Coupled Bending–bending–torsion Vibration Analysis of Rotating Pretwisted Blades: An Integral Formulation and Numerical Examples

Surace, G.; Anghel, Viorel; Mares, C.

doi:10.1006/jsvi.1997.1092

Cited by 49 publications

(26 citation statements)

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“…(12)- (14) are impossible because there are integral terms that arise from rotation and because the blade is nonuniform. The numerical method based on Green's functions [25] can be adopted to deal with such problems. According to Refs.…”

Section: Dynamic Characteristics Of Blade With Balance Weightmentioning

confidence: 99%

“…According to Refs. [25][26][27], for the following ordinary differential equations corresponding to the modal problem of the coupled extensional-bending-bending vibration,…”

Section: Dynamic Characteristics Of Blade With Balance Weightmentioning

confidence: 99%

“…Given the geometric and physical parameters, approximate methods (for example, the dynamic stiffness method [20], the differential transform method [21], Galerkin's method [22,23], the Rayleigh-Ritz method [22,24], the assumed-modes method [22], and the method of weighted residuals [22]) can be employed with the aid of a reasonable mathematical model. In this work, the modal problem is solved by applying a numerical approach based on Green's functions (structural influence functions) [25][26][27] that can deal with the modal problem of nonuniform structures conveniently and that has not been used for wind turbine blades. Based on a concrete computational model, the effects of the balance weight on the natural frequencies and vibrating shapes of the blade are discussed.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Dynamic Characteristics Of Blade With Balance Weightmentioning

confidence: 99%

“…According to Refs. [25][26][27], for the following ordinary differential equations corresponding to the modal problem of the coupled extensional-bending-bending vibration,…”

Section: Dynamic Characteristics Of Blade With Balance Weightmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Liu

et al. 2015

J Eng Math

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“…The coupled bending vibration analysis in the case of pretwisted blades was presented in [6]. Then, a general case of the coupled bending-bending-torsion vibration analysis of straight beams and blades was described in [7]. The papers [8,9] concern the dynamic analysis of rotating beams with tip mass.…”

Section: Introductionmentioning

confidence: 99%

Integral Method for Static, Dynamic, Stability and Aeroelastic Analysis of Beam-like Structure Configurations

Anghel¹

2017

INCAS BULLETIN

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“…Surace et al [13] presented an approximate method for dynamic analysis. Young and Lin [14] studied the stability of a cantilever tapered pre-twisted beam with varying speed using the Galerkin method.…”

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confidence: 99%

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Talebi

Ariaei

2014

Arch Appl Mech

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An analytical method is presented to determine the vibration characteristics of a rotating Timoshenko beam with variable cross section and intermediate flexible connections using the differential transform method. Based on the application of Timoshenko beam theory on separate beams and the compatibility requirements on each connection point, the correlations between every two adjacent spans are obtained. The formulation is extended to a point where it would be able to evaluate the cases with internal and external flexible connections. The results will be validated against those reported in the literature and compared with the ones from the modal test. A number of parametric studies are conducted to assess the stiffness of elastic connections, rotating speed, hub radius and tapered ratio effects on the beam natural frequencies and mode shapes. It is observed that by changing the stiffness of the intermediate springs, the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams.

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Coupled Bending–bending–torsion Vibration Analysis of Rotating Pretwisted Blades: An Integral Formulation and Numerical Examples

Cited by 49 publications

References 0 publications

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

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

Integral Method for Static, Dynamic, Stability and Aeroelastic Analysis of Beam-like Structure Configurations

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

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