Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks

Zhang, Yewei; Zhang, Zhen; Chen, Liqun; Yang, Tianzhi; Fang, Bo; Zang, Jian

doi:10.1007/s11071-015-2138-6

Cited by 84 publications

(19 citation statements)

References 30 publications

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“…A single NES (coupled to the primary system) was the NES configuration the most often studied. Multi-Degree-Of-Freedom (multi-DOF) NES in series [21,22,23,24] or in parallel [13,25,26,27,28] were also considered. The use of several NESs allow to increase the range of excitations (level and frequency) within which the NES can absorb energy efficiently and/or to extract vibration energy simultaneously from multiple linear modes of the primary system.…”

Section: Introductionmentioning

confidence: 99%

“…To capture the complexity of the dynamic of the coupled system (primary system + NES) due to the nonlinear behaviour of the NES, various analysis have been developed including direct time integration method [25,9], harmonic balance method [29,6] or complex-averaging method [5]. The complex-averaging method [30] gives also access to the slow-flow model of the nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

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Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Bergeot

Bellizzi

2019

Mechanical Systems and Signal Processing

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A general method to predict the steady-state regimes of a multi-degree-of-freedom unstable vibrating system (the primary system) coupled to several nonlinear energy sinks (NESs) is proposed. The method has three main steps. The first step consists in the diagonalization of the primary underline linear system using the so-called biorthogonal transformation. Within the assumption of a primary system with only one unstable mode the dynamics of the diagonalized system is reduced ignoring the stable modes and keeping only the unstable mode. The complexification method is applied in the second step with the aim of obtaining the slowflow of the reduced system. Then, the third step is an asymptotic analysis of the slow-flow based geometric singular perturbation theory. The analysis shows that the critical manifold of the system can be reduced to a one dimensional parametric curve evolving in a multidimensional space. The shape and the stability properties of the critical manifold and the stability properties of the fixed points of the slow-flow provide an analytical tool to predict the nature of the possible steady-state regimes of the system. Finally, two examples are considered to evaluate the effectiveness and advancement of the proposed method. The method is first applied to the prediction of the mitigation limit of a breaking system subject to friction-induced vibrations coupled to two NESs, and next an airfoil model undergoing an aeroelastic instability coupled to a NESs setup (from one to four) is discussed. Theoretical results are compared, for validation purposes, to direct numerical integration of the system. The comparisons show good agreement.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Bergeot

Bellizzi

2019

Mechanical Systems and Signal Processing

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“…They showed that the vibrations of the string could be effectively dampened through negative linear velocity feedback at either the upstream or downstream of the system. Zhang et al [23] attended the passive and adaptive vibration attenuation of axially moving beams attached to nonlinear energy sinks. Their results indicated that the performance of the nonlinear absorbers could be appropriately promoted by adjusting the mass parameter.…”

Section: Introductionmentioning

confidence: 99%

Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

et al. 2020

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In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler-Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an exact analytical expression for the critical velocity of the AFG moving Rayleigh beams is presented. The stability maps and critical velocity contours for various material distributions are examined. In the case of variable density and elastic modulus, it is demonstrated that linear and exponential distributions provide a more stable system, respectively. Furthermore, the results revealed that the decrease of density gradient parameter and the increase of the elastic modulus gradient parameter enhance the natural frequencies and enlarge the instability threshold of the system. Hence, the density and elastic modulus gradients play opposite roles in the dynamic behavior of the system.

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“…Applications of the NES for the vibration suppression in various structures were reported in several papers. Theoretical and experimental studies indicated that the vibrations of beams [9,10], plates [11,12], circular cylinders [13], and stay-cables [14] can be effectively suppressed by the NES attachment. With the deepening of research, NES has been applied increasingly to suppress vibration of complicated engineering systems such as rotorblisk-journal bearing system [15], helicopter [16], and wholespacecraft [17].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Nonlinear Primary Oscillator with Nonlinear Energy Sink under Harmonic Excitation: Effects of Nonlinear Stiffness

Sun

Chen

2018

Mathematical Problems in Engineering

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The dynamics of a system consisting of a nonlinear primary oscillator, subjected to a harmonic external force, and a nonlinear energy sink (NES) are investigated. The analytical solutions for the steady-state responses are obtained by the complexification-averaging method and the analytical model is confirmed by numerical simulations. The results indicate that the introduction of the NES can effectively suppress the vibrations of the primary oscillator. However, as the excitation amplitude increased, the NES may lose its efficiency within certain frequency range due to the appearance of the high response branches. Following the results analysis, it is concluded that this failure can be eliminated by reducing the nonlinear stiffness of the NES properly. The effects of nonlinear stiffness of the primary oscillator on the corresponding responses are also studied. The increase in this nonlinear stiffness can reduce the response amplitude and alter the frequency band where the high branches exist.

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Impulse-induced vibration suppression of an axially moving beam with parallel nonlinear energy sinks

Cited by 84 publications

References 30 publications

Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Steady-state regimes prediction of a multi-degree-of-freedom unstable dynamical system coupled to a set of nonlinear energy sinks

Stability and Dynamics of Viscoelastic Moving Rayleigh Beams with an Asymmetrical Distribution of Material Parameters

Dynamics of Nonlinear Primary Oscillator with Nonlinear Energy Sink under Harmonic Excitation: Effects of Nonlinear Stiffness

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