中間に一支黠を有し、一端が固着或は滑節支持の半片持桁の振動
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概要
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The natural vibration of the semi-cantilever beam having uniform section which is fixed at one end, free at the other and supported at the intermediate point is studied. Also the effects of the position and elasticity of the intermediate support, and the axial force in the inner bay are investigated in general case, and compared with the case of a beam with one end pin-jointed, the latter case without axial force in the inner bay having been studied by J. Morrow. The modes of vibration of such beams in fundamental tone, and also first, second and third harmonics are calculated for a special wing spar as an example. The effect of the friction in the intermediate support and pin-jointed end on the vibration frequency is studied by a simple model experiment. Our conclusions are as follows:- (1) The frequency of the fundamental vibration of a semi-cantilever beam changes considerably with the position of the intermediate support and it is maximum when the length of overhang is about 28 and 36 per cent respectively of the length of inner bay according as the other end is fixed or pin-jointed. (2) Effect of the condition of the end on the frequency of the fundamental vibration is comparatively large when the ratio of length of overhang to the length of inner bay is small, but it is small when the ratio is great. For the natural vibration of the semi-cantilever beam of aeroplane wing the effect of the end condition on the frequency is generally small. (3) Effect of the elasticity of the intermediate support on the natural vibration of the beam is small when the rigity of the support is comparatively large as for the case of aeroplane wing beam. (4) Friction of the end opposite to the overhang and the intermediate support influences considerably on the natural frequency in the case of semi-cantilever beam with pin-jointed end. But, for the case of semi-cantilever beam the friction at the intermediate support changes the frequency by only a small amount.
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