MODES OF VIBRATION 



165 



Figures 7.13 and 7.14 show the distribution of the principle stresses as a 

 function of position along the length. It is seen that for the particular 



DISPLACEMENT 5CALE 



Fig. 7.12 — Distortion of bar vibrating in first free-free flexure mode 

 0.05 



0.04 



0.03 



X 



x 



^ 0.02 



0.01 



■ 



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 



X 



Fig. 7.13 — Distribution of longitudinal stress for free-free bar vibrating in first 



flexure mode 



I 2 



0.001 



"3 



0.006 



0.2 04 0.6 0.8 1.0 12 1.4 1.6 1.8 2.0 2.2 2.4 



X 

 Fig. 7.14 — Distribution of shear stress for free-free bar vibrating in first flexure mode 



example cited, the maximum shear stress is only about one-tenth the 

 maximum Xx extensional stress. Both of these stresses reduce to zero at 



