In this paper, the problem of determining stresses in a plate containing a circular hole with a circular notch, which has arbitrary shape, is taken up, when the plate is subjected to uniaxial tension. The stress function concerned is constructed by three parts, which are a basic function and two auxiliary ones. And they satisfy the boundary conditions along the rim of circular hole. The parametric coefficients involved in the solution are determined from the given conditions along the notch with the aid of Fourier's transforms. Three fundamental stress systems are discussed. Expressions of the stress along the rim of notch are derived, and the stress concentration factors are calculated.

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This paper deals with a calculation of stress distribution in a spirally corrugated tube subjected to torsional deformation. The formulas for analyzing the stress on the basis of the general bending theory reduce to a system of ordinary differential equations, which is integrated numerically. To obtain the torsional stiffness of the tube, the twisting moment applied to the tube is also caluclated.Results of calculation make clear the properties of the tube as follows. The largest component of stress is the shearing membrane stress. It takes, just like the maximum shearing stress, the largest value on the spiral of minimum radius.An increase in the depth of corrugation makes smaller the largest values of the shearing membrane stress and the maximum shearing stress. The former is nearly independent of the wall thickness, but the latter becomes larger as the thickness becomes larger. The torsional stiffness decreases as the depth of corrugation increases.

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This paper contains a three-dimensional solution for the stresses and deformations arising in a semi-infinite body with a spherical cavity stressed at infinity.Formerly, such a problem approached by means of spherical dipolar co-ordinates. The method used here is based on the Boussinesq's stress-function approach referred to the cylindrical and spherical co-ordinates.The problem can be reduced to one in two simply connected domains, i.e., a semi-infinite region and an infinite region excluding the cavity. The two stress functions in each region are given by simple expressions of the cylindrical and spherical harmonics.The boundary conditions on the face of the semi-infinite body and the surface of the cavity are satisfied by the relations between the cylindrical and spherical harmonics.Numerical results are given for six different radii of the cavity.

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On the elasto-plastic torsion problem, many investigations have been made by following approaches. In the case of perfect-plastic body, the relaxation methods have been used and numerical calculations have been fulfilled adopting the non-linear stress-strain relation.In this paper, authers suggest and analytical method to solve theoretically the elasto-plastic torsion problem. At first, we employ the new parameters (τ', α), where τ' and α are the resultant shear stress derived from Saint-Venant's torsion function and the argument of τ' respectively. Then the basic equation for the elastic torsion problem is reduced to Laplace's equation in term of these parameters (τ', α). Developing the above (τ', α)-theory, a solution for elastoplastic torsin is obtained using the total strain theory of plasticity. At last, we can describe the torsion function (ω) in the form of the hypergeometric series, provided that the Ramberg-Osgood's law is employed as the non-linear stress-strain relation.

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A new numerical method for computing the roots of an equation is proposed. By this merhod, we set up technically an auxiliary equation, the roots of which are known to us, corresponding to the given equation, and then introduce a parameter by which the roots of the original equation are connected with those of the auxiliary equation in a one-to-one relationship and continuously. Finally, we solve numerically an initial value problam of a first-order differential equation.In order to show how to apply this method to actual problems, and in order to demonstrate the usefulness of the method, several problems, such as the numerical solutions of algebraic equations or the computation of the natural frequencies of the lateral vibrations of a continuous beam, are considered.The programming for an electronic computer is very easy, and one program can be utilized for general use by giving the values of the constants included in the equation as the input data.

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A necessary condition (junction condition) is derived for the discontinuous optimal control problems in which system elements such as coulomb friction and non-linear feedback exist, or the performance functionals have discontinuity. The junction condition, together with previously known necessary conditions, opens the way for solving these problems. Some examples of a second-order system are treated in detail and some of them have several solutions that satisfy the necessary conditions. A method of obtaining optimal solutions is presented in these cases.

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The aerodynamic characteristics of a wing with tip clearance are studied. A theoretical investigation of wings of semi-infinite or finite span is made on the lifting-line theory. The author tried to introduce as many as possible images of the wing in order to satisfy the boundary condition at the wall facing the wing tip. Experimental results obtained on a 70mm chord wing (aspect ratio 4.15) with tip clrarance are also reported. Chordwise pressure distribution measured as a function of the angle of incidence is obtained at various spanwise positions and for various tip clearances. The experimental and calculated characteristics of the wing are compared and their discrepancies are explained quantitatively. The effect of the flow pattern of the main stream in the neighborhood of the wing tip on the wing characteristics is also investigated by experiment.

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The effect of the inducer tip clearance on the pump suction performance is investigated with an inducer and two main impellers having different eye diameters. The experiment revealed the following : (1) When the eye diameter of the main impeller is nearly equal to the normal inducer tip diameter, the pump suction performance decreases with increasing tip clearance.(2) When the eye diameter is 90% of the normal inducer tip diameter, the pump suction performance scarcely changes with increasing tip clearance, provided that the inducer tip diameter is larger than the eye diameter.(3) When an inducer is followed by a different main impeller, the pump suction performance becomes different.Besides, the reason for the above relationship between the tip clearance and the pump suction performance is studied with the velocity and total head distributions measured at the inducer outlet.

