A geometrically exact approach to the overall dynamics of elastic rotating blades—part 1: linear modal properties

Lacarbonara, Walter; Arvin, Hadi; Bakhtiari-Nejad, Firooz

doi:10.1007/s11071-012-0486-z

Cited by 66 publications

(32 citation statements)

References 16 publications

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“…In order to explore the effects of nonlinearities of both geometric and dynamic origin when investigating the free vibration characteristics of rotating beams, interested readers are referred to the works of Turhan and Bulut [21], Lacarbonara et al [22], Arvin et al [23], Kim et al [24] and Sotoudeh and Hodges [25,26].…”

Section: Scope and Limitations Of The Theorymentioning

confidence: 99%

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Banerjee

Kennedy

2014

Journal of Sound and Vibration

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a b s t r a c tThe paper addresses the in-plane free vibration analysis of rotating beams using an exact dynamic stiffness method. The analysis includes the Coriolis effects in the free vibratory motion as well as the effects of an arbitrary hub radius and an outboard force. The investigation focuses on the formulation of the frequency dependent dynamic stiffness matrix to perform exact modal analysis of rotating beams or beam assemblies. The governing differential equations of motion, derived from Hamilton's principle, are solved using the Frobenius method. Natural boundary conditions resulting from the Hamiltonian formulation enable expressions for nodal forces to be obtained in terms of arbitrary constants. The dynamic stiffness matrix is developed by relating the amplitudes of the nodal forces to those of the corresponding responses, thereby eliminating the arbitrary constants. Then the natural frequencies and mode shapes follow from the application of the Wittrick-Williams algorithm. Numerical results for an individual rotating beam for cantilever boundary condition are given and some results are validated. The influences of Coriolis effects, rotational speed and hub radius on the natural frequencies and mode shapes are illustrated.

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Section: Scope and Limitations Of The Theorymentioning

confidence: 99%

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Banerjee

Kennedy

2014

Journal of Sound and Vibration

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“…where EA is the axial rigidity, F T = A σ dA is the nonlinear axial force whose steady-state part is the centrifugal force N p = L x m(y)Ω 2 (e + y cos β p )dy [29,30] (so F T -terms include the influence of the centrifugal effect), m = m + m 0 δ(x − x 0 ), and E I 1 and E I 2 are the thicknesswise and chordwise bending rigidity, respectively. The associated boundary conditions are…”

Section: Governing Equationsmentioning

confidence: 99%

Effect of balance weight on dynamic characteristics of a rotating wind turbine blade

Liu

et al. 2015

J Eng Math

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Iron pellets are often added in blades to maintain moment balance in the design process of a wind turbine. The balance weight will change the natural vibration characteristics of the wind turbine blade. Resonant frequencies may appear for this reason, so it is necessary to study the effects of balance weight on the dynamic characteristics of a blade. In this paper, the wind turbine blade, after the weight balance process, is modeled as an Euler-Bernoulli beam with lumped masses. A mathematical model for a rotating nonuniform blade with a lumped mass on an arbitrary section is established, while nonlinear partial differential equations governing the coupled extensional-bending-bending vibration are obtained by applying the Hamiltonian principle. The associated modal problem is obtained from the governing equations, and then the differential form of the modal problem is transformed to integral form based on Green's functions (structural influence functions). A direct numerical approach is applied to calculate natural frequencies and vibrating modes. The effects of the mass and position of the balance weight and the rotating speed on the natural frequencies and mode shapes of the blade are discussed.

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“…and next substituted in (15)(16)(17)(18)(19)(20)(21). After unknowns reordering one arrives at final formulas for onedimensional stress measures…”

Section: Potential Energymentioning

confidence: 99%

“…A nonlinear model of rotating isotropic blades based on the Cosserat theory of rods without restrictions on the geometry of deformation was presented in [18]. The roles of internal kinematic constraints such as unshearability of the slender blades, coupling between flapping, lagging, axial and torsional deformations were studied.…”

Section: Introductionmentioning

confidence: 99%

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

2014

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In the presented paper the equations of motion of a rotating composite Timoshenko beam are derived by utilising the Hamilton principle. The nonclassical effects like material anisotropy, transverse shear and both primary and secondary cross-section warpings are taken into account in the analysis. As an extension of the other papers known to the authors a nonconstant rotating speed and an arbitrary beam's preset (pitch) angle are considered. It is shown that the resulting general equations of motion are coupled together and form a nonlinear system of PDEs. Two cases of an open and closed box-beam cross-section made of symmetric laminate are analysed in details. It is shown that considering different pitch angles there is a strong effect in coupling of flapwise bending with chordwise bending motions due to a centrifugal force. Moreover, a consequence of terms related to nonconstant rotating speed is presented. Therefore it is shown that both the variable rotating speed and nonzero pitch angle have significant impact on systems dynamics and need to be considered in modelling of rotating beams.

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A geometrically exact approach to the overall dynamics of elastic rotating blades—part 1: linear modal properties

Cited by 66 publications

References 16 publications

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Dynamic stiffness method for inplane free vibration of rotating beams including Coriolis effects

Effect of balance weight on dynamic characteristics of a rotating wind turbine blade

Equations of motion of rotating composite beam with a nonconstant rotation speed and an arbitrary preset angle

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