Frequency Analysis of a Rotating Cantilever Beam Using Assumed Mode Method with Coupling Effect^#

Abstract

Abstract A frequency response analysis for a rotating cantilever beam is presented in this study. The equations of motion are derived from Hamilton's principle. An assumed mode method is used for analyzing the vibration frequency characteristic. The equations are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of rotating angular speed are investigated through numerical study. With the coupling effect ignored, the analysis results are consistent with the results obtained by the conventional method. As the angular speed increases, the bending natural frequencies increase monotonically and the stretching natural frequencies decrease. With the coupling effect considered, when the angular speed increases up to a certain value, there exists the warping speed that is in relation with the slenderness ratio. Keywords: Assumed mode methodChord-wise bending vibrationFlap-wise bending vibration ACKNOWLEDGMENT This work is supported by the National Nature Science Foundation of China (code: 10372076) for which the authors are grateful. Notes #Communicated by I. Elishakoff.