This note gives a theoretical solution to a disk with an eccentric circular hole when it is compressed by two equal and opposite forces acting at a radius of the outer circle on the centre of inner circle. The method of solution adds to the given stress system a suitable biharmonic function, which gives no normal and tangential stress on the outer edge. The parametric coefficients involved in the solution are adjusted so as to satisfy the boundary conditions at the inner edge. Bipolar coordinates are used in the solution, by means of which explicit expressions are obtained for the parametric coefficients. Formulas of stress along the edge of circles are derived, and, in particular, the stress distributions of the inner hole are calculated.

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As a means of reducing the circumferential stress concentration in plate, the coaming plate is usually introduced around the edge of the hole to supplement the doubling plate. This paper deals with the effect of the coaming plate on the stress distribution in orthogonally aeolotropic plate under uniform tension. That is, we assume the coaming plate is a circular ring and by using the following formula for the edge stress of the plate, namely, [numerical formula] the problem can be solved theoretically and simply. In conclusion, the larger the Young's modulus of the coaming plate is, and the greater its height is, and the greater its thickness is, the more the circumferential stress is reduced.

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The frequencies of the fundamental and second modes of lateral vibration of a cantilever beam under the action of its own weight are determined approximately by using the Galerkin method. The corrected formulas for calculating the Young's modulus of the beam material are derived from these solutions. The experimental results for the fundamental mode of vibration of cantilevers are presented. It is shown that Young's modulus of the material can be obtained exactly by treating the experimental data with the corrected equation. An expedient to foreknow the amount of the effect of weight on the given specimen is proposed.

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Free lateral vibrations of rectangular bars with many circular holes are studied, in which the vibrations are produced in the direction perpendicular to the axes of holes. The boundary conditions considered are as follows : one end built-in and the other free ; built-in ends ; free ends ; hinged ends and one end built-in and the other hinged. The method used is to determine the coefficients of normal functions according to Ritz, and it is possible to obtain the frequencies of any mode. Numerical calculations are carried out for the bars with one end built-in and the other free with respect to the first and second modes, and a part of the calculated results is compared with experiments.

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Formerly, one of us (T.A.) studied the elastostatic properties of the corrugated diaphragm, assuming it as an orthotropic elastic plate by smearing out the effect of the corrugations over a wave length, and found that the calculated results agreed well with those of the experiments. In this paper, analyzing the vibration properties of the corrugated diaphragm under the same assumptions as the static case, we obtained the approximate formulas for the natural frequencies of symmetric and asymmetric modes including the effect of concentrated mass. Furthermore, by the energy method, we studied the effects of initial tension and concentrated mass on the natural frequencies. In order to check this analysis, some experiments were performed. The experimental results showed good coincidence with the correspondig formulas, when the anisotropy parameter α is not so large.

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Characteristics of rubber vibration-isolator vary evidently by its curing conditions. As the temperature and the time of vulcanization have large influences upon its characteristics, the present author prepared some test pieces, which were devided into two groups viz. (A) group, in which the temperature was kept constant and the curing time was varied, (B) group, in which the curing time was kept constant, while the temperature was varied, as the curing conditions. Then some experiments were made on the influences of these conditions. In dynamic and creep tests the following results were obtained : (1) Shore hardness increases with the advance of cure, and it decreases with the thermal degradation caused by too high temperature. (2) Real part of complex modulus and coefficients of frequency characteristics increase with hardness, and imaginary part of this modulus increases in spite of degradation. (3) Loss factor and creep deformation proved to have minimum values under same curing conditions. In conclusion the best condition for vulcanization is that of loss factor and creep are both in the minimum values.

