This paper discusses the stability of a periodically time-varying, spinning blade with cubic geometric nonlinearity. The modal reduction method is adopted to simplify the nonlinear partial differential equations to the ordinary differential equations, and the geometric stiffening is approximated by the axial inertia membrane force. The method of multiple time scale is employed to study the steady state motions, the corresponding stability and bifurcation for such a periodically time-varying rotating blade. The backbone curves for steady-state motions are achieved, and the parameter map for stability and bifurcation is developed. Illustration of the steady-state motions is presented for an understanding of rotational motions of the rotating blade.
- Design Engineering Division and Computers and Information in Engineering Division
On Stability of a Nonlinear, Periodically Time Varying, Rotating Blade
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Wang, F. "On Stability of a Nonlinear, Periodically Time Varying, Rotating Blade." Proceedings of the ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts A and B. Washington, DC, USA. August 28–31, 2011. pp. 151-158. ASME. https://doi.org/10.1115/DETC2011-48574
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