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概要

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This paper presents the transient vibrations of a beam subjected to the variable rotations. Taking account of rotary inertia, the fundamental equations of motion for the rotating Timoshenko-beam are derived from the Hamilton's principle. They are simplified by assuming that the shear deformation and rotary inertia can be negligible. The simplified equations become the same the ones for the Euler-Bernoulli's beam. The natural frequencies ω can be represented by where ω_0 is the natural frequency for the non-rotating beam, Ω, is the angular speed of the rotating beam and φ is called the Southwell coefficient depending on the geometries of the beam and the mode shape. The Southwell coefficient is calculated by the several methods which have been proposed so far. Finally, the time-responses of the rotating Euler-Bernoulli beam are analyzed numerically when the beam is subjected to the impulsive-like rotations, which is given by Ω(t)=Ω_0 [1-exp (-ct)] The fundamental equation is transformed into the finite-difference equation. The dynamic responses of the beam are obtained for the variuos values of c in the above equation. The variations of the deflection at the beam-tip with respect to time are discussed. The amplitude and period of the cyclic deflection at the beam-tip are obtained for c.
1986-01-30