Forced oscillations of a vertical continuous rotor with geometric nonlinearity

Ishida, Yukio; Nagasaka, Imao; Inoue, Tsuyoshi; Lee, SeongWoo

doi:10.1007/bf00044997

Cited by 31 publications

(19 citation statements)

References 8 publications

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“…Equation (14) shows that the nonlinearity in the system is isotropic. Therefore, only the combination resonances of the type Ω = ω f,n − ω b,n + ω f,m can occur [5]. To express the closeness of resonances we introduce a detuning parameter σ such that…”

Section: Methods Of Harmonic Balancementioning

confidence: 99%

“…This assumption implies that the stretching effect is negligible. This situation is more realistic than some previous works, in which nonlinearity was due to the stretching of the shaft centerline [5], i.e. both supports are fixed in longitudinal direction.…”

Section: Introductionmentioning

confidence: 91%

“…Furthermore, subharmonic oscillations of order 1/2 in a nonlinear rotating shaft with internal damping were also considered [4]. They discussed the nonlinear forced oscillations of a continuous rotor [5]. The geometric nonlinearity in the rotor was due to the extension of the rotor centerline.…”

Section: Introductionmentioning

confidence: 99%

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Two-mode combination resonances of an in-extensional rotating shaft with large amplitude

2010

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In this paper, two-mode combination resonances of a simply supported rotating shaft are investigated. The shaft is modeled as an in-extensional spinning beam with large amplitude. Rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The equations of motion are derived with the aid of the Hamilton principle and then transformed to the complex form. The method of harmonic balance is applied to obtain analytical solutions. Frequencyresponse curves are plotted for the combination resonances of the first and the second modes. The effects of eccentricity and external damping are investigated on the steady state response of the rotating shaft. The loci of saddle node bifurcation points are plotted as functions of external damping and eccentricity. The results are validated with numerical simulations.

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Section: Methods Of Harmonic Balancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 91%

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Two-mode combination resonances of an in-extensional rotating shaft with large amplitude

2010

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“…Nonlinear resonance of a continuous rotor with geometric nonlinearity was first studied by Bolotin (55) . In Japan, Ishida et al (56) studied various nonlinear resonances of a slender vertical shaft. They showed that the resonance curve bend towards the higher speed side as shaft becomes slender (See Fig.11) and two kinds of combination resonance occur.…”

Section: Nonlinear Resonances In Continuous Rotor Systemsmentioning

confidence: 99%

Review of Research on Nonlinear Rotordynamics in Japan

Ishida

2013

JSDD

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This article introduces research on nonlinear rotordynamics in Japan. In most cases, the nonlinearity treated there was weak and it was approximated by a power series of low order. Firstly, the research on various nonlinear resonances due to the weak nonlinearity is introduced. Next, those on more complicated nonlinear phenomena, such as entrainment, internal resonances, chaotic vibrations, nonstationary vibrations, and more complicated systems, such as cracked rotors and continuous rotors, are explained. Then, research on phenomena due to strong nonlinearity is introduced. Various vibration suppression methods where the nonlinearity plays an important role are also explained. Finally, studies on the models representing helicopters and wind turbines are explained.

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“…This article investigates the dynamics of the rotor system analytically and numerically, by considering nonlinearity due to higher order large deformations in bending. In addition, if the supports of the rotor do not allow the shaft to move in the axial direction, then dynamic force will act on the rotor axially as it operates [15]. This force will also produce large deformations in bending.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

Shad

Michon

Berlioz

2011

Applied Mathematical Modelling

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a b s t r a c tA mathematical model incorporating the higher order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors. The rotor system considered for the present work consists of a flexible shaft and a rigid disk. The shaft is modeled as a beam with a circular cross section and the Euler Bernoulli beam theory is applied with added effects such as rotary inertia, gyroscopic effect, higher order large deformations, rotor mass unbalance and dynamic axial force. The kinetic and strain (deformation) energies of the rotor system are derived and the Rayleigh-Ritz method is used to discretize these energy expressions. Hamilton's principle is then applied to obtain the mathematical model consisting of second order coupled nonlinear differential equations of motion. In order to solve these equations and hence obtain the nonlinear dynamic response of the rotor system, the method of multiple scales is applied. Furthermore, this response is examined for different possible resonant conditions and resonant curves are plotted and discussed. It is concluded that nonlinearity due to higher order deformations significantly affects the dynamic behavior of the rotor system leading to resonant hard spring type curves. It is also observed that variations in the values of different parameters like mass unbalance and shaft diameter greatly influence dynamic response. These influences are also presented graphically and discussed.

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Forced oscillations of a vertical continuous rotor with geometric nonlinearity

Cited by 31 publications

References 8 publications

Two-mode combination resonances of an in-extensional rotating shaft with large amplitude

Two-mode combination resonances of an in-extensional rotating shaft with large amplitude

Review of Research on Nonlinear Rotordynamics in Japan

Modeling and analysis of nonlinear rotordynamics due to higher order deformations in bending

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