回転円板の振動

概要

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The Vibrations of a rotating circular plate are very important ploblem in Engineering. The difficulties of an exact solution for the equation of motion have developed some approximate methods.　For example, Southwell published the very interesting paper in 1922. He analyzed this ploblem by treating the two following cases separately, (1) considering only the flexural rigidity (2) neglecting the flexural rigidity and considering only the effect of centrifugai force.　In this paper, we treat the transverse vibrations of a circular plate of uniform thickness rotating about its axies with constant velocity. The circular plate is clamped with inner circle, having the uniform load on the outer circle. We solve this problem by Ritz's method and Galerkin's. The Lagrangian consists of three energies,　(1) works by centrifugal force,　(2) kinetic energy of a disk,　(3) strain energy of a disk.　We assume the deflection of a circular disk as a linear series of the admissible functions, and obtain the frequency equations adjusting the arbitrary coefficients in the series so as to minimize the Lagrangian.　Considering the amount of calculations and their accuracy, Ritz's method is more convenient than Galerin's in this case. So we treat the all by Ritz's method. The experiments are carried out and their results are compared with theoretical ones.
山形大学の論文
1968-01-20