Dynamic modeling and analysis of an axially moving and spinning Rayleigh beam based on a time-varying element

Shao‐Horn, Yang; Hu, Huajun; Mo, Guidong; Zhang, Qizhou; Qin, Junjie; Yin, Shen; Zhang, Jiabo

doi:10.1016/j.apm.2021.01.049

Cited by 22 publications

(4 citation statements)

References 47 publications

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“…46 The importance of thermal impact on the dynamics of moving systems is even more significant in the case of small-size structures. [47][48][49] Thermal effect on the buckling of moving microbeam was investigated in Nateghi and Salamat-talab. 50 Strain gradient and thermal effect on the dynamic response of a nanobeam were considered in Li.…”

Section: Introductionmentioning

confidence: 99%

“…Nonlocal strain gradient theory is another theoretical approach used in the modeling of small size effect 46 . The importance of thermal impact on the dynamics of moving systems is even more significant in the case of small‐size structures 47–49 . Thermal effect on the buckling of moving microbeam was investigated in Nateghi and Salamat‐talab 50 .…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali

2023

Math Methods in App Sciences

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Nonlinear transverse vibration of a micro‐size moving beam like structure under the influence of thermal conditions is studied. Hamilton principle is used to derive the nonlinear equation of motion. The derived equation of transverse motion is discretized using the Galerkin technique. The vibration attributes of the moving beam, such as frequencies of the transverse response, time response, and stability analysis, are investigated at different temperatures. For stability analysis, bifurcation diagrams are presented under the influence of temperature, length‐scale parameter, and excitation frequencies at various axial speeds of the beam.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Ali

2023

Math Methods in App Sciences

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“…Zhang et al (2020a) studied the frequency and mode of a flexible rotor system using Hamilton's principle and Euler's angle, and discussed the effect of centrifugal forces on the stability of the system. In recent years, researchers have been concerned with vibration of shafts under simultaneous effects of axial movement and rotational motion (Zhu and Chung, 2019;Ebrahimi-Mamaghani et al, 2021;Yang et al, 2021;Li et al, 2018;Katz, 2001). For example, applying the Hamilton principle, Zhu and Chung (2019) derived the governing equation of motion for a simply supported Rayleigh beam with spinning and axial motions.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a spinning shaft in the concentric cylinder filled with an incompressible fluid

Jiang,

Wang,

Yuan

2023

Journal of Theoretical and Applied Mechanics

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This paper deals with the stability of a spinning shaft in a concentric cylinder filled with an incompressible fluid. The steady-state momentum and continuity equations for the external fluid are established. Using Taylor expansion, the fluid forces exerted on the shaft are calculated. The shaft is in the Rayleigh model taking into account the rotary inertia and gyroscopic effects. Accordingly, the governing equation of the considered system is formulated analytically. The explicit characteristic frequency equation for the pinned-pinned spinning shaft system is then derived. Finally, the stability of the system is studied by means of characteristic value analysis.

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“…The rotor was represented as a homogenous and continuous Rayleigh beam. Yang and colleagues [11] used a new sort of TVRBSE based on the formulation of absolute node coordinates and Rayleigh beam theory under an arbitrary Lagrange-Euler description to develop a dynamic model of a moving and axially rotating Rayleigh beam. Zhu and J. Chung [12] used the proposed dynamical model to investigate the vibration and stability of a rotating Rayleigh beam with axial motion.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of vibration analysis in rotary shafts between Rayleigh's and Dunkerley's methods

Baher

Atiyah

Abdulsahib

2022

alkej

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The importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It proved that there is very little error between the experimental and theoretical results. The vibration signal from the sensors was analyzed using the LABVIEW program. Rayleigh's method was compared to the exact method, and it was considered the most accurate method. It was found that it made very little difference, up to about 0.06%. As for the Dunkerley method, the difference between it and the proper method is about 4%, which is acceptable. Then a comparison was made between Rayleigh's and Dunkerley's methods, and it was found that Dunkerley's method is the most appropriate in the calculations.

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Dynamic modeling and analysis of an axially moving and spinning Rayleigh beam based on a time-varying element

Cited by 22 publications

References 47 publications

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Nonlinear dynamic and stability of a small size moving beam under thermal conditions

Stability analysis of a spinning shaft in the concentric cylinder filled with an incompressible fluid

Comparative study of vibration analysis in rotary shafts between Rayleigh's and Dunkerley's methods

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