In the present paper, cavitation erosion of several structure materials is studied by means of continuous observations by a scanning electron microscope, etc. Erosion damages are affected by the grain orientation on testing surfaces as well as the crystal structure of test materials. On the whole, erosion resistance decreases according to an increase in the plastic deformation of grains.

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The elastic deformation of inhomogeneous materials, especially materials with spherical or ellipsoidal inclusion and polycrystals is investigated, by expressing them with several models. Constraint ratio proposed previously is used to express deformation behaviour of materials, which is obtained from the strain distribution calculated numerically based on the models. At first, inclusion imbedded in matrix is studied by finite element model of inclusion as well as by Eshelby's analysis. The value of constraint ratio is nearly equal to 0.5 when the inclusion is spherical. The result is closely related to that of the self-consistent model of polycrystals. The value of constraint ratio in spheroidal inclusion increases when it is oblate in the stress direction, while it decreases when it is prolate. Next, the influence of irregularity of grain size in polycrystals on deformation behaviour is discussed. The overall deformation behaviour of the polycrystals is correlated with constraint ratio in each grain. The deformation mode of ply crystals changes into that under constant strain when the irregularity increases.

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A theoretical method of analysis is presented for the study of the free vibration of a rectangular plate supported on the sides and elastically supported on some segments parallel to the sides. Applying the method to (1) a rectangular plate simply supported on the sides and elastically supported on a cross-shaped support located in the center of the plate and (2) a rectangular plate clamped on the sides and a rectangular support inside the plate, the equations for determining the natural frequencies and the mode shapes of the symmetrical and antisymmetrical vibration of such plates are derived. And the results of the numerical calculation carried out by the use of these equations are presented in some figures.

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A two-degree-of-freedom vibrating system tuned to internal resonance with the higher natural frequency twice the lower natural frequency, having nonlinear characteristic of second and third order polynomials of the displacements, subjected to harmonic excitation, is taken up. Steady forced vibrations are investigated in the vicinity of the higher resonance point of the system. Through the theoretical analysis it is found that the system has two types of resonances depending on the excitation frequency, namely one in which only harmonic occurs, and the other in which sub-harmonic with the frequency half the excitation frequency occurs strongly in addition to harmonic. Also found is the phenomenon that almost periodic motions occur in a certain range of the excitation frequencies. It is shown that the results of the theoretical analysis agree with those of an analog computer.

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This paper describes the vibration characteristics of a resonance feeder which is susceptible to the reaction force of the load. When the conveyed bodies move on the vibrating plate, the resonance frequency of the system decreases and the damping effect increases. It is found that the resonance frequency of the feeder varies not only with the inertia force of the load but also with the frictional force. The effect of the load is substituted by the equivalent weight and the equivalent coefficient of viscous damping so that the most suitable exciting force and the exciting frequency are found easily. To keep the amplitude constant in spite of variations of the exciting frequency and the load, the exciting frequency has to be set 2-3% lower than the resonance frequency.

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To suppress the resonance of a simply supported bean and a clamped-clamped beam supporting a machine, the case in which the machine-suspension system is worked like a dynamic absorber and in which a dynamic absorber is attached to the machine are discussed theoretically. The adjusting conditions of the springs and the dashpots to the first or second resonances of the beams are determined and the effects of vibration isolation are discussed. Roughly speaking, the former method is particularly effective with respect to the suppression of vibration of the beams and the latter method is particularly effective with respect to that of the machine.

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The purpose of this paper is to present a numerical method for the optimal control problems with inequality constraints. In this method such problems are solved by converting them to a sequence of problems without inequalities and by searching for the saddle point of the unconstrained function. The features in this method are as follows. 1. The optimal value of parameter is closely related to the optimal Lagrange multiplier. 2. The optimal solution is obtained as a finite value of the parameter. Thus, the fact does not yield an ill-conditioning for the penalty function in this method, as opposed to the penalty methods. 3. On account of the existence of the saddle point this method is superior to the ordinary Lagrange method. 4. This method can approach the optimal solution from the interior or exterior of constraints by choosing a parameter corresponding to the Lagrange multiplier. This method has been successfully applied to the problem with state inequality constraint.

