Vibration and stability of an axially moving Rayleigh beam

Chang, J. R.; Lin, Wei Jr; Huang, Chun-Jung; Choi, Siu-Tong

doi:10.1016/j.apm.2009.08.022

Cited by 88 publications

(25 citation statements)

References 19 publications

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“…If the influence of flow is ignored, the stability of the deploying/retracting beam was investigated by Gosselin et al [20] via the dynamical behaviors of the beam, Zhang et al [22] based on the varying rate of total energy, and Chang et al [24] by the eigenvalues of the equations of motion. Among them, the eigenvalues based method is the simplest one.…”

Section: Stability Analysismentioning

confidence: 99%

Dynamic analysis of a vertically deploying/retracting cantilevered pipe conveying fluid

Yin-lei

Wang

2016

Journal of Sound and Vibration

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Section: Stability Analysismentioning

confidence: 99%

Dynamic analysis of a vertically deploying/retracting cantilevered pipe conveying fluid

Yin-lei

Wang

2016

Journal of Sound and Vibration

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“…Many researchers have used finite element method, FEM, for solving the beam with prismatic joint, Refs. [14][15][16]. Ref.…”

Section: Introductionmentioning

confidence: 99%

A constrained assumed modes method for solution of a new dynamic equation for an axially moving beam

Sharifnia

Akbarzadeh

2016

Computers & Mathematics with Applications

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a b s t r a c tFlexible beams with prismatic joints have complicated differential equations. This complexity is mostly due to axial motion of the beam. In the present research, a horizontal flexible link sliding through a passive prismatic joint while attached to a rigid link of a robot moving in a vertical direction is considered. A body coordinate system is used which aids in obtaining a new and rather simple form of the differential equation without the loss of generality. To model the passive prismatic joint, the motion differential equation is written in a form of virtual displacement. Next, a solution method is presented for the lateral vibrations of the beam referred to as ''constrained assumed modes method''. Unlike the traditional assumed modes method, in the proposed constrained assumed modes method, the assumed mode shapes do not each satisfy the geometrical boundary conditions of the point where passive prismatic joint is located. Instead, by writing additional constraint equations the combination of the assumed modes will satisfy the geometrical boundary conditions at location of the passive prismatic joint. Two case studies for the effect of axial motion on lateral vibration of the beam are presented. Approximate analytical results are compared with FEM results.

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“…A nonlocal viscoelastic constitutive model and external velocity-dependent damping model to analyze the dynamic characteristics of Timoshenko beams with different boundary conditions using the transfer function method was considered by Lei et al [6]. Based on Rayleigh beam theory and by using the finite element method, Chang et al [7] derived the equations of motion of an axially moving beam. Floquet theory was employed to investigate the effect of the axial-movement frequency on instantaneous natural frequencies and the stability of a telescopically moving beam with time-dependent velocity.…”

Section: Introductionmentioning

confidence: 99%