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One of the reasons why the fatigue limit remarkably rises in the notched specimen of steel which is induction-hardened, is that, the cracks produced do not propagate any further. In this connection, some experiments on rotary bending were made with the specimens of a plain carbon steel with 0.18%C, some of which are ordinary plain specimens and others have some crack, both were tested for two cases, ie. non-heat treated and induction-hardened. The results are as follows : (1) without any heat treatment fatigue limit a) ordinary plain specimens 20 kg/mm² b) specimens with some crack 10 kg/mm² (2) induction hardened a) ordinary plain specimens 54 kg/mm² b) specimens with some crack 48 kg/mm² The reduction rate of the crack is apparently less in the latter than in the former, which is less hardend. To explain this seemingly contradictory fact, Prof. Ishibashi's opinion has been applied that the tip of crack must be subjected only to tension stress during rotating bending tests.

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In this paper are described fatigue tests carried out to determine the fatigue strength of artificially cracked specimens made from mild steel, 0.45% C steel, 13Cr steel and Ni-Cr steel under rotary bending. Axially cracked specimens gave considerably lower fatigue strengthreduction factors, compared with that of partial circumferentially cracked or round cracked specimens, which have the value 2.4-3.4 when crack length or depth is nearly equal to 2 mm. The strength-reduction factor of a specimen with semicircular groove containing axial or circumferential cracks is equal to the product of the strength-reduction factor of the notch itself and that of the crack itself. And then the reduction factor depending on the diameter of artificially cracked specimens is nearly equal to 1.1. The shot peening process gave an increased fatigue strength of 18% for mild steel and 30% for Ni-Cr steel specimens with artificial cracks.

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When single-row radial ball bearings are used, several critical speeds take place in a vertical shaft at certain rotating speeds lower than the major critical speed. When the bearing center line of both bearing pedestals is not in alignment and the shaft is not in a perfectly straight line, there is the possibility that these critical speeds occur. The frequencies of vibrations of these critical speeds are represented by zω₁, zω₁+1 and zω₁-1, where ω₁ is the precessional rotating speed of balls in bearing and z is the number of balls. The whirling motions of these critical speeds are those of both forward and backward precessions. When self-aligning double-row ball bearings are used, these critical speeds do not occur ; they occur only in the shaft supported by single-row radial ball bearings.

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The tensile strength of the glass fiber reinforced polyester (FRP) increases by the glass content by volume in the linear relationship. However, it decreases when the glass content exceeds a certain critical point. According to the consideration that this is caused by the damaged glass fiber in the pressing procedure for forming, the tensile strength of the glass cloth was examined after being pressed by a known pressure, and it was revealed that the strength was reduced suddenly beyond a certain critical pressure. This pressing pressure coinsides with the forming pressure of FRP at its critical tensile strength, which leads us to the conclusion that the chief factor for this phenomenon should be the damage of glass fiber due to the forming pressure of FRP. In addition, by the experiments for dried and wet specimen, it was clarified that the critical pressure is higher for dried specimen than the wet, the strength is reduced by moisture not only for alkali glass fiber, but also non alkali ones and that the strength in wet condition is restored by heating or redrying. This was explained by means of design of experiment.

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The laminar free convection problem of a flat plate which is hung vertically in the air is solved, taking into account the variation of properties of air which depends on temperature. Previously the author solved the same problem by perturbation theory using ε=(T₀-T₁)/T₁ as a small parameter, where T₀ and T₁ are the absolute temperatures of the surface and the surrounding air, respectively. In this report the rigorous solution for a larger value of ε(=2.0 and 4.0) by successive approach method is presented. The heat-transfer coefficient can be expressed as follows : α=α_ε=0(1-0.055ε)

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On the assumptions that a radiating gas mass having a uniform coefficient of absorption exists in the center of the furnace and that between radiating gas mass and walls exists transparent gas, the emissivity of a gas mass radiating to furnace walls and the frequency distribution of the heat-flow intensity on furnace walls are calculated. When the volume ratio of radiating gas to furnace is about 0.2, the frequency distribution calculated coinsides closely with that of actual furnaces, which is independent of the form of furnace or operating conditions. The average absorptivity of the gas mass for the radiation between any two of the furnace walls is also presented in the present paper. The results will be able to be utilized for calculating the heat absorption in any one of the furnace walls.

