Dynamic stability of a radially rotating beam subjected to base excitation

Tan, Ting; Lee, H.P.; Leng, Gerard

doi:10.1016/s0045-7825(96)01238-8

Cited by 24 publications

(11 citation statements)

References 14 publications

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“…Tan et al (1997) developed the equations of motion of a rotating cantilever beam induced by a base excitation by employing the Euler-Bernoulli beam theory. They used the method of multiple scales for determining the instability regions and presented numerical results to illustrate the influence of the hub radius to length ratio, the steady-state rotational speed and the base excitation frequency on the dynamic stability of the system.…”

Section: Introductionmentioning

confidence: 99%

Steady-state dynamic behavior of an on-board rotor under combined base motions

Dakel

Baguet

Dufour

2013

Journal of Vibration and Control

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To cite this version:M. Zaki Dakel, Sébastien Baguet, Régis Dufour. Steady-state dynamic behavior of an on-board rotor under combined base motions.. Journal of Vibration and Control, SAGE Publications, 2014, 20 (15) AbstractIn the transportation domain, on-board rotors in bending are subjected not only to rotating mass unbalance but also to several movements of their base. The main objective of this article is to predict the dynamic behavior of a rotor in the presence of base excitations. The proposed on-board rotor model is based on the Timoshenko beam finite element. It takes into account the effects corresponding to the rotary inertia, the gyroscopic inertia, the shear deformation of shaft as well as the geometric asymmetry of disk and/or shaft and considers six types of deterministic motions (rotations and translations) of the rotor rigid base. The use of Lagrange's equations associated with the finite element method yields the linear second-order differential equations of vibratory motion of the rotating rotor in bending relative to the moving rigid base which forms a non-inertial frame of reference. The linear equations of motion highlight periodic parametric terms due to the geometric asymmetry of the rotor components and time-varying parametric terms due to the rotational motions of the rotor rigid base. These parametric terms are considered as sources of internal excitation and can lead to lateral dynamic instability. In the presented applications, the rotor is excited by a rotating mass unbalance combined with constant rotation and sinusoidal translation of the base. Quasi-analytical and numerical solutions for two different rotor configurations (symmetric and asymmetric) are analyzed by means of stability charts, Campbell diagrams, steady-state responses as well as orbits of the rotor.

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Section: Introductionmentioning

confidence: 99%

Steady-state dynamic behavior of an on-board rotor under combined base motions

Dakel

Baguet

Dufour

2013

Journal of Vibration and Control

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“…The second part is due to the centrifugal force acting on the beam, which causes axial elongation (see, for example, reference [26]). It is given by:…”

Section: Modelingmentioning

confidence: 99%

“…See, for example, the work of Lin and Hsiao [19] which investigates the effect of Coriolis force on the natural frequencies of the rotating beam. More complex models including base excitation can be found in references [12,26]. Also, the fundamental frequency of rotating beams with pre-twist was studied by, for example, Hu et al [11].…”

Section: Introductionmentioning

confidence: 99%

On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

Mazzei

2012

Shock and Vibration

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Abstract. Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

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“…Steigmann and Faulkner [8] have presented the simplest theory of spatial rods. Using the assumed mode method and Lagrangian's approach, Tan et al [9] have derived the equations of motion of a rotating cantilever Euler-Bernoulli beam subjected to base excitation. O'Reilly and Turcotte [10] have developed and analyzed a model for the deformation of a rotating prismatic rod-like body.…”

Section: Introductionmentioning

confidence: 99%