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BELL SYSTEM TECHNICAL JOURNAL 



The motion of the ends of the plate in the case of the first flexure are similar 

 to those of the second shear. In the case of the second flexure the similarity 

 is observed in the case of the third shear. The end motion in the case of the 

 third shear is also the same in the case of the first or any odd shear. Like- 

 wise, the end motion of the first flexure is similar to the second shear or any 

 even shear. We may then generalize and say that it is very likely that an 

 odd order flexure would be coupled to an even shear; and also an even flexure 

 would be coupled to an odd shear. 



T 

 w 



Jl 



\ ST FLEXURE 



2 ND SHEAR 



2 ND FLEXURE 



3 RD SHEAR 



ODD FLEXURE 



EVEN SHEAR 



EVEN FLtXURE ODD SHEAR 



Fig. 6.10 — Similarities in shear and flexure motions in a bar. 



To illustrate the coupling between flexure and shear type motions, the 

 frequencies of flexure and shear modes in a Z-cut quartz plate as shown in 

 Fig. 6.11 have been measured. These measured frequencies are shown by 

 the solid lines for various widths of the plate. It will be seen that there are 

 no observed resonances following an unbroken continuous line to represent 

 the shear frequency, but they are interrupted by several other frequencies 

 which we must interpret as being various even modes of the flexure in the 

 plane of the plate. It is clearly shown here that only even order flexures are 



