Free Vibration Analysis of Rotating Blades With Uniform Tapers

Wang, Gang; Wereley, Norman M.

doi:10.2514/1.4302

Cited by 140 publications

(65 citation statements)

References 18 publications

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“…The effect of rotational speed for fixed taper ratios of τ b = 0 and τ b = 0.5 is shown in Table 3. Results manifested in Table 3 are in good agreement with those of G. Wang and N.M. Wereley [8] who used Spectral Finite Element Method.…”

Section: Resultssupporting

confidence: 85%

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Effect of Tapering on Natural Frequencies of Rotating Beams

Bazoune

Arabia²

2007

Shock and Vibration

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The problem of free vibration of a rotating tapered beam is investigated by developing explicit expressions for the mass, elastic and centrifugal stiffness matrices in terms of the taper ratios. This investigation takes into account the effect of tapering in two planes, the effect of hub radius as well as the stiffening effect of rotation. The equations of motion are derived; the associated generalized eigenvalue problem is defined in conjunction with a suitable Lagrangian form and solved for a wide range of parameter changes. The effect of tapering on the natural frequencies of the beam is examined with all parameter changes present. Results are compared with those available in literature and are found to be in excellent agreement.

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Section: Resultssupporting

confidence: 85%

“…Storti and Aboelnaga [7] have studied the transverse deflections of a straight tapered symmetric beam attached to a rotating hub as a model for bending vibration of blades in turbomachinery. Wang and Werely [8] extended the work of [2] to rotating tapered beams. They proposed a Spectral Finite Element Method (SFEM).…”

Section: Introductionmentioning

confidence: 99%

Effect of Tapering on Natural Frequencies of Rotating Beams

Bazoune

Arabia²

2007

Shock and Vibration

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“…He concluded that this approximation gives a lower bound of the natural frequencies. Another common technique for modelling tapered beams, found in literature, is by expressing the cross sectional properties as functions of the longitudinal coordinate [28,29]. Ozgemus and Kaya [30] derived the three-dimensional equation of motion of rotating tapered beams by the Hamilton's principle.…”

mentioning

confidence: 99%

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Stoykov

Manoach

Margenov

2015

Z. Angew. Math. Mech.

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A 3D beam model, i.e. a beam that may deform in space and experience longitudinal and torsional deformations, is developed considering Timoshenko's theory for bending and assuming that the cross section rotates as a rigid body but may deform in longitudinal direction due to warping. The cross sectional properties are firstly calculated and then inserted at the equation of motion. The beam is assumed to be with an arbitrary cross section, with linearly varying thickness and width, and with an initial twist. The model is appropriate for open and closed thin-walled cross sections, and also for solid cross sections. The objective of the current research is to demonstrate that complex beam structures can be modeled accurately with reduced number of degrees of freedom.

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“…The governing equation of rotating non‐prismatic beams is a general fourth order differential equation with variable coefficients introduced by the axially varying centrifugal force and cross‐sectional dimensions along the beam element. This equation generally cannot be solved in closed form; however, there are different approximate techniques to solve such differential equations such as Rayleigh–Ritz 1, Galerkin 2, 3, finite element 4–8, power series 9–12, differential transform method 13–16 and differential quadrature method 17, 18 that have been used in free vibration analysis of rotating beams.…”

Section: Introductionmentioning

confidence: 99%

Basic displacement functions for centrifugally stiffened tapered beams

Attarnejad¹,

Shahba²

2011

Numer Methods Biomed Eng

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SUMMARYIntroducing the concept of basic displacement functions (BDFs), free vibration analysis of rotating tapered beams is studied from a mechanical point of view. Holding pure structural/mechanical interpretations, BDFs are obtained by solving the governing static differential equation of flapwise motion of rotating EulerBernoulli beams and imposing appropriate boundary conditions. Following the principles of structural mechanics, it is shown that exact shape functions and consequently structural matrices could be derived in terms of BDFs. The new shape functions capture the effects of variation of both cross-sectional area and moment of inertia along the element and the stiffening effect of centrifugal force. The method is employed to determine the natural frequencies of tapered rotating beams with different variations of cross-sectional dimensions and the results are in good agreement with those in the literature. Finally, the effects of rotational speed and taper ratio on the natural frequencies are investigated.

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Free Vibration Analysis of Rotating Blades With Uniform Tapers

Cited by 140 publications

References 18 publications

Effect of Tapering on Natural Frequencies of Rotating Beams

Effect of Tapering on Natural Frequencies of Rotating Beams

An efficient 3D numerical beam model based on cross sectional analysis and Ritz approximations

Basic displacement functions for centrifugally stiffened tapered beams

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