Tapered Timoshenko finite elements for rotor dynamics analysis

Edney, Stephen L.; Fox, Colin; Williams, Edward J.

doi:10.1016/0022-460x(90)90812-e

Cited by 16 publications

(17 citation statements)

References 4 publications

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“…The bending stiffness matrices can be deduced along in lines similar to art. 2.6.1.1 as, (40) [k e e ] = l…”

Section: Formulation Of Tapered and Hollow Rotor Element Matrices Conmentioning

confidence: 99%

“…6 has been considered. The rotor is the same as that of reference [40] (example 2). The equations of motion of the rotor are obtained using the present element, and eigenvalues are calculated.…”

Section: Example 2: Tapered Hollow Elastic Rotormentioning

confidence: 99%

“…However, shear parameter ̄z is kept constant (average of two nodal value) throughout the axial length, and numerical integration is used to find out element matrices. Edeny et al [40] developed two models considering linear geometrical parameters and exact geometrical parameters with numerical integration. For both formulations, the shear parameter is the average of the two nodal values.…”

Section: Introductionmentioning

confidence: 99%

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A shaft finite element for analysis of viscoelastic tapered Timoshenko rotors

Bhowmick

Ganguly²,

Neogy

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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Finite element modeling of thick rotor (deep rotor) requires the use of the Timoshenko element, which takes care of shear deformation. Modeling a rotor whose cross section varies can be done using uniform stepped cylindrical elements, but the number of elements required for the converged results is enormous. Further modeling of doubly tapered rotors and rotors with sharp changes in taper angle using such methods become difficult and does not appear feasible that is why the formulation of conical rotor elements is necessary. The complexity in formulations arises due to the presence of the shear parameter in the denominator. Till now, in the literature of the Timoshenko rotor, geometric properties are taken to be linearly varying; the shear parameter is the approximation of average values of two end nodes. On the other hand, the modeling of damping in rotors becomes essential as it controls the stability limit. The present paper develops three different viscoelastic tapered rotor elements using the Maxwell-Wiechert model. While the first element (VTRE 1) uses the average shear parameter, the second element (VTRE 2) uses a higher degree polynomial to approximate the shear parameter. While the first two-rotor elements are solid, the third element (VTRE 3) is hollow. Results show that viscoelastic tapered elements provide better results with the lesser number of elements. For the rotor with a large taper angle, VTRE 2 performs better than VTRE 1. Further modeling of the hollow tapered rotor with a linear variation of taper angle and discontinuities at definite points is not possible by the use of uniform elements. Modeling such a rotor using VTRE 3 is rendered simple. Practical usage of such rotors further enhances the importance of the present work.

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“…The bending stiffness matrices can be deduced along in lines similar to art. 2.6.1.1 as, (40) [k e e ] = l…”

Section: Formulation Of Tapered and Hollow Rotor Element Matrices Conmentioning

confidence: 99%

Section: Example 2: Tapered Hollow Elastic Rotormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A shaft finite element for analysis of viscoelastic tapered Timoshenko rotors

Bhowmick

Ganguly²,

Neogy

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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“…Several papers have concentrated on finite beam elements of various kinds (e.g. conical or tapered), which include Rouch & Kao (1979), Nelson (1980), Genta (1985), Greenhill et al (1985), Genta & Gugliotta (1988), Edney et al (1990) and Gmür & Rodrigues (1991). Several other papers also studied Jeffcott rotors (a rotor with a point mass attached to a massless shaft) or simple variations thereof.…”

Section: Literature Reviewmentioning

confidence: 99%

Modal projections for synchronous rotor whirl

2008

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We consider the synchronous whirl of arbitrary axisymmetric rotors supported on rigid bearings. Prior computational treatments of this problem were based on adding elementlevel gyroscopic terms to the governing equations. Here, we begin with a direct continuum formulation wherein gyroscopic terms need not be added on separately and explicitly: all gyroscopic effects are captured implicitly within the continuum elastodynamics. We present two new methods for obtaining the whirl speed, where we project the dynamic equilibrium equations of the rotor on to a few of its non-spinning vibration mode shapes. The first modal projection method is direct and more accurate, but requires numerical evaluation of more demanding integrals. The second method is iterative and involves a small approximation, but is simpler. Both the methods are based on one new insight: the gyroscopic terms used in other treatments are essentially the result of a prestress in the rotor caused by the non-zero spin rate, and may be incorporated as such in the continuum formulation. The accuracy of the results obtained, for several examples, is verified against detailed calculations with a commercial finiteelement package, against our own nonlinear finite-element code or against analytical estimates. For further verification and illustration, a closed-form analytical solution for a simple problem, obtained using our method, matches the results obtained with explicit gyroscopic terms.

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“…Hence, to model rotors, it is better to use Timoshenko beam theory. This theory can be used for investigating frequency response of both large and nano scale structures (Torabi et al, 2013a;Samaei, 2015) at Using finite element method, Nelson (1980) studied the vibration analysis of the Timoshenko rotor with internal damping under axial load and Edney et al (1990) proposed dynamic analysis of the tapered Timoshenko rotor. They considered In this paper, an exact solution for whirling analysis of Timoshenko rotor subjected to axial load is presented.…”

Section: Introductionmentioning

confidence: 99%

Exact solution for whirling analysis of axial-loaded Timoshenko rotor using basic functions

Torabi

Afshari²

2016

10.5267/j.esm

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In this paper, an analytical solution for whirling analysis of axial-loaded Timoshenko rotor is presented and corresponding basic functions are derived. The set of governing equations for whirling analysis of the rotor consists of four coupled partial differential equations; using complex displacements, these equations can be reduced to two coupled partial differential equations. The versatility of the proposed solution is confirmed using published results and the effect of angular velocity of spin, axial load, slenderness and Poisson's ratio on the natural frequencies of the rotor are investigated.

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Tapered Timoshenko finite elements for rotor dynamics analysis

Cited by 16 publications

References 4 publications

A shaft finite element for analysis of viscoelastic tapered Timoshenko rotors

A shaft finite element for analysis of viscoelastic tapered Timoshenko rotors

Modal projections for synchronous rotor whirl

Exact solution for whirling analysis of axial-loaded Timoshenko rotor using basic functions

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