丸棒の軸対称縦振動

概要

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The axis-symmetical longitudinal free vibration of a circular bar is studied. The circular bar is free on all its surfaces. The equations of motion and the compatibility conditions are solved and the solutions are expressed by stress functions of the integral forms. The stress functions are integrated with Gegenbauer integration formula, the 4-boundary conditions are satisfied and the frequency equation is obtained. In this paper, the general case is discussed shortly and the case in which the height of bar is relatively larger than its diametre is discussed in detail. It is known by experiments that there is the frequency of free vibration between the 1st and 2nd modes of the long bar. Such a frequency that is not obtained with the customary solutions is observed in the case that the bar is short. In this paper, it is obtained in the numerical examples and it agrees approximately with the experimental result.
山形大学の論文
1960-03-30