Abstract

Flexural vibrations of a slender rotating beam whose centre line is assumed to be naturally curved are considered. The beam, simply supported and axially restrained rotates at a constant speed about a horizontal axis in a gravity field. In one case, the rotational axis is parallel to the line connecting the centroids of the end cross-sections, and, in the other case, it is perpendicular to that line. A modal truncation of the governing nonlinear boundary value problem yields a set of ordinary gyroscopic differential equations of the Duffing type. For the cases of a cross-section with extremely different bending stiffnesses and a circular cross-section, the vibrational behaviour is analyzed in detail. The steady-state response (neglecting the influence of gravity) and its stability are considered first. A numerical investigation of weight-excited oscillations follows, where both periodic and even chaotic motions may occur. The effect of different damping mechanisms is addressed. A comparison with the dynamic snap-through of a non-rotating arch and the nonlinear vibrations of a rotating straight bar concludes the contribution.

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