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The characteristic function of a uniform beam has been widely used for the solution to the problem in vibrations of a uniform plate, but it has not been used yet for vibrations of plate systems as seen in box-type structures.　In this paper are considered free flexural vibrations of an open triangular box free at the edges and those of an open rectangular box, the base edges of which are built-in and the other edges free. The corners of the boxes are assumed free in rotation and fixed in translation and the stretching of the middle surface of the constituent plates is neglected. The functions used to represent the plate deflections are combinations of the characteristic functions of a uniform beam with both free ends or built-in-free ends and those of a triangular or a rectangular frame work. By using the functions we obtain the Lagrangians of the boxes, and from the minimum conditions of the Lagrangians we derive the frequency equations and modes of vibration. The frequencies and the mode shapes obtained from the numerical computations are compared with the experimental results.
山形大学の論文
1975-02-20