Analysis of forced vibrations by nonlinear modes

Аврамов, К. В.

doi:10.1007/s11071-007-9300-8

Cited by 26 publications

(17 citation statements)

References 15 publications

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“…The development of the theory of NNMs in nonautonomous systems is considered in Refs. [26,[135][136][137]. NNMs in near-conservative self-excited systems were analyzed in Ref.…”

Section: Nnms In Nonautonomous Systemsmentioning

confidence: 99%

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Mikhlin

Аврамов

2010

Applied Mechanics Reviews

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Two principal concepts of nonlinear normal vibrations modes (NNMs), namely the Kauderer-Rosenberg and Shaw-Pierre concepts, are analyzed. Properties of the NNMs and methods of their analysis are presented. NNMs stability and bifurcations are discussed. Combined application of the NNMs and the Rauscher method to analyze forced and parametric vibrations is discussed. Generalization of the NNMs to continuous systems dynamics is also described.

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“…The development of the theory of NNMs in nonautonomous systems is considered in Refs. [26,[135][136][137]. NNMs in near-conservative self-excited systems were analyzed in Ref.…”

Section: Nnms In Nonautonomous Systemsmentioning

confidence: 99%

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Mikhlin

Аврамов

2010

Applied Mechanics Reviews

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“…where Q is the matrix of eigenvectors of the matrix K 1 . In the modal coordinates, the dynamical system (3) takes the form…”

Section: Numerical Analysis Of Nonlinear Normal Modes For Nonautonomomentioning

confidence: 99%

“…First, we consider the nonlinear normal modes in the autonomous dynamical system that follows from (4) if the external periodic forces are neglected. According to the procedure of finding the Shaw-Pierre nonlinear normal modes [1,3], we choose one of the modal coordinates η and its velocity as driving. We denote these coordinates by (η 1 , !…”

Section: Numerical Analysis Of Nonlinear Normal Modes For Nonautonomomentioning

confidence: 99%

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Non-linear dynamics of a one-way clutch in belt–pulley systems

Zhu

Parker

2005

Journal of Sound and Vibration

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A method for the numerical analysis of nonlinear normal modes of forced vibrations in strongly nonlinear systems with piecewise linear elastic characteristics is proposed. The approach is based on the combination of the Shaw-Pierre method of nonlinear normal modes with the Rauscher technique. As a result of application of this approach, the nonautonomous piecewise linear system is transformed into an autonomous system. For this system, we determine the Shaw-Pierre nonlinear normal modes. We also study the nonlinear torsional vibrations of the power transmission in a three-cylinder transport engine.

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“…The Shaw-Pierre nonlinear normal modes are currently used as a modern method for studying nonlinear dynamic systems [9][10][11] and widely applied for solving many technical problems [12,13]. A modified version of this method for studying self-excited vibrations of the rotor is presented below.…”

mentioning

confidence: 99%

A model of asymmetric single-disk rotor self-vibrations

Аврамов

2010

Strength Mater

Self Cite

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A model for self-excited vibrations of a single-disk asymmetric rotor with short sliding bearings is proposed, which is reduced to a system of four ordinary differential equations of the second order. The obtained dynamic system is described by the Shaw-Pierre nonlinear normal modes.Keywords: short sliding bearings, the Reynolds equation, nonlinear normal modes of vibration. Introduction. Self-excited vibrations in the rotor system can occur due to interaction between oil film of the bearing and the rotor shaft pivot (journal). It is shown in [1] that such interaction results in failure of some rotor systems. At present, modern analytical and numerical methods of the nonlinear dynamics [2] are widely used for studying vibrations in rotor systems. The analytical results which describe the pressure of the oil film in the bearings were obtained in [3]. The asymptotic solution to the Reynolds equation was obtained using the variational approach in [4]. Stability of the pivot rotating in the bearing was considered in [5]. The model describing the pressure distribution in the oil film of short sliding bearings was proposed in [6], where the impact of oil film inertia forces on the pressure was studied. The authors [7] use the asymptotic methods for studying self-excited vibrations in rotors. Forced vibrations of rotor with account for oil film in short sliding bearings were analyzed in [8], whereas the rotor dynamics was described using the design model consisting of elastic shaft with three discrete lumps.Nowadays, nonlinear normal modes of vibrations are considered to be the most effective approaches to the theory of nonlinear mechanical vibrations used for analyzing both natural and forced vibrations [9-11].A new model for self-excited vibrations of the single-disk asymmetric rotor in short sliding bearings is proposed in this study. Pressure in the oil film is described using the model of short sliding bearing. To study self-excited vibrations of rotor, modified method of the nonlinear normal modes is given.Equations of Motion for the System. Let us consider the dynamics of the rigid disk which is mounted on the rotating shaft in short sliding bearings (Fig. 1). When the shaft pivot vibrates, pivots A and B (Fig. 1) move. These motions are described by generalized coordinates (x y

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Analysis of forced vibrations by nonlinear modes

Cited by 26 publications

References 15 publications

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Nonlinears Normal Modes for Vibrating Mechanical Systems. Review of Theoretical Developments

Non-linear dynamics of a one-way clutch in belt–pulley systems

A model of asymmetric single-disk rotor self-vibrations

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