non-linear dynamic vibration absorber moving in normal direction are chosen sequentially based on the stability maximization criterion. The analytical analysis shows that the two-dynamic vibration absorber scheme has small benefit in comparison with the single-dynamic vibration absorber scheme. The analytical conclusions are verified by numerical calculations. Although the conclusion of the article is unexpected, it is important in practice because the two-dynamic vibration absorber arrangement can be excluded in the design.

Application of a Dynamic Vibration Absorber to a Piecewise Linear Beam System

This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many subharmonics appear. The damped DVA suppresses the first harmonic resonance as well as its super- and subharmonics.

Design of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Magnification Factor. Derivation of Algebraic Exact Solution.

Fixed points design methods for dynamic vibration absorbers are very well-known in the field of vibration control and commonly applied for practical absorber design. However, they must be understood to be approximation methods from the point of view of their design criterion that the resonance amplitude magnification factor is minimized. In this study, the exact algebraic expressions of optimum tuning and damping parameters for the minimization of the largest resonance amplitude magnification factor of linear dynamic vibration absorbers have been derived for undamped primary systems. The existence of two equal height resonance points is reduced to a multiple root condition of an algebraic equation. The determinant is handled as an equation with respect to the resonance amplitude. It has became very clear that the fixed points theory design by Brock is highly accurate. In particular, it exhibits very small error in the practical mass ratio range, e.g., below unity. Algebraic solutions also exist for the resonance frequencies and the anti-resonance frequency. A numerical extension of the method is introduced in order to investigate the optimization problem for damped primary systems.

Dynamic vibration absorbers: theory and technical applications

Theory of the linear dynamic vibration absorber at various citations constructional shapes and complicated models of dynamic vibration absorbers vibrations of systems with infinite degrees of freedom equipped with dynamic absorbers practical applications of the theory and examples of realized vibration protection systems.