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Heating characteristics of passenger car are determined not only by those of the body itself, but also those of radiator for room temperature, wall radiation characteristics, number of passengers and ventilating air volume. Especially, in the running state, boundary conditions in-and out-doors are very changeable and, moreover, in the case of preheating, the room temperature has to be raised to a necessary degree in a short time. On the contrary, if the heating quantity is too much, the passenger feels very uncomfortable. For this reason, we must control the room temperature considering the wall temperature as well as the change of outdoor temperature. For heating load estimation of the car, we cannot get proper quantity by the steady state heat estimation alone. In such case, heat capacities of car itstelf and room equipments are very important factors. The author carried out many tests on a passenger car of J.N.R. (SUHA-439). In this paper some estimation data obtained from these tests are reported as follows.

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In the previous paper, it has been shown that the pump lift or the sealing pressure is proportional to the viscosity of the working fluid. We have therefore carried out some experiments, using greases of viscosity higher than that of liquid oils. A summary of the results is as follows ; a) The sealing pressure for the grease is proportional to the rotor speed (N) and the coefficient of sealing performance (S), as shown in the previous papers for oils. b) When using some greases, the sealing pressure is about 30 to 70 times that for oils. c) The filling state of greases in grooves of rotating shaft is considerably varied with the kinds of greases, so that we must select the suitable depth of groove. d) To keep the viscosity of the sealing substance at a higher value, it is extremely important to cool the sealing apparatus.

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The flow distribution throughout the passages of rotating impeller has been studied in detail about two types of the impellers, one is with straight-radial blades and the other is with logarithmic-spiral blades, and the results are presented in the form of relative velocity and direction of flow. In the former case, the measurments are carried out under various numbers of rotation and flow quantities, and those results are compared with the result of two-dimensional potential theory which has been published. From those results, it is understood that the flow in the impeller cannot be conjectured by the theories. The real flow at the experiment, especially when flow quantity is large, passes through the impeller with nearly the same angle as the incidence angle, and the region of the slowest velocity occurs at the negative side in the passage. In the latter case, the fluid flows comparatively along the blades. The velocity distributions and the direction of flow indicate that the secondary flows in the boundary layer tend to shift the low-energy air toward the negative side within the passage. There is a counter effect at the casing surface apparently caused by leakage flow coming through the blade to casing clearance space. This results in a vortex flow in the passage.

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The authors measured the pipe friction losses up to consistency of about 6%, using groundwood pulp suspensions which have comparatively stable properties for flow, with brass pipes 23.3, 36.6, and 48.8 mm in diameter and galvanized gas pipes 1", 11/2", and 2". As the results, the pipe friction coefficients λ vs. a new dimensionless number : [numerical formula] (N is flow number, ρ : density, v : mean velocity in pipe and τ_w : shearing stress on pipe wall) which corresponds to Reynolds number in the case of water, coinciding well on the line of λ=64/N. Moreover, the authors gave the calculation formulas of pipe friction losses which are more accurate thao previous ones.

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The characteristics of flat-seated valves provided with guide cylinders as used in some types of safety valve are treated in this paper. Discharging water through a valve (39 mm in diam.) under a constant head of about 2 meters, either into the air, or into the vessel filled with water, we measured the discharge and lifting force for each valve lift, thus observing the performance of the guide cylinder. In the next place, to eliminate the effect of the cylinder edge, we kept the guide cylinder always a little higher than the valve, while the water was issued into the air. Under these conditions we measured the discharge and the lifting force as well as the angle of jet for each of the flat-seated valves of nine kinds, widely differing in diameter ratios. The relations between the quantities thus obtained were made clear by the use of the momentum equation.

