In fluidic and pneumatic control systems, vinyl hoses and tubes made of rubber-like materiah have come to be widely used as transmission conduits. Therefore, any analysis of the dynamics of those systems must consider the effects of the transmission tubing. So far, most of the studies conducted on gases have been limited to rigid tubes. Those studies limited to a certain extent, are not expected to give an adequate description of the system dynamics. Therefore, in this research the propagation of small amplitude harmonic pressure waves through gas contained in an infinitely long, thin-walled, viscoelastic tube is analyzed when the effects of the gas viscosity and heat transfer are included while the tube is assumed to move in the radial and axial directions.
Axially symmetric wave solutions are obtained for the linearized equations governing the motion of the fluid and the tube. The solution leads to a complicated equation, the so-called frequency equation, relating the propagation constant with the system parameters. Furthermore, this equation is simplified and two fundamental modes of propagation are obtained. One mode of motion has a phase velocity similar to the speed of sound in the tube; whereas, the other one has a phase velocity similar to the speed of sound in the gas. In this analysis the latter mode, which is defined as the first mode, is mainly discussed. The effect of the viscoelastic parameters of the tube materials on the dispersion of waves through the fluid is made clear for different viscoelastic models.

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An oil-hydraulic system including a control valve often induces self-exciting oscillation and causes significant troubles. Especially, the oscillation caused by interference between the valve and passive elements (chambers, restrictions, pipelines etc. ) occurs easily and is difficult to prevent.
As a rust step, the authors began their study using mathematical models for the control valve, the passive elements and a system consisting of them. The characteristic equation and a stability theory was derived from the model for the system. Stability discriminations were performed for a few simple systems.
The results obtained from this research aye as follows;
(a) A characteristic equation was derived for a system including a control valve with passive elements existing for both the upstream and downstream sides and withoug any branch lines.
(b) A new stability criterion was derived from the Hermite-Hurwitz's theory. The advantage of this method is that, instead of solving to the characteristic equation to order m(assumed to be odd), one needs only to solve a few equations to order (m-1)/2. By this method, the approximate value of the natural frequency of the system can be easily estimated in the case where the real parts of the roots of the characteristic equation are very small compared to the imaginary parts.
(c) As a limiting case, the characteristic equation for a valve-pipeline system (distributed system) was derived, and it was shown that the result coincides exactly with the solution of the wave equation.

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In the first report, the authors discussed the stability of an oil-hydraulic system that included a control valve and passive elements (chambers, restrictions, pipelines etc. ).
In this report, the authors have tried to stabilize an oil-hydraulic system with a control valve at the downstream end and a pressure source at the upstream end.
First, a method for dividing a system into two dynamically independent subsystems was developed by using a large restriction or a big chamber.
Secondly, after dividing the system, an effort was made to stabilize that part of the system including the control valve.
Thirdly, as it is well known that a pipeline system with a valve at the downstream end is unstable, the authors have tried to develop a criterion to prevent the instability of the system by inserting restrictions and chambers theoretically.
The experiment was performed for a poppet type valve. The results are in fair agreement with the theory. Finally the following conclusions were drawn;
(a) A theory was developed for dividing a system into two independent subsystems using a big restriction or a big chamber.
(b) In valve-pipeline system, though they are essentially unstable, they can be made stable by inserting restrictions and chambers between the valve and the pipeline.
(c) When the valve is the spool type, the valve-pipeline system can be stabilized with one restriction and one chamber.
(d) When the valve is the poppet type, two restrictions and two chambers are necessary in order to make the valve-pipeline system stable. In this case, the restriction next to the pipeline should be big, and the chamber next to the valve should be small. The other restriction must have an adequate size as shown by Eqs. (27) and (28).

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