軸圧縮をうける長方形板の固有振動数に及ぼす初期撓みの影響について

抄録

It is well known that the natural frequency for flexural vibration of plate under compressive load decreases, as the load increases. According to the theoretical studies of this phenomenon in the past, the natural frequency becomes zero when the load reaches the buckling load. By the contrast, the authors' experiments have shown that the natural frequencies do not decrease so much as the theoretical values. This disagreement is considered to be because of the initial deflection. In this paper, the authors have studied the flexural vibration of rectangular plate with initial deflection under compressive load by using the energy method and appling the theory of thin shells. And in order to verify the theoretical results, a vibration experiment has been carried out. The results have been compared with the theoretical calculations and a reasonable agreement has been confirmed. The results obtained are as follows: (1) When the compressive load increases and its magnitude is small in comparison with the buckling load, the natural frequency of plate with initial deflection decreases. But when the load approaches the buckling load, the deflection of plate becomes large rapidly and so the natural frequency increases. (2) The above-mentioned phenomenon can be explained by the calculations given in this paper and a simplified formula of natural frequency based on these the oretical calculations has a good accuracy. (3) In the case of ship plating, the effects of the compressive load and initial deflection on the natural frequency are considerably large.