Axisymmetric Vibrations of Thin Drums

抄録

In this paper the author investigates the axisymmetric vibrations of a thin drum which consists of a circular cylindrical shell and two circular end plates. He obtains the Lagrangian of a drum from the ones of a cylindrical shell and two plates using the conditions of continuity and then gets the frequency equations and the displacements minimizing the Lagrangian. If the length is sufficiently large in comparison with the radius, the vibrations of drum are much the same as the ones of cylindrical shell free at both ends. So we can say that the influence of the end plates is negligible in such a case. But the decrease of its length causes the increase of its frequency and the vibrations of its plate to shift to the higher mode patterns successively, while the ones of its cylindrical shell shift to the lower ones correspondingly. If the radius is very large in comparison with the length, the vibrations become nearly the same as the ones of the circular plate clamped or free on the edge circle.