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The author considered theoretically viscous flows at a rounded pipe exit. It is well known that separation occurs at a slight by divergent angle. In this report, the author formed the equation of momentum with general orthogonal coordinates, solved it by an iso-clined method which is the same as Pohlhausen's one and obtained approximately the position of separation point. The results are as follows. (1) The position of separation point exists at a large angle if it is measured with the angle which corresponds to a cone angel.(2) Separation point is changed by Reynolds number. According as Reynolds number becomes smaller, separation point moves outward.(3) The valueΛ at the end of a straight pipe is decided from the condition that the equation of momentum does not become indefinite. This method corresponds to one which decided Λ at a stagnation point in a boundary layer.

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This paper deals with the application of Karman vortex shedding phenomena to measurement of the flow rate in a channel or a pipe. The fundamental principle of this application is that the vortex shedding frequency is proportional to the flow velocity near the body which is the cause of vortex shedding. The important point resulting from the experimental investigation is that (i) this flow meter is a direct digital transducer system at primary element, (ii) it is not necessary in flow rate measurement for vortex street in the wake to be stable, (iii) the detection of vortex shedding frequency is possible at Reynolds numbers from thousands to about 2×10⁵, and this leads to the digital flow rate measurement, (iv) the accuracy of this digital measurement is within ±1.5 per-cent through out the range.

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In the first report, the three rate-determining steps of the sublimation of ice had been clarified by the experiments. In this paper, we investigated the mechanisms of mass transfer in each step and obtained the following results. (1) The mass transfer rate of free molecular flow shown by Hertz-Kundsen's equation should be corrected by the effect of net mass flow to the velocity distribution at the low pressure side. The correction coefficient was calculated and was verified by the experiments.(2) The condition of transition of rate-determining step from the diffusion region to the phase change region was decided by the saturation of the water vepor on the ice surface.(3) The relation among the degree of super heat, the increasing of surface area of ice and the mass transfer rate of sublimation was investigated from the observation of ice surface in the region determined by the rate of phase change.

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A method to express the relationship between pressure drop and flow rate in steam generating tubes is presented. The characteristics of the pressure drops is represented in nondimensional generalized forms. In a case of uniform heat flux along a tube, it is given by the following equation : ΔP^*=2/1κξ³+(1-κ)ξ²+2/1κξ Here, ΔP^*=nondimensional pressure drop defined in this report, ξ=nondimensional flow rate, υ"=specific volume of saturated steam, υ'=specific volume of saturated water, r₀=subcooling, r=latent heat of evaporation, κ={(υ"/υ')-1}r₀/r. The charts in cases of various heat flux distributions along tubes are showm. They can be used to study the influence of each factor such as pressure, subcooling and heat flux distribution and so on characteristics of pressure drop and to estimate the flow stability and the distribution of flow rates in parallel tubes.

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Effects of operating conditions of a CFR engine on variations of flame travel time were studied statistically. Cyclic variations of falme travel time showed some departure form a normal distribution, but those of the "apparent flame propagation velocity", the distance of flame travel divided by the flame travel time, were shown to follow a normal one in general.The mean apparent flame propagation velocity υ^^-_f was found to have linear correlation with the standard deviation σ. It was shown also that υ^^-_f/S_L (S_L : laminar burning velocity) was directly proportional to σ/S_L in all the results obtained at different inlet mixture temperatures, and to Harrow's Reynolds number of the mixture before combustion over a wide range.An explanation for actual pattern of cyclic distribution of flame travel was made by incorporating the effects of cyclic variation of mixture stregth and the flame velocity due to the turbulence in the combustion chamber.

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By extending the Freudenstein's method for the approximate synthesis of the plane four-bar mechanism, the analytical approach for synthesizing the spherical four-bar mechanism is investigated and the basic equation for the point approximation is obtained.Especially, the six point approximation whose design parameters are the central angles α₁2, α₂2, α₃4, α₄1 and the starting angles θ_s, ψ_s is established, and the sine wave generator is designed with acceptable accuracy as an example of its applications.

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Experiments have been made to study self-excited vibration in cylindrical grinding. The results are as follows : (1) Remarkable vibration with considerably large amplitude occurs in higher work speed range, in plunge grinding always and in traverse grinding at considerably smaller feed as compared with the wheel width. (2) The frequency of the vibration relates with the natural frequency of bending vibration of the work. (3) Spiral chatter marks are generated in traverse grinding.. (4) The work vibrates almost in line with the resultant grinding force. It is concluded from the experimental results that the self-excited vibration due to regenerative effect occurs in cylindrical grinding.

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An analysis of self-excited vibration in cylindrical grinding is made. The equation of motion of the work is derived assuming that the dynamic grinding force is proportional to the time derivative of the removed work volume. The conclusions are as follows : (1) Self-excited vibration is caused by regenerative effect, and not by negative damping. (2) Self-excited vibration does not occur in low work speed range, and the work speed at which instability appears becomes higher with increasing depth of grinding or infeed. These conclusions generally agree with experimental results. The rango of phase lag in which regenerative self-excited vibration with finite amplitude can be maintained is calculated by a digital computer and found to become narrower with increasing amplitude.

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