矩形板の屈曲及振動に就て
1932 年 1932 巻 50 号 p. 209-230
詳細
1932 年 1932 巻 50 号 p. 209-230
The problem of the bending of a rectangular plate 2a×2b×2h clamped at its four edges (or clamped at the two opposite edges and supported at the other) and loaded with a uniformly distributed pressure is solved from the differential equation, assuming the deflection to be
w=∞Σm=1∞Σn=1Amncosmπx/2acosnπy/2b+ (1-x2/a2) ∞Σn=1Bncosnπy/2b+ (1-y2/b2) ∞Σm=1Cmcosmπx/2a,
where m and n are positive odd integers. The bending moments at several points and the deflection at the centre are calculated for rectangular plates with various ratios of b/a by the second approximation, taking the first double series and the first two terms of each of the single series, in which a high degree of perfection in clamping, especially on the middle half length, is attained.
The solution for the transverse vibration of the same plate is also obtained to satisfy the differential equation, using a similar form for the normal function as in the case of bending.Frequencies for different values ofb/aare calculated and compared with those obtained by other methods.
