MODES OF VIBRATION 



153 



ments are proportional to sin w/ where co = 27r times frequency) the following 

 simplified equations result. 



Fig. 7.3 — Stresses acting on small cube 



dXx , dXy dXz 



dx dy dz 



dYy dX_y dY, 



dy dx dz 



dZ, dXz SYz 



dz dx dy 



— po) u 



= — poj V > 



= —p<j)W 



(7.1) 



Since stresses are related to strains in a very definite manner, the above 

 equations may be converted into a more useful form involving only displace- 

 ments. For isotropic media, the following results. 