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The numerical methods for the solution of unsteady two-dimensional laminar flows proposed in the previous papers are extended to the flow problems in which the flow field geometry is deformed due to the displacement of some boundary walls. For the nonuniform rectangular grid varying with time, the finite-difference equations and the boundary condition formulas are derived, and the computational procedures are shown. As numerical examples, the nozzle flow characteristics with a moving flapper are determined for the prescribed inlet total pressure and the exit static pressure, and some numerical treatments are discussed.

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An analytical method is given for the determination of the lift fluctuation on flat plate airfoils in cascade due to transverse and chordwise gusts. The acceleration potential method is used in combination with conformal mapping method. In order to take account of the phase difference of the gusts between adjacent blades, a new mapping function is introduced. The blades are mapped to several unit circles on which the acceleration potential is given to satisfy the boundary conditions. Unsteady lift forces are given for three different stagger angles, five different pitches of the cascades and three different phase differences. The phase difference has the effect to make the lift forces greater than that for the case of the same phase, and this tendency is remarkable when the reduced frequency of the gust is small.

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In the past, several papers on hydraulic losses and secondary flow in various combinations of commercial elbows have been published, but the effects of the radius of curvature and surface roughness on the flow patterns and hydraulic losses remain unsolved. In the present paper, by use of four sets of pipe bends having different radii of curvature, the effects of curvature and surface roughness were studied.

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Free-molecule internal flows through a circular tube with sudden enlargement or contraction are analyzed by kinetic theory of gases. Attention is paid to the formulation of the surface-collision density, and then simultaneous integral equations with discontinuous kernel are derived for the up- and downstream circular tubes. Numerical solutions show that the fluid-dynamic effect due to the sudden change of a cross-sectional area brings about a peculiar behavior of the distribution of the surface-collision densities, and it depends more strongly on the length to diameter ratio than on the degree of enlargement or contraction. The total conductance of tubes having a relatively short length differs significantly from a conductance for each tube element.

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A theoretical and experimental study was carried out on a vortex oscillator which has a double input vortex chamber (i.e. a confined vortex oscillator). A mathematical model for the oscillator is proposed and examined by experiments. An oscillator with a single capacity is also examined. The results obtained are summarized as follows: (i) The mechanism of the occurrence of a self-excited oscillation has been clarified. (ii) The experimental data as to the frequency, the wave form of the oscillation and the condition of self-excitation are found to be in good agreement with analytically predicted ones.

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The oscillation of a gas-column, which occurs when a heater is held in a tube, being open at both ends and having a steady inner flow of gas, has been studied experimentally in order to clarify the fundamental natures of the limiting condition for the onset of oscillation. At the present stage, various experimental results obtained cannot yet be interpreted systematically on the basis of theoretical study, but it has been shown that the limiting condition exists in a clear form for the onset of oscillation, suggesting a possible means which enables to develope quantitative study on the thermal onset of oscillation. This type of oscillation occurs when a cooler as well as a heater is held in a tube with no inner flow, yielding a conclusion that there is a common feature in some fundamental respects with the case of having an inner flow.

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Experimental study has been made on the limiting condition for the onset of oscillation in a straight tube holding a heater and a cooler in it. Under the experimental conditions of the tube length l set at 1410 mm to 3200 mm, the relative location of heater l_h/l, 1/12, 1/8, 3/16, 1/4, 5/16 and 3/8, and the distance between heater and coolerδ 5mm, 6mm and 7mm, the temperature difference between heat and cooler at the limiting condition of oscillation ΔT is found to be correlated by ((ΔT)/δ)ⁿl/δsin(l_h/lπ)cos(l_h/lπ)=C when n and C are constants depending on the shape and the orientation of heater and cooler. The above correlation is not in a sufficient form dimensionally, but it may be assumed that quantitative regularity obtained by this study gives an important guide to the future study of the thermal onset of oscillation of a gas-column.

