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BELL SYSTEM TECHNICAL JOURNAL 



If the plate is thin we may neglect the .Tx strain as far as its efifect on the 

 resonant frequencies associated with the length and width are concerned. 

 From the plot of the elastic constants on Fig. 6.8 we may determine the 

 strains resulting from a stress along the length of an X cut plate for various 

 orientations about the A'' axis. In addition to the expected extension along 

 the length we have for a +18° cut, a large amount of length-width or y^ 

 shear strain due to 524 and very little width or s^ strain. For the 0° cut there 

 is also large length-width or y^ shear strain and a width or z^ strain. In the 

 case of the — 18° cut the shear strain vanishes due to 524 being zero, leaving 

 in addition to the expected length or yy strain a width or z^ strain. These 

 relationships are more clearly shown if we plot the resonant frequencies 

 resulting from the three modes of motion namely, the extensional modes 

 along the length and width and the shear mode in the length-width plane 



\ 



u 3S0 



_) 

 o 

 >- 

 o 

 o 



=) 300 



2 0.4 0.6 0.8 I.O 



0.2 0.4 0.6 O.f 



w (i,= Y= lomm.' 



0.2 0.4 0.6 0.8 :.o 



Fig. 6.9 — Effect of rotation about the .Y axis on the resonant frequencies 

 of an X cut plate. 



A plot of measured resonances is shown in Fig. 6.9 for the above described 

 three cases as a function of the change in width. The resonant frequencies 

 for these three types of motion are given in section 6.3 as 



— , extensional along I 

 PS22 



fz' = — A/ —r > extensional along w 

 2w y pssz 



J_ /ill 



^su y /2 + ^2 ' 



shear in tw plane 



6.12 



6.13 



6.14 



These equations specify only the uncoupled modes and do not take into 

 consideration the effect of coupling to other modes of motion. In the case 

 of Fig. 6.9 it is shown that when only the width is changed the extensional 



