MODES OF MOT I OX IX QUARTZ CRYSTALS 



55 



w-i plane. Considering the motion of the plate as a flexure vibration along 

 the length vibrating in the thickness, then we may also have a distortion 

 along the width and thickness corresponding to similar or higher types of 

 flexure motion. The illustration at the bottom of the figure shows a plate 

 vibrating in its second order flexure along the length and thickness and the 

 fourth order flexure along the width and thickness. The effect of these 

 higher orders in the uf-t plane is to slightly modify the frequency of the 

 (-W mode. 



A thorough treatment of this t}'pe of double flexure in plates will be given 

 in Chapter VHI by H. J. McSkimin. 



1ST 



2.ND 



• • • 



3RD 



Fig. 6.3 — Motion of a bar in free-free extension. 



6.22 Extensional 



The extensional or sometimes termed longitudinal motion of a bar free 

 to vibrate is shown on Fig. 6.3. This motion is somewhat simpler than the 

 flexure motion and consists simply of a displacement in the direction of the 

 length of the bar of a wave propagated along the length. This means that 

 the first mode of vibration will be simply an expansion and contraction of all 

 points with respect to the center of the bar. This motion will be along the 

 length. The displacements along the bar will then be in proportion to the 

 sine of the angular distance from the center. The distortion of a free bar 

 in its simplest mode is then illustrated in Fig. 6.3 labeled 1st. Since the 



