54 



BELL SYSTEM TECHNICAL JOURNAL 



interest in flexure vibration as seen in Fig. 6.1 is that the ends of the bar 

 will be vibrating in the same direction for odd order modes and the motion 

 of the two ends will be in opposing directions for even order modes. The 

 frequency of a bar vibrating in flexure may be easily computed for low orders 

 when the width is small in comparison with the length. When the width is 

 appreciable other factors must be considered as will be shown later. In 

 general, the flexure frequency of a bar will be the lowest frequency of 

 vibration. 



In the case of a plate where we are concerned with flexural vibrations 

 propagated along the length with motion in the direction of the thickness it 



Fig. 6.2 — Motion of a plate in free-free flexure. 



is necessary to consider also the width. As noted in Fig. 6.1, our concern 

 was only for a bar of small third dimension. When considering the case of a 

 plate in flexure along its length and thickness, then the third dimension must 

 also be considered for more complicated types of motion. In a manner 

 somewhat similar to the vibration of a bar, we can consider a plate vibrating 

 in its thickness-length plane. Since a plate also has width, we must also 

 consider this dimension. The simplest type of motion would be that of a 

 simple flexure which would bend the plate into the shape of an arch. If 

 now, the third dimension is permitted to flex, the distortion of a plate 

 shown in Fig. 6.2 could be illustrated by a flexure in the t-t plane and in the 



