Analytical solution for primary resonances of a rotating shaft with stretching non-linearity

Hosseini, S.A.A.; Khadem, S.E.

doi:10.1243/09544062jmes923

Cited by 17 publications

(14 citation statements)

References 18 publications

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“…The characteristic of the steady-state amplitude curve of the unbalanced rotor system with weak stiffness is similar to that of the linear unbalanced rotor system when k s is small and the value of the amplitude reaches the peak near the first critical speed. This phenomenon clearly implies that the larger nonlinear stiffness can induce more obvious nonlinear vibration characteristics and balancing the rotating shaft is necessary especially if it operates beyond the first critical speed [18]. In Figure 4b, the nonlinear amplitude curves exhibit a similar twisting property for different ω 0 and the larger ω 0 corresponds to the larger maximum amplitude, which means that the decreasing system natural frequency is beneficial to reducing the vibration amplitude.…”

Section: Resultsmentioning

confidence: 89%

“…The numerical results exhibited rich forms of multiperiodic, quasi-periodic and chaotic motion and implied that the nonlinear sealing force had great influence on the dynamic characteristics of the rotor system. Hosseini and Khadem [18] studied the primary resonances of a rotating shaft with stretching nonlinearity and the characteristics of free vibration considering nonlinear inertia and curvature were further analyzed [19]. Vlajic [20,21] studied torsional vibrations of a Jeffcott rotor subjected to the continuous stator contact numerically and analytically for both backward and forward whirling motions.…”

Section: Introductionmentioning

confidence: 99%

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Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

Zhang

et al. 2018

TFAMENA

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Steady-state vibration response characteristics of a motion model of a centrifugal pump rotor system with weak nonlinear stiffness have been calculated by using the multiple scale method (MSM). The theoretical results were in good agreement with the numerical results. Based on the MSM and the numerical method, the effects of detuning parameter, nonlinear stiffness parameter and natural frequency on steady-state amplitude were also investigated. Finally, Lyapunov's theorem on stability in the first approximation was applied for the determination of the system's stable and unstable solution regions. The calculated results imply that the centrifugal pump rotor system with weak nonlinear stiffness exhibits typical nonlinear vibration characteristics. The variation of detuning parameter, nonlinear stiffness parameter and natural frequency can result in a jump phenomenon, and their corresponding curves present 'hard spring', 'soft spring' and 'S'-shaped amplitude characteristic, respectively. Smaller detuning parameter and natural frequency or greater nonlinear stiffness parameter are beneficial to decreasing the steady-state response amplitude. The results can provide reference for an investigation into nonlinear vibration characteristics of a centrifugal pump rotor system.

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Section: Resultsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Zhou

Qiu

Zhang

et al. 2018

TFAMENA

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“…On the other hand, nonlinear analysis of rotating shafts with constant spin was carried out in previous works. [19][20][21][22] The aim of the present study is the investigation of nonstationary motion of rotating shafts with stretching nonlinearity and gyroscopic effect due to the large deformation excited by nonideal energy source. Indeed, combined effect of nonlinearity, gyroscopic effect, and non-ideal energy source is investigated.…”

Section: Introductionmentioning

confidence: 99%

Nonstationary analysis of nonlinear rotating shafts passing through critical speed excited by a nonideal energy source

Mahmoudi

Hosseini

Zamanian

2016

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, the effect of nonlinearity on vibration of a rotating shaft passing through critical speed excited by nonideal energy source is investigated. Here, the interaction between a nonlinear gyroscopic continuous system (i.e. rotating shaft) and the energy source is considered. In the shaft model, the rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The nonlinearity is due to large deflection of the shaft. Firstly, nonlinear equations of motion governing the flexural–flexural–extensional vibrations of the rotating shaft with nonconstant spin are derived by the Hamilton principle. Then, the equations are simplified using stretching assumption. To analyze the nonstationary vibration of the nonideal system, multiple-scale method is directly applied to the equations expressed in complex coordinates. Three analytical expressions that describe variation of amplitude, phase, and angular acceleration during passage through critical speed are derived. It is shown that Sommerfeld effect in specific range of driving torque occurs. Finally, effect of damping and nonlinearity on occurrence of Sommerfeld effect is investigated. It is shown that the linear model predicts the range of Sommerfeld effect occurrence inaccurately and, therefore, nonlinear analysis is necessary in the present problem.

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“…They showed that prediction of the instability region is different for the linear and nonlinear equations of motion. Hosseini et al [3,4] investigated the nonlinear vibration behavior of rotating shafts with stretching nonlinearity and nonlinearity in curvature and inertia. Łuczko [5] proposed a method for modeling geometrically nonlinear rotating shafts.…”

Section: Introductionmentioning

confidence: 99%

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

Khanlo¹,

Ghayour

Ziaei-Rad

2012

J. mech.

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This study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

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Analytical solution for primary resonances of a rotating shaft with stretching non-linearity

Cited by 17 publications

References 18 publications

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Research on Steady-State Characteristics of Centrifugal Pump Rotor System with Weak Nonlinear Stiffness

Nonstationary analysis of nonlinear rotating shafts passing through critical speed excited by a nonideal energy source

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

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