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Cantilever Beam Natural Frequencies in Centrifugal Inertia Field

Abstract

In the advanced mechanical science the well known fact is that the gravity influences on the natural frequencies and modes even for the vertical structures and pillars. But, the condition that should be fulfilled in order for the gravity to be taken into account is connected with the ration between the gravity value and the geometrical cross section inertia. The gravity is related to the earth acceleration but for moving structures there exist many other acceleration exaggerated forces and such are forces caused by the centrifugal accelerations. Large rotating structures, as wind power generators, chopper wings, large antennas and radars, unfolding space structures and many others are such examples. It is expected, that acceleration based forces influence on the structure modal and frequency properties, which is a subject of the present investigations.

In the paper, rotating beams are subject to investigations and modal and frequency analysis is carried out. Analytical dependences for the natural resonances are derived and their dependences on the angular velocity and centrifugal accelerations are derived. Several examples of large rotating beams with different orientations of the rotating shaft are presented. Numerical experiments are conducted. Time histories of the beam tip deflections, that depict the beam oscillations are presented.

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