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

Khadem, S.E.; Shahgholi, Majid; Hosseini, Seyed Ali

doi:10.1007/s11071-010-9884-2

Cited by 30 publications

(10 citation statements)

References 25 publications

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“…The present paper tries to answer these questions. This article is a continuation of the author's previous papers [29][30][31][32], in which bifurcation and chaotic behavior of the rotor system is investigated. The shaft is modeled as a Rayleigh simply supported beam, spinning with 4 constant rotational speed.…”

Section: Introductionmentioning

confidence: 91%

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Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Hosseini

2018

Scientia Iranica

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In this paper, bifurcation and chaotic behavior of in-extensional rotating shafts are investigated. The shaft is modeled as a Rayleigh simply supported beam, spinning with constant rotational speed. Using two-mode Galerkin truncation, the partial differential equations of motion are discretized and then with the aid of numerical simulations, the dynamical behavior of the rotating shaft is studied. Using tools from nonlinear dynamics, such as time history, bifurcation diagram, Poincaré map, Lyapunov exponents, and amplitude spectra, a comprehensive analysis is made to characterize the complex behavior of the rotating shaft. Periodic (synchronous), quasiperiodic, chaotic and transient chaotic responses are observed in the neighborhood of the second critical speed. The effect of rotary inertia and damping on the dynamics of the rotating shaft is considered. It is shown that the chaotic response is possible for a shaft with weak nonlinearity without the existence of any internal resonance.

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Section: Introductionmentioning

confidence: 91%

“…In previous articles [29][30][31][32], dynamical behavior of nonlinear inextensional rotating shafts was studied by the author. In those papers, the periodic response of the shaft was considered and other types of shaft motion like quasi periodic and chaotic responses were not studied.…”

Section: Introductionmentioning

confidence: 99%

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Hosseini

2018

Scientia Iranica

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“…(22), creates first-and second-order nonlinearity in the temporal equation of motion. If the gravity effects are neglected, nonlinearity terms are only cubic [11][12][13][14]. Due to this fact, to apply the multiple scales method, three time scales are applied, T 0 = t, T 1 = εt and T 2 = ε 2 t. q (t) and p (t) are expanded in the following forms…”

Section: Formulation Of Dynamic Displacementmentioning

confidence: 99%

“…According to Eq. (14), the nondimensional parameters weight and moment of inertia are related to mass ratio by the following relationship…”

Section: Primary Resonancesmentioning

confidence: 99%

Nonlinear forced vibrations analysis of overhung rotors with unbalanced disk

2015

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In this paper, primary resonances of a cantilever flexible shaft carrying a rigid disk at its free end (overhung rotor) are investigated. Unbalance forces due to eccentricity and disk skew are simultaneously considered, and the shaft has initially static deflection due to the rotor's weight which causes asymmetry in the equations of motion. The rotor has large amplitude vibrations, which lead to nonlinearities in curvature and inertia. In the model, rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The method of multiple scales is applied to the discretize differential equations of motion. It is shown that the static deflection creates second-order nonlinear terms and near the primary resonances only the forward modes are excited. With considering the gravity, the inertial nonlinearities become stronger near the primary resonances. So, gravity decreases the hardening effect, and the nonlinear system tends to a linear system. It is concluded that the gravity effect has a softening effect. By using this property of gravity, a relation between weight and external forces is derived, in which by applying this relation the jumping phenomenon is eliminated. Numerical examples are presented, and the result is verified by numerical simulations.

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“…The multiple scales method was utilized to solve the governing equation and frequency response curves were presented. Khadem et al [13] studied the vibrations of a spinning metallic shaft with geometric nonlinearities by the use of the harmonic balance method at the combination resonance condition. The shaft was assumed to be inextensional, and the first two modes were utilized for the discretization process.…”

Section: Introductionmentioning

confidence: 99%

Combination resonances of spinning composite shafts considering geometric nonlinearity

Nezhad

Hosseini

Tiaki

2019

J Braz. Soc. Mech. Sci. Eng.

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In this paper, the combination resonance of a spinning composite shaft with geometric nonlinearity is studied by the method of harmonic balance. The full equations of motion containing the flexural-flexural-extensional-torsional coupling are employed for the analysis. The equations were discretized by both one and two modes, so two different forms of combination resonances can be analyzed. The shear deformation is neglected due to the shaft slenderness, whereas the rotary inertia and the gyroscopic effects are considered. The effects of different parameters such as external damping and the eccentricity on the response bifurcation of the shaft are investigated. The effect of the fiber orientation angle was also investigated. The results obtained for the composite shaft are compared to those of its metallic counterpart. It is shown that two geometrically identical shafts, one metallic and one composite, have different behaviors under the condition of combination resonance. It is observed that the vibration of the composite shaft occurs with smaller amplitude. This confirms the superiority of the composite shafts over metallic ones. Finally, the results were validated by the numerical simulations and there was a good agreement between the results.

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

Cited by 30 publications

References 25 publications

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Chaos and Bifurcation in Nonlinear Inextensional Rotating Shafts

Nonlinear forced vibrations analysis of overhung rotors with unbalanced disk

Combination resonances of spinning composite shafts considering geometric nonlinearity

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