Dynamic Analysis of a Rotating Cantilever Beam by Using the Finite Element Method

Chung, Jintai; Yoo, Hong Hee

doi:10.1006/jsvi.2001.3856

Cited by 184 publications

(62 citation statements)

References 18 publications

(12 reference statements)

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“…It is notable that various dynamic models have been proposed to represent the dynamics of rotating beams (e.g. [12][13][14][15]). In these models different approaches, leading to various results, are utilized to account for the axial displacement and centrifugal force.…”

Section: The Dynamic Modelmentioning

confidence: 99%

Analytical approximate solutions for investigating non-damped system of cantilever beams

Jafari¹,

Ahmadi²,

Ghasempour³

et al. 2018

ntmsci

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In the current study, a comprehensive analysis of nonlinear free vibrations of a flexible rotating beam attached with a setting angle to a rigid hub is perused. The system is supposed to be subjected to an external torque and a rotation dissipation load which collectively referred to as perturbations. A set of two strongly coupled second-order ordinary nonlinear differential equations with an ignorable coordinate is used to depict the dynamics of the individual mode in plane flexural deflection of the arm and its overall rotational motion. For the unperturbed system which is our especial case in this work, the system angular momentum parameter, not the hub rotational speed, becomes a specified constant of motion. Furthermore, in order to consider the effect of beam deflections on the overall motion and vice versa, utilizing torque-controlled approach is necessary. It is noteworthy that here three powerful analytical methods for instance Modified Differential Transformation Method (MDTM), Variation Iteration Method (VIM) and finally Homotopy Perturbation Method (HPM) have been introduced to investigate the comportment and frequency of cantilever rotating beams with a setting angle. These methods are useful and practical for solving a wide variety of nonlinear equations. Comparisons amongst the obtained results by all the presented methods and Numerical solution reveal that all the afore-mentioned methods are significantly effective and efficient especially MDTM.

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Section: The Dynamic Modelmentioning

confidence: 99%

Analytical approximate solutions for investigating non-damped system of cantilever beams

Jafari¹,

Ahmadi²,

Ghasempour³

et al. 2018

ntmsci

View full text Add to dashboard Cite

show abstract

“…The Euler-Bernoulli beam model is used to describe a slender blade with coupled extensional-bending-bending vibration. To solve the modal problem of rotating nonuniform blades or beams, the FEM can achieve more accurate results based on the concrete geometric model [16][17][18][19]. 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.…”

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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“…The perturbation analysis was used to obtain the natural frequencies and the frequency responses. Chung and Yoo [2] used the finite element method and the discretized equations to investigate the behaviors of the natural frequencies with the variation of the rotating speed. Tsai [3] used the FEM to explore the dynamic characteristics of a single blade, 6-blade groups, and 12-blade groups and found that the vibration frequency and mode shape of single blade are in good agreement with that of the whole blade.…”

Section: Introductionmentioning

confidence: 99%

Study on the Nonlinear Characteristics of a Rotating Flexible Blade with Dovetail Interface Feature

Shen

Zhong

et al. 2018

Shock and Vibration

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A dynamic model is proposed in this paper for analyzing the nonlinear characteristics of a flexible blade. The dynamical equation of motion for a rotational flexible blade in a centrifugal force field is established based on the finite element method. A macro-stickslip mechanical model of dry friction is established to simulate the constraint condition of the flexible blade. The combined motion of the external excitation and friction produces a piecewise linear vibration which is actually nonlinear. The numerical integration method is employed to calculate the vibration reduction characteristics of the nonlinear constrained rotating blade. The results show that the nonlinear dry friction force produced by the dovetail interface plays an important role in vibration reduction. And the effect of dry friction vibration reduction is significant when the rotating speed is slow or the friction coefficient is small. Besides, the magnitude of external excitation also has a great impact on the state of the friction. Therefore, some relevant experimental researches should be done in the future.

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Dynamic Analysis of a Rotating Cantilever Beam by Using the Finite Element Method

Cited by 184 publications

References 18 publications

Analytical approximate solutions for investigating non-damped system of cantilever beams

Analytical approximate solutions for investigating non-damped system of cantilever beams

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

Study on the Nonlinear Characteristics of a Rotating Flexible Blade with Dovetail Interface Feature

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