| Summary: | 碩士 === 國立中央大學 === 物理研究所 === 97 === This study is intended as an investigation of the dynamic process of a vertical hanging flexible rod rotating with motor. As the motor rotates, the rod will curve out of rotating axis and whirl. The purpose is to examine those phenomena by observing the shape of rod changing with time at different motor rate.
First, the critical frequency which predicted the rotating rod curves out of the rotating axis is larger than experimental results in our observation. The shape of rod is located in 2 dimension and fixed shape to rotate. This shape is described by beam theory for eigen-frequency . Furthermore, there exists another frequency which the rod will curve back to the rotating axis. It is like a spoon or a half wave. And it is same with eigen-frequency by beam theory. Between and in the rotating axis, the trajectory of rod could be associated with two frequencies effect. One is due to motor rotating rate; the other is probably due to non-linear effect. There exists a range in which the motor rotating rate increases but the rod selects a specific frequency to rotate with shape of . That is, whirling frequency of rod and magnitude of deflection of rod is almost constant, despite increasing motor rate. The shape of rod is also located in 2 dimension and fixed shape to rotate.
Before the motor rotating rate of rod forms shape of , the motor frequency will be involved into the motion of rod. Since there are two frequencies involved, the shape of rod will become 3D changing with time. We use two CCD cameras to rebuild the 3 dimensional figure of rod and illuminate this process by tracing the trajectory of rod. We depict the structure of rod in different motor rate. From the 3D reconstruction of rod, we see that as motor rate smaller than 574 rpm, the shape of rod is composed of two parts, one is shape of , and the other is with different ratio. Our system could neglect the gravity, the torsion, and the Magnus effect.
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