Control of circular-disk stability with membrane stresses

Membrane stresses alter the dynamic behavior and stability of circular-disk elements, such as circular saws and grinding wheels, by shifting the disk's natural frequency spectrum. Such shifts are directly related to variation in the critical rotation speed at which standing-wave-resonance instability occurs. Negative critical-speed variations reduce the disk stability, and positive critical-speed variations increase stability. The present paper theoretically and experimentally investigates the relationship between the state of disk-membrane stress, critical rotation speed, and the frequency spectrum in radially symmetric disk problems. The observed critical-speed variations are theoretically predictable and well understood. The approach of a shifting critical-speed instability can be predicted by monitoring the disk-frequency spectrum.     

Flow of a vortical stream in the neighborhood of the critical point

A study was made of the axisymmetric flow of a viscous incompressible fluid in the neighborhood of the critical point of an obstacle when steady-state vortices oriented in the direction of the angular coordinate are introduced into the oncoming flow. A solution is presented of the equation for the transfer of a vortex in the case of an external flow containing a single largesize vortex in the low-frequency part of the spectrum. Using a finite integral Hankel transform, the problem is reduced to the solution of a system of ordinary differential equations. It is shown that a sufficiently large-size vortex can have a considerable effect on the structure of viscous flow near an obstacle.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 85–89, November–December, 1970.     

Dependence of the yield stresses of certain materials on loading rate

The dependence of the dynamic yield stresses of certain metals and alloys on loading rate has been investigated at temperatures of +20 and –196°C. In the experiments the loading rate remained constant up to the appearance of plastic strains, i.e., , where . The yield stresses of the materials and the time to the appearance of plastic strains were determined from the oscillograms representing the strain and load as functions of time.     

Pulsating regime corresponding to an obstacle in a stationary inhomogeneous flow

The pulsating regime produced by the presence of a cylindrical cavity in a stationary inhomogeneous supersonic flow is simulated mathematically. The system of equations for an inviscid thermally nonconducting gas is solved by a numerical method based on a two-step difference scheme of second order of approximation. This method makes it possible to calculate in each time step the complete flow field at once, which makes it possible to follow the development of the nonstationary flow, which in the present case is a pulsating flow. The flow pattern in the pulsating regime is studied in detail. The pressure pulsations in the cavity are due to the alternating passage through it of shock waves and rarefaction waves, and the pulsations are nonlinear. The influence of the basic parameters on the characteristics of the pulsating flow is studied and some estimates are made.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 64–71, September–October, 1979.     

Calibration of and measurements on a rheogoniometer by means of a small computer

Summary In this paper we propose a method for measurements with and calibration of the Weissenberg Rheogoniometer by means of a small computer.For Newtonian fluids we found that the dynamic viscosity is changed by a superposition of a steady shear flow on an oscillatory one, dependent on the direction of the steady shear flow.

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Zusammenfassung In diesem Aufsatz wird eine neue Methode zur Eichung eines Weissenberg-Rheogoniometers und für das Messen mit diesem Apparat dargestellt. Wir haben an newtonschen Flüssigkeiten beobachtet, daß die dynamische Viskosität bei der Überlagerung einer stationären und einer oszillierenden Scherströmung je nach der Richtung der stationären Strömung ihren Wert ändert.

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With 3 figures     

Separation of isochromatics and isopachics using a Faraday rotator in dynamic-holographic photoelasticity

A method is presented that allows the simultaneous separation of isochromatic- and isopachic-fringe patterns for transient-plane stress problems. Isopachic fringes are obtained by means of holography with a Faraday cell and a pulsed ruby laser flashing dual pulses. As usual isochromatic whole-order fringes are recorded in a circular-light polariscope. The shock generator (air-gun) and its synchronizing system with the ruby laser is described. The procedure is applied to the recording of the isochromatic- and isopachic-fringe patterns in a disk under radial dynamic loads.     

Experimental investigation of the development of motion of liquid in conduits

Only a few studies have been devoted to the experimental study of the initial stage of the motion of a liquid from the state of rest in a closed delivery conduit [1]. It can be concluded on the basis of the results of these studies that at the beginning of the process the mechanical energy losses are smaller than in quasistationary flow. These studies also suggest that the laminar nature of the flow persists in the nonstationary flow. However, investigations are of an integral nature and therefore in them the flow structure is not determined. In the present study the development of the motion of the liquid in a delivery conduit from the state of rest is investigated. The tangential frictional stresses at the wall of the conduit, measured by the thermal anemometric method, show that the transitional Reynolds number, at which the laminar flow regime changes into turbulent, depends on the acceleration of the flow and far exceeds the critical value for the case of the stationary flow. At maximum acceleration of the flow equal to 11.78 m/sec² the transition of the laminar regime to the turbulent at the wall of the conduit occurs at Re = 234, 500. The loss coefficients of mechanical energy have been computed from experimental results, which show that the use of the corresponding coefficient of quasistationary turbulent flow in the computation leads to appreciable errors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–85, November–December, 1977.     

Hydrodynamic instability in fluid layers with uniform volumetric energy sources

Linear and energy theory stability criteria are presented for fluid layers of infinite horizontal extent heated internally by a uniform volumetric energy source. The thermal coupling between the layer and its environment is modeled by a general mixed boundary condition in both the conduction state and the disturbance temperature. Rigid-rigid, free-free, free-rigid, and rigid-free boundaries are considered in the computations. For a fixed ratio of upper surface Biot number to that at the lower surface, decreasing the Biot number is strictly destabilizing for both linear and energy theory criteria. A region of possible subcritical instability is found; its size is strongly dependent on Biot number and becomes small for small values of lower surface Biot number and large Biot number ratio. For two rigid surfaces and an upper and lower surface Biot number of 47.5, mean energy transport measurementswithin the convecting layer indicate a critical Reyleigh number close to that predicted by linear theory. Subcritical instability is not observed when finite amplitude disturbances are introduced at a Rayleigh number between the critical values predicted by the linear theory and the energy theory.