Development of a dynamic stiffness matrix for free vibration analysis of spinning beams

Banerjee, J.R.; Su, Huijuan

doi:10.1016/j.compstruc.2004.03.058

Cited by 56 publications

(57 citation statements)

References 16 publications

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“…(2.8) are fully consistent with the results by Banerjee and Su (2004). Also, it can be concluded that the eccentricity induces the coupling between transverse deformations and torsional motion.…”

Section: Equations Of Motionsupporting

confidence: 81%

“…The example for validating is taken from literature (Banerjee and Su, 2004). The beam has a rectangular cross section and possesses equal flexural rigidities in the two principal directions of the cross section.…”

Section: Validationmentioning

confidence: 99%

“…At a certain spinning speed, which is defined as the critical speed, the first natural frequency becomes negative, resulting in instability. For the spinning beam with circular or rectangular cross-section, the natural frequencies are obtained by subtracting or adding the natural frequencies when Ω * = 0 to the spinning speed parameter (Banerjee and Su, 2004). So the value of the critical spinning speed when the beam becomes unstable equals to the first frequency of the beam with Ω * = 0.…”

Section: Spinning Speedmentioning

confidence: 99%

“…The non-dimensional natural frequency and the spinning speed parameter are defined as in literature (Banerjee and Su, 2004)…”

Section: Validationmentioning

confidence: 99%

“…Yoon and Kim (2002) utilized the finite element method to analyze the dynamic stability of an unconstrained spinning beam subjected to a pulsating follower force. Banerjee and Su (2004) developed the dynamic stiffness method and the Wittrick--Williams algorithm was applied to compute natural frequencies and mode shapes. This method was also used in the free vibration analysis of a spinning composite beam (Banerjee and Su, 2006).…”

Section: Introductionmentioning

confidence: 99%

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Modeling and analysis for coupled flexural-torsional spinning beams with unsymmetrical cross sections

Wang

Jiang

2017

jtam

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The structural modeling and dynamic properties of a spinning beam with an unsymmetrical cross section are studied. Due to the eccentricity and spinning, transverse deflections along the two principal directions and the torsional motion about the longitudinal axis are coupled. The structural model of the beam is established based on the Hamilton principle and by incorporating the torsional inertia. Moreover, because of its significant influence on characteristics for the non-circular cross-sectional beam, the warping effect is considered in the formulation. The proposed model is effectively validated in two cases: the spinning beam with a symmetric cross section and the cantilevered beam with an unsymmetrical cross section. Then the effects of the spinning speed on natural frequencies and mode shapes are investigated. Numerical results reveal that the critical speed is altered with respect to noncoincidence of the centroid and the shear center. For the beams with strong warping rigidities, the warping effect cannot be neglected due to significant influence on natural frequencies.

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Section: Equations Of Motionsupporting

confidence: 81%

Section: Validationmentioning

confidence: 99%

Section: Spinning Speedmentioning

confidence: 99%

“…The non-dimensional natural frequency and the spinning speed parameter are defined as in literature (Banerjee and Su, 2004)…”

Section: Validationmentioning

confidence: 99%