Dynamical interaction of an elastic system and essentially nonlinear absorber

Mikhlin, Yuri V.; Решетникова, С Н

doi:10.1016/j.jsv.2004.03.061

Cited by 25 publications

(23 citation statements)

References 20 publications

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“…Following the paper [13], (16) are substituted into the system (17) and matching the coefficients at the same summands ξ j 1 l v j 2 l ; j 1 = 0, 1, 2, . .…”

Section: Combination Of Rausher Approach and Nonlinear Modesmentioning

confidence: 99%

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Analysis of forced vibrations by nonlinear modes

Аврамов

2007

Nonlinear Dyn

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The combination of Rausher method and nonlinear modes is suggested to analyze the forced vibrations of nonlinear discrete systems. The basis of the Rausher method is iterative procedure. In this case, the analysis of a nonautonomous dynamical system reduces to the multiple solutions of the autonomous ones. As an example, the forced vibrations of shallow arch close to equilibrium position are considered in this paper. The results of the analysis are shown on the frequency response.

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“…Following the paper [13], (16) are substituted into the system (17) and matching the coefficients at the same summands ξ j 1 l v j 2 l ; j 1 = 0, 1, 2, . .…”

Section: Combination Of Rausher Approach and Nonlinear Modesmentioning

confidence: 99%

“…They are used to analyze the problems of absorption of mechanical vibrations in the papers [15,16]. Nonlinear modes are used to analyze the nonlinear vibrations of rotating pretwisted beams [17].…”

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confidence: 99%

Analysis of forced vibrations by nonlinear modes

Аврамов

2007

Nonlinear Dyn

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“…The use of asymptotic techniques to find approximate solutions was addressed in several works; Vakakis et al [29] used an averaging method, Gendelman et al [28] used a multiple scale method, Mikhlin and Reshetnikova [29] used an expansion method in combining with a Mathieu equation comparison to investigate the stability of periodic solutions. Moreover Vakakis and Rand [30] proposed a method to derive exact solutions for systems with cubic nonlinearities based on the use of elliptic functions.…”

Section: Introductionmentioning

confidence: 99%

Effects of mistuning on dynamic behavior of nonlinear cyclic systems with lump masses and cubic nonlinearity

Estabragh

Rad

Rahimi

2016

Mechanics & Industry

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-Mistuning in cyclic symmetric systems increases severely the forced response of system and splits the modes. This paper concerns with nonlinear behavior of mistuned cyclic systems. A nonlinear, mistuned model based on the method of multiple scales is proposed and formulated in which nonlinearity and mistuning parameter is assumed to be in of low order. Next, two mistuned systems were considered and solved by the multiple scale technique. Numerical results demonstrate that mistuning can lead to repeating and scattering of jump phenomena during the excitation frequency whereas in tuned cyclic system it occurs simultaneously (synchronously).

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“…Georgiades and Vakakis solved the impact response of a linear beam with a local nonlinear energy sink (NES) numerically [14]. Mikhlin and Reshetnikova analyzed the forced response of a beam with a NES by assuming the beam being a mass-spring system [15]. Some certain nonlinear systems were studied analytically by applying approximate methods in these references.…”

Section: Introductionmentioning

confidence: 99%

Vibration of two beams connected by nonlinear isolators: analytical and experimental study

Wang

Zheng

2010

Nonlinear Dyn

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To study the coupling vibration of nonlinear isolators and flexible bodies, test rigs of two flexible beams connected by wire mesh isolators are constructed and investigated both experimentally and analytically. A five-parameter polynomial model of wire mesh isolators is derived by identifying parameters in the frequency domain with the sine-sweep test. For obtaining the parameters that are valid in a wide range of frequency, a numerically assisted identification method is developed. With this model, the vibration of two flexible beams connected by wire mesh isolators is studied. The frequency response is obtained analytically by employing the Green's function method and harmonic balance method. Sine-sweep test results with three test rigs show good coherence with the corresponding numerical results. With obtained experimental results and numerical results, effect of connection parameters is studied in detail. It is found that traditional design rules for isolators are no longer effective and the coupling vibration must be investigated in the design phase. Another phenomenon is that the damping has a function of weakening the effect of nonlinear stiffness. Nonlinear stiffness and nonlinear damping can decrease the transmissibility along with the increase of the excitation level.

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Dynamical interaction of an elastic system and essentially nonlinear absorber

Cited by 25 publications

References 20 publications

Analysis of forced vibrations by nonlinear modes

Analysis of forced vibrations by nonlinear modes

Effects of mistuning on dynamic behavior of nonlinear cyclic systems with lump masses and cubic nonlinearity

Vibration of two beams connected by nonlinear isolators: analytical and experimental study

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