Summary
Bending vibrations of a rotating curved cantilever beam with, centroidal axis represented by a circular arc have been investigated by using Galerkin's method. Legendre polynomials are used to represent the shape functions. Longitudinal inertia and Coriolis effects are neglected in the analysis. At various rotating speeds, frequencies accounting for hub size, beam cross-section orientation and curvature have been computed and presented by curves. The beam curvature has only little effect on the frequency for nonrotating beams. For rotating beams the frequency generally decreases as the curvature increases, and the reduction from the straight beam frequency increases as the rotating speed increases. The effect of the beam cross-section orientation is significant only for the fundamental frequencies.
Übersicht
Es werden Biegeschwingungen einer rotierenden, gekrümmten, balkenförmigen Schaufel von kreisförmiger Vorkrümmung unter Verwendung des Galerkin-Verfahrens untersucht. Die Verschiebungsansätze werden durch Legendre-Polynome ausgedrückt. Trägheitskräfte in Längsrichtung und Corrioliseffekte sind vernachlässigt worden. Für unterschiedliche Drehzahlen sind die Schaufeleigenfrequenzen in Abhängigkeit von Rotordurchmesser, Schaufelquerschnittsorientierung und Vorkrümmung berechnet und in Kurvenform dargestellt worden. Die Vorkrümmung hat nur geringen Einfluß auf das Frequenzspektrum der stehenden Schaufel. Bei der rotierenden Schaufel sinken die Schaufeleigenfrequenzen mit zunehmender Vorkrümmung, und die Abnahme gegenüber den Eigenfrequenzen des geraden Balkens wächst mit der Drehzahl. Hingegen hat die Orientierung des Schaufelquerschnittes nur auf die Grundfrequenzen merklichen Einfluß.
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Senior U. S. Scientist Awardee of the Alexander von Humboldt-Stiftung. Presently on leave from the Georgia Institute of Technology, U.S.A., visiting the Technical University of Hannover, W. Germany.
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Wang, J.T.S., Mahrenholtz, O. Bending frequencies of a rotating curved beam. Ing. arch 44, 399–407 (1975). https://doi.org/10.1007/BF00534621
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DOI: https://doi.org/10.1007/BF00534621