Effect of Spinning Speed Fluctuation along with the Twist Angle on the Nonlinear Vibration and stability of an Asymmetrical Twisted Slender Beam

Document Type : Research Article

Authors

Faculty of Mechanical Engineering, Shahrood University of Technology

Abstract

In this study, the effect of spinning speed fluctuations along with the twist angle, on the stability and bifurcation of spinning slender twisted beams, with linear twist angle and large transverse deflections, near the primary and parametric resonances have been analyzed using the Euler–Bernoulli model. The spinning speed fluctuation along with the twist angle, asymmetry and imbalance, plays an important role on the frequency response of the twisted beam. The equations of motion, in the case of pure single mode motion, are analyzed by using the multiple scales method after discretization by the Galerkin's procedure. The instability of the twisted and untwisted beams is investigated and cases and domains are determined in which bifurcation could occur. Effects of the speed fluctuations, twist angle, damping ratio, asymmetry, eccentricity and mass moment of inertia about the longitudinal axis ( ) on the frequency response of the twisted beam are investigated. This is explained that the spinning speed fluctuation effect is weak in lower modes and smaller twist angles while asymmetry effect is dominant. By ascending the mode number and twist angle, spinning speed fluctuation effect amplifies the amplitude of system. Hence, it can be concluded that spinning speed fluctuation effect is considerable in twisted asymmetrical beams by ascending the mode number and twist angles. The results are compared and validated with the results obtained from Runge-Kutta numerical method in steady state, and confirmed with some previous researches.

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