Dynamics modelling of a flexible hub–beam system with a tip mass

Yang, Hui; Hong, Jin; Yu, Zhengyue

doi:10.1016/s0022-460x(02)01332-9

Cited by 60 publications

(24 citation statements)

References 13 publications

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“…A cubic polynomial is employed to describe both components of the positions. Therefore, the global shape function matrix S can be written as [20] S = s 1 s 2 = s 1 0 ls 2 0 s 3 0 ls 4 0 0 s 1 0 ls 2 0 s 3 0 ls 4 (5) in which the functions s i = s i (ξ ) are defined as…”

Section: Equation Derivationmentioning

confidence: 99%

“…And a modal formulation method was also introduced to calculate the tuned angular speed of a rotating beam where resonance occurs. Hong [4][5][6][7] presented the first-order approximation coupling (FOAC) model which was based on the theory of continuum medium mechanics and the theory of analytical dynamics. This model considers the secondorder coupling term of the longitudinal displacement caused by transversal deformation, but it ignores the high-order terms of the second-order coupling term.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, those structures should be simplified as flexible beams with an additional concentrated mass. Yang et al [5] and Cai et al [6] studied the characteristics of a flexible hubbeam system with a tip mass based on the first-order approximation coupling model. Simulation and comparison show that even a small tip mass may affect the dynamic characteristics and the end position of the hub-beam system greatly, which may also result in the largening of vibrating amplitude and the descending of vibrating frequency of the beam.…”

Section: Introductionmentioning

confidence: 99%

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Modal characteristics of a rotating flexible beam with a concentrated mass based on the absolute nodal coordinate formulation

Zhang

Chen

et al. 2016

Nonlinear Dyn

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A new dynamic model of a rotating flexible beam with a concentrated mass located in arbitrary position is derived based on the absolute nodal coordinate formulation, and its modal characteristics are investigated in this paper. To consider the concentrated mass at an arbitrary location of the beam, a Dirac's delta function is used to express the mass per unit length of the beam. Based on the proposed dynamic model, the frequency analysis is performed. The nonlinear equation is transformed into the linear one via employing the linear perturbation analysis method. The stiffness matrix of static equilibrium of the system under the deformed condition is obtained, in which the effect of coupling between the longitudinal deformation and transversal deformation is included. This means even if only the chordwise bending equation is solved, the longitudinal vibration effect can be still considered. As we know, once the longitudinal deformation is large, it will significantly affect the chordwise bending vibration. So the proposed model in this paper is more accurate than the traditional dynamic models which are usually lack of the coupling terms between the longitudinal deformation and transversal deformation. In fact, the traditional dynamic models for the chordwise vibration analysis in the existing literature are usually linear due to neglecting the coupling terms, and consequently, they are only suitable for the modal characteristic analysis of a beam under small deformations. In order to get some general conclusions of the natural frequencies and mode shapes, the equation which governs the chordwise bending vibration of the rotating beam is transformed into a dimensionless form. The dynamic model presented in this paper is nonlinear and can be conveniently used to analyze the modal characteristics of a rotating flexible beam with large deformations. To demonstrate the power of the new dynamic model presented in this paper, the dynamic simulations involving the comparisons between the different frequencies obtained using the model proposed in this paper and the models in the existing literature and the investigating in frequency veering and mode shift phenomena are given. The simulation results show that the angular velocity of the flexible beam will give rise to the phenomena of the natural frequency loci veering and the associated mode shift which is verified in the previous studies. In addition, the phenomena of the natural frequency loci veering rather than crossing can 123 X. Zhang et al.be observed due to the changing of the magnitude of the concentrated mass or of the location of the concentrated mass which are found for the first time. Furthermore, there is an interesting phenomenon that the natural frequency loci will veer more than once due to different types of mode coupling between the bending and stretching vibrations of the rotating beam. At the same time, the mode shift phenomenon will occur correspondingly. Additionally, the characteristics of the vibration nodes are also investigated in this paper.

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Section: Equation Derivationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Modal characteristics of a rotating flexible beam with a concentrated mass based on the absolute nodal coordinate formulation

Zhang

Chen

et al. 2016

Nonlinear Dyn

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“…Song and Librescu [3] discussed the effects of rotating speed and the tip mass ratio on the natural frequencies of a uniform blade by adopting a thin-wall beam model. Yang et al [4] studied the dynamic behavior of a flexible hub-beam system with a tip mass in conjunction with the finite-element method (FEM). Oguamanam [5] analyzed the effects of certain parameters on the fundamental frequency of an Euler-Bernoulli beam with coupling between the torsion and planar bend; these parameters include the magnitude of the tip mass, the offset of the tip mass center of gravity from the point of attachment, moments of inertia of the tip mass about the center of gravity, beam length, the slenderness ratio, bending stiffness, and torsional rigidity.…”

Section: Introductionmentioning

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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“…On the other hand, Al-Bedoor and Khulief 26 have employed transition elements in FEM to study sliding flexible links. In the same line, dynamics modeling of a flexible hub-beam system with tip mass has been carried out by Yang et al 27 via FEM. Free vibration characteristics of rotating axially functionally graded tapered beams have been investigated by Zarrinzadeh et al 28 through a finite element approach.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytical solutions of an axially moving spacecraft appendage subjected to tip mass

Ghaleh

Khayyat

Farjami

et al. 2013

Proceedings of the Institution of Mechanical Engineers, Part G:

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Approximate solutions for vibrations of flexible beam-type appendages subjected to tip mass are studied while uniform and exponential profiles for arm deployment are simulated. Applying an equivalent dynamical system and following Lagrangian approach, the equations of motion of the system are derived as nonlinear ordinary differential equations (ODEs) (with time-varying coefficients), in which the effect of the tip mass can be considered as some nonlinearity added to the 'no tip mass' case dynamics. The approximate closed-form solutions are obtained through a novel methodology using a computer algorithm, in which the solutions of the 'no tip mass' case are expanded by imposing quadratic perturbations on the independent variable. The mean square of errors (MSEs) for the obtained approximate analytical solution is computed. Using this method, the amplitude and frequency of the arm response are presented by the algebraic equations, which help the parametric design of such systems. In addition, effects of tip mass as an indicator of nonlinearities added to the system dynamics, on the amplitude and frequency of the beam response, are investigated during arm deployment.

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Dynamics modelling of a flexible hub–beam system with a tip mass

Cited by 60 publications

References 13 publications

Modal characteristics of a rotating flexible beam with a concentrated mass based on the absolute nodal coordinate formulation

Modal characteristics of a rotating flexible beam with a concentrated mass based on the absolute nodal coordinate formulation

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

Approximate analytical solutions of an axially moving spacecraft appendage subjected to tip mass

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