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An infinitely long cylindrical wall d₂ of circular cross-section is assumed to exist. Inside which, another cylindrical wall d₁, also of infinite length, is assumed to exist, their axes being parallel to each other. The axes of these two cylindrical walls need not necessarily coincide. The annular space lying between these two walls d₁ and d₂ is assumed to be filled up with an ideal fluid (non-viscous, incompressible). When the inner cylindrical wall d₁ makes a transverse vibration, while the outer cylindrical wall d₂ remains fixed, particles of the fluid contained between these walls will also make a vibratory motion. In this report, theoretical calculation is made of the vibratory hydraulic pressure thus set up in the fluid, for a case in which the amplitude of vibration is of finite value, not necessarily confining to the case of very small amplitude.

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Our experimental study revealed that the severest vibrations in the draft tube of water turbines can be eliminated or greatly reduced by the admission of air into the draft tube, but unless just the right amount of air is admitted, instead of reducing vibration, a large amount of draft head is destroyed, and, conversely, vibrations are increased. To verify this fact, we used models of draft tubes. We obtained the relations among amplitude of vibration, flow ratio of air to water, draft tube efficiency, and ratio of circulatory component to axial component of water. Here the optimum amount of water to be admitted is studied and results are presented graphically.

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The pressure drop in the hydrocyclone is an important factor along with its performance, since the pump used for the cyclone must be selected according to the pressure drop and also because the amount of necessary energy is dependent upon the pressure drop and the quantity of liquid. The author has measured the differences in pressure between the inlet and the overflow pipes under various operating conditions. The influences of the following factors on the pressure drop were investigated : (1) Feed inlet velocity v_i, (2) Diameters of vortex finder D_o, underflow nozzle D_u and cylindrical portion D, (3) Dimension of inlet nozzle √(bh), (4) Height of cyclone H, (5) Inserted length of vortex finder S, (6) Types of feeding and (7) Pulp density of feed slurries δ_f. From the results of his experiments, the author has shown that the pressure drop through the cyclone may be represented by the Eq. (4.2).

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On the hypothesis that the thickening characteristics of the hydrocyclone will depend upon the dimensions of the unit and operating conditions, performance tests were carried out using an experiment unit. This paper gives the results of the work, including some suggestions with respect to the thickening ratio δ_u/δ_f, i.e. the underflow density δ_u divided by the feed density δ_f. The influences of the following factors upon the thickening ratio δ_u/δ_f were investigated : (1) Diameters of vortex finder D_o, underflow nozzle D_u and cylindrical portion D, (2) Feed inlet velocity v_i, (3) Dimension of inlet nozzle √(bh), (4) Height of cyclone H, (5) Inserted length of vortex finder S, (6) Types of feeding pipe, (7) Pulp density δ_f and particle size of feed slurries d. In addition to the above, the author has shown the following two experimental formulas : (1) Flow ratio G_u/G_o, i.e. the underflow quantity G_u divided by the overflow quantity G₀ may be expressed as Eq. (4.5), (2) Thickening ratio δ_u/δ_f may be expressed as Eq. (5.8).

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In the light of the fact that the hydrocyclone is essentially a classifier, performance tests were carried out using an experimental unit. In order to evaluate the results of classification, Tromp's distribution curve method was adopted in relation to particle size. This paper gives the results of the work, including some suggestions with respect to the cut size d_T ; in the afore-mentioned distribution curve, d_T is the particle size at 50% partition of the underflow discharge. The influences of the following factors upon the cut size d_T were investigated : (1) Feed inlet velocity v_i, (2) Diameters of vortex finder D_o, underflow nozzle D_u and cylindrical portion D, (3) Dimension of inlet nozzle √(bh), (4) Height of cyclone H, (5) Inserted length of vortex finder S, (6) Pulp density δ_f and specific gravity of feed slurries s. In addition to the above, the author has shown the following theoretical formula : cut size d_T may be expressed as Eq. (4.2).

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