In a coupled rotational vibration system, there may exist some characteristic nature so called self-excited instability which imply a relaxational transformation of rotational energy of the system into its translational one.
As it is difficult to treat such an instability phenomena in general, a similar coupled tow degrees of freedom system is taken up and some theoretical investigations to clarify the dynamic behaviours of this system are undertaken.
In this paper, the author succeeds to develop one useful method for constructing graphical solutions of such an autonomous two degrees of freedom system upon the reduced phase plane.
Applying this method to the concerned system, the dependency of its dynamic behaviours of the system to its initial state is clearly understood and also the periodic solutions which may exsit in this system can be detected as the closed trajectories on that phase plane.
The periodic solutions of this kind are also decided by the perturbation method and the FOURIER expansion method.
Each result of this graphical or analytical method is compared with that of analogue simulations of the system and the validity of these methods is justified.

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Performances of the compressor type cascade of blades with small aspect ratio AR were experimentally obtained at the center of blade span. All blades had same span of 50mm and their aspect ratio were 2.08, 1.39, 1.04 and 0.83. Stagger angle (α) was changed from 0° to 60° and attack angle (α_i) from 0° to 15°. Results indicate that total pressure loss coefficient takes a minimum value at AR_??_1 irresspectively of α and α_i. At α_i over about 5° turning angle (ε) increases and at α_i=0° it decreases gradually with increasing AR. Axial velocity ratio, in the case α=0°, decreases gradually with incresing AR, and in the case α=30° it keeps almost constant value irrespectively of AR at α_i=constant, but in cases α=50° and 60° it increases at α_i≥5-10° with increasing AR.

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