Effect of axially functionally graded material on whirling frequencies and critical speeds of a spinning Timoshenko beam

Huang, Yixin; Wang, Tianshu; Zhao, Yang; Wang, Pingping

doi:10.1016/j.compstruct.2018.02.039

Cited by 32 publications

(9 citation statements)

References 46 publications

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“…3 Results The transverse vibrations natural frequency expression with one degree of freedom, with respect to the beam`s deflection from the load given, has the form [14]: (6) Lateral oscillations calculation allows you to check the ship`s shafting supports location, the length and selection of stern tube bearings elastic properties, their number, as well as mass and dimensions of the propeller. The ship`s shafting line lateral vibrations natural frequency value is affected by deflection parameter V0 at the propeller`s attachment point [15,16].…”

Section: Methodsmentioning

confidence: 99%

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Analysis of boundary conditions in design circuits influence on the shaft line operating state

Khalyavkin¹,

Makeev

Salamekh³

et al. 2020

E3S Web Conf.

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The work investigates the bearing piece boundary conditions influence on the shaft line operating state, with respect to elastic properties of stern-tube bearings. It is noted that the shaft line is a part of the ship’s power plant and it is a shaft system, located on the same axis. Performance criterion is the deflection of the concentrated load in the design scheme`s action point, modeling the propeller`s weight, bearing parts reactions and the natural frequency of linear lateral oscillations. The design scheme itself is a beam, resting on two elastic supports with a k stiffness factor, with concentrated load acting on the one end and three variants of the boundary conditions: pinched, hinged and sliding supports on another one. The results of calculations are given for different boundary conditions and the stiffness factors of elastic supports. The diagram of natural frequencies of linear lateral oscillations of ship`s shafting line is presented.

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Section: Methodsmentioning

confidence: 99%

“…Therefore, the uninterrupted and reliable shaft line operation is an actual problem nowadays. It can be proved by the large number of publications worldwide [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Analysis of boundary conditions in design circuits influence on the shaft line operating state

Khalyavkin¹,

Makeev

Salamekh³

et al. 2020

E3S Web Conf.

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“…Afshari et al 23 studied the influence of lumped masses on the whirling speeds of a rotating Timoshenko shaft carrying multiple concentrated masses and found that: the influence of a concentrated mass on the forward and backward frequencies is nil if it is located at the “nodal points” of that natural mode shape and is highest when it is located at an “antinode” of that mode. By the way, the following References 24‐28, may be useful for some readers. Huang et al 24 studied the free vibration of an axially functionally graded beam spinning with constant angular speed about its longitudinal axis.…”

Section: Introductionmentioning

confidence: 99%

“…By the way, the following References 24‐28, may be useful for some readers. Huang et al 24 studied the free vibration of an axially functionally graded beam spinning with constant angular speed about its longitudinal axis. She et al 25 investigated the coupled vibration in a flexible‐disk blades system with the influence of shaft bending vibration considered.…”

Section: Introductionmentioning

confidence: 99%

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Hsu

2020

Engineering Reports

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In theory, the whirling motion of a shaft-disk system is three-dimensional (3D), however, if the transverse displacement in the vertical principal xy-plane and that in the horizontal principal xz-plane for the cross-section of the shaft located at the axial coordinate x are represented by a complex number, then the mass moment of inertia for unit shaft length (at x) and that for each rigid disk i can be combined with their associated gyroscopic moments (GMs) to form the frequency-dependent equivalent mass moments of inertia, respectively, in the equations of motion for the rotating Timoshenko shaft carrying arbitrary rigid disks. It is found that the above-mentioned equations for the rotating 3D shaft-disk system take the same forms as the corresponding ones for the associated stationary two-dimensional (2D) Timoshenko beam carrying the same number of disks, so that the approaches for the free vibration analyses of the stationary 2D beam-disk system can be used to solve the title problem for obtaining the whirling speeds and mode shapes of a rotating 3D shaft-disk system. Since the order of the eigenproblem equation derived from the presented approach is much smaller than that derived from the conventional finite element method (FEM), the computer time consumed by the former is much less than that by the latter. In addition, the solutions obtained from the presented approach are exact and may be the benchmark for evaluating the accuracy of solutions of the other approximate methods. Numerical examples reveal that the presented approach is available for the uniform or nonuniform shaft-disk system, and the obtained results are very close to those obtained from existing literature or the FEM. The formulation of this article is available for a shaft-disk system with various boundary conditions (BCs), to save space, only the cases with pinned-pinned BCs are illustrated. K E Y W O R D S Timoshenko shaft, gyroscopic moment, equivalent mass moment of inertia, whirling speeds and mode shapes This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…From a dynamic perspective, coupling factors of shaft alignment and whirling vibration characteristics mainly include: vertical and axial bearing displacement, bearing stiffness, number of shafting support points, propeller excitation, main engine excitation, structural parameters of shafting etc. [5][6][7][8]. Murawski and Ostachowicz [9] firstly conduct the static shaft alignment of main engine under cold and hot state, where he considered the stiffness and damping of ship base, bearing stiffness, oil lubrication bearing film characteristics and other factors, based on the multi-fulcrum shaft system alignment model established for stern bearing, was implemented.…”

Section: Introductionmentioning

confidence: 99%

Coupling characteristic analysis of ship shafting design parameters and research on multidisciplinary design optimization

Yin¹,

Liu²,

Zeng³

2020

J. vibroeng.

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In the design process of traditional ship shafting, the design quality is generally hard to get guaranteed for the lack of discipline coupling. In this paper, Multidisciplinary Design Optimization (MDO) is innovatively introduced to ensure design quality. Multidisciplinary decomposition of shafting can help to construct the MDO model of ship shafting based on multidisciplinary feasibility method. Then the sub-discipline model of shifting design can be further established, including calibration neutron discipline model, whirling vibration model, and dynamic stiffness of radial oil film bearing model. Collaborative operation is implemented by the multidisciplinary model of shifting to obtain the experimental results. Based on Radial Basis Function (RBF) neural network, the responsive surfaces of variable, bearing load, and support stiffness can be constructed, in the meanwhile the dynamic stiffness decoupling of vibration model can be obtained. Fireworks algorithm is used to establish multidisciplinary optimization of seven-dimensional design variable. The results show that MDO helps improve the quality of shafting alignment and whirling vibration. The work in present paper also provides insight for the future optimization of research methods, design quality, and engineering experiments.

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Effect of axially functionally graded material on whirling frequencies and critical speeds of a spinning Timoshenko beam

Cited by 32 publications

References 46 publications

Analysis of boundary conditions in design circuits influence on the shaft line operating state

Analysis of boundary conditions in design circuits influence on the shaft line operating state

An efficient approach for whirling speeds and mode shapes of uniform and nonuniform Timoshenko shafts mounted by arbitrary rigid disks

Coupling characteristic analysis of ship shafting design parameters and research on multidisciplinary design optimization

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