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SummaryA general expression is obtained according to ray theory for the Doppler frequency shift observed when both receiver and transmitter are in motion in a time-varying anisotropic but lossless medium. The result is obtained using Hamilton's optical method. The range of application of the resulting expression and its relationship to a number of published results are considered. The method of analysis is also applied to the calculation of the group path of a radio wave.

The damaging effect of fatigue stressing above the endurance limit was investigated with notched specimens of SAE X4130 steel. The damage was measured by the decrease in endurance at another stress. A deflection method for detecting the formation of a fatigue crack permitted the damage measurement to be limited chiefly to the pre crack stage. The results showed that the apparent rate of damage depends on the stress history. If the prestress is higher than the test stress, the damage occurs rapidly at first, then more slowly. The reverse is true if the damaging stress is lower than that used to measure the damage.Tests also were made with smooth specimens in an effort to determine the cumulative damage caused by fatigue at more than one stress. Two methods were developed for extrapolating to determine the point at which fatigue cracking starts, so the damaging cycle ratios could be based on the life of the specimens prior to cracking. Complete S-N curves were determined for specimens after each of eight different damaging treatments. With these curves a method of expressing damage was developed that permitted the direct addit ion of damage occurring at different stresses. The reliability of this method was checked by testing specimens after fatigue loading at two or more different stresses and comparing the results with predictions based on the addition of the indicated damage. The agreement was within the p.xperimental error.

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