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Experimental data of the heat transfer coefficient during annular flow condensation of steam inside a horizontal tube are presented and compared with the data on vertical downflow condensation and analytical predictions presented so far. Based on an ideal annular flow model, a method for predicting the heat transfer coefficient is proposed for both horizontal flow and vertical downflow.

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Air cooled heat exchangers with corrugated fin surfaces are now in mass production for automotive and air conditioning applications. In these heat exchangers, the fin length is short relative to the equivalent diameter, and particularly, in heat exchangers with corrugated straight fins, heat transfer and flow friction characteristics are governed mainly by the entrance flow region. Most design data so far reported are, however, concerned with a fully developed flow rather than an entrance flow. In this paper, basic heat transfer and flow friction characteristics are presented on corrugated straight fin surfaces with the ratio of fin length to equivalent diameter, less than 26.5, by employing the steady state and transient techniques. These data were rearranged by the aid of analysis on the entrance region between parallel flat plates, and the result expressed in a correlation in the form, N_u=φ[R_e, P_r, (d_e/L), R], f=Ψ[R_e, (d_e/L)], applicable to the optimum design of air cooled heat exchangers with corrugated straight fin surfaces.

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To clarify the quenching characteristics of flame for a narrow cylindrical passage, the critical velocity of flame likely to ignite the outer mixture over a passage exit was investigated in relation to the dimensions of the passage. As the result of experiment, it was found that there existed two critical velocities of flame for given dimensions of passage in lower and considerably higher ranges of velocities. After some discussions about two critical limits from several points of view, it was shown that the lower limits were mainly concerned with cooling effect in passage and the higher limits had close relation to the flow conditions of hot jet issuing from the passage, and that in the latter case, quenching of flame by turbulent eddies might be considered one of the possible mechanisms.

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Livengood and Wu offered the following integration equation to predict the time of knock ^te, ∫^te₀ (1/τ)dt=1, along the end gas pressure time and temperature time histories, under the assumptions of zero order reaction and critical concentration of chain carriers, and showed that the agreement between the predicted and actual times of occurrence of autoignition is reasonable. An attempt is made in this paper to check on the utility of the integration procedure for cool flame explosions along the state time history of mixture during the motoring compression period. The pre-cool flame reaction which is primarily a degenerated branching reaction is taken to be similar to the zero order reaction and the critical concentration of active intermediate products is supposed to give rise to cool flame. Empirical coefficient and exponent in the general Arrhenius equation for the cool flame ignition delay τ₁ are found by the results obtained using a rapid compression machine developed here. Experimental results verify that this integration procedure is valid in the limited range of motoring compression temperatures where cool flame explosions occur T_c no more than the temperature at the end of the compression stroke of the rapid compression machine T_E, but falls over in the range of T_E≠T_c, especially T_E<T_c. It can be suggested that the reaction mechanism depends on the mixture temperature and seems to change from the low temperature autoignition mechanism to the high temperature one.

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The tooth profiles of the finish rolled spur gears are analyzed theoretically assuming a simple deformation model. The die is assumed elastic and the work elastic, perfectly-plastic. Deflections of the teeth and local elasto-plastic indentations of the tooth surfaces at the points of contact are considered. Effects of contact ratio, rolling stock, stiffness of the tooth, tangential force and the tooth profile error of the work before rolling on the finish rolled tooth profiles are discussed. And it is concluded that deflections of the teeth of the die and the work have a principal effect on the finish rolled tooth profiles. Finally a method is suggested to determine the profiles of the die theoretically based on this deformation model which generates a true involute profile on the tooth surface of the finish rolled gears.

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