In this paper, we consider the problem of a semi-infinite thin plate subjected to uniform tension and having a circular hole which is filled with the elastic inclusion of another material. The analysis is treated by applying the bipolar co-ordinates with help of a method of perturbation. Numerical calculations about the stress distribution along main parts of the semi-infinite plate and the inclusion are also carried out, in order to clarify the effect of an inclusion.

View full abstract

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated moment. The elastic properties of the insert are generally different from those of the plate, and a perfect bond case and a smooth joint one are both treated. The solutions for the perfect bond case and for the identical materials of a smooth joint case, are in closed forms in terms of elementary functions. Explicit formulas are given for the stress components in Cartesian coordinates, and also in polar coordinates at the circumference of the insert.

View full abstract

In this paper, the three-dimensional solutions of a thick plate having a spherical cavity are given when it is compressed between rigid bodies. The harmonic stress functions approach is used in this analysis. The two harmonic stress functions are obtained by solving the harmonic equations in the region of the thick plate and the infinite one involving the cavity. The boundary conditions on the faces of the thick plate and the surface of the cavity are satisfied by the aid of the relations between Bessel functions and Legendre functions. Further, numerical calculations are carried out for three different radii of the cavity.

View full abstract

Stress analysis is carried out under the uniformly distributed impact loads applied along the inner and outer surfaces of a hollow sphere. These loads are assumed to be q₁e^<-a₁t> and q₂e^<-a₂t>. The relationships among the stresses along inner surface of a sphere, the dimensions of a sphere and time are obtained. From these results, it becomes evident that the ratio K of the stress concentration factors under impact and static load is much different from K=2 and is larger than that in the case of a ring. The problem is analysed by using Laplace transformation.

View full abstract

To investigate stress distributions in crane hooks, we consider an eccentric circular ring with a cut-out portion undergoing equal and opposite concentrated loads at the ends of its inner diameter. Applying the theory of two-dimensional elasticity and using bipolar coordinates, we solve the problem by method of superposition of a closed ring subjected to the same loads and a ring with a cut-out portion loaded by forces and bending couples at both ends. As the result, we can obtain exact solutions for stress distributions along the inner and outer circumferences in the form of infinite series and computing residues, derive simplified formulas, from which it is verified that the outside parts of the ring bordered by the loading points are free from stresses. Further, using the solutions, we calculate stress distributions for several examples and compare them with results on "curved bars" in the elementary theory.

View full abstract

This paper deals with the problem of buckling of rectangular plates under uniform compression, which are simply supported along two loading edges and are simply supported but partially clamped along the other two sides. The energy method is used in investigating this problem which was proposed in our previous papers for solving the general problems of statical deflection, stationary vibration, buckling, etc. of rectangular plates. Numerical calculations are carried out on ten cases, and the diagrams are obtained which give the buckling loads for the rectangular plates of the aspect ratio 1, 2/3 and 1/2. These results are checked by experiments.

View full abstract

Surface strain distributions of rubber cylinders with various shape factors and fillet radii are measured and the relation between these distributions and fatigue failure is considered. The experiment indicates that the major part of axial strain distribution of the specimen without a fillet is nearly equal to the applied strain and the surface strain increases near the bonded plane. In the case of a filleted specimen, the strain over the central region of distribution is different from the applied one and the strain concentration appears in both fillets and the strain reduces to zero near the bonded plane. The strain concentration factor is greater for smaller fillet radius and for larger shape factor, but the position of concentration is scarcely influenced by the shape of specimen. Furthermore, the changes of these distributions with the applied strain and the appearance of wrinkle under compression are described. The incompressibility of the specimens is also discussed.

View full abstract

Regarding a multi-degree-of-freedom linear system, it has become possible to obtain the solution of the forced vibration and the natural frequencies of the system by using computers. It is still necessary to introduce the equations of motion and analize them, in order to study the relations between the system constants and their solutions. For this purpose, the author proposed a dividing method in this paper. As for the dividing method concerning forced vibration, the overall system is divided into several partial systems and by the successive appoxiomation the solution is obtained. This successive computation converges towards the exact solution, in general, within a wide range of the forcing frequency. As to the dividing method concerning natural frequencies, the overall system is divided into two partial systems and the graphical or computer calculations are utilized.

View full abstract

In this paper, the states of vibrations of a cylindrical shell are discussed when the shell contains a flowing imcompressible perfect fluid. The effects of the speed, density and pressure of the fluid on the modes of vibrations are elucidated according to the distances between the supports of the pipe utilizing the fundamental differential equation introduced by the present author.

View full abstract

There have been developed many methods to identify a process. Among them, statistical methods using the correlation function are most popular and practical methods. But these methods have been developed independently. In this paper, it is shown that they can be dealt with systematically when input is white noise. And from the practical point of view, the specified signal named pseudo-random signal is introduced in the analysis. Some consideration about the characteristics of this signal are presented and it is shown that it is applicable for measuring a zeromemory nonlinearity with ease. Measurement data of a distillation column are also presented. From consideration about these data, the obtained results are found to present the average dynamics of the plant.

View full abstract

Experiments were carried out on the boundary layer along plates artificially roughened by both wire-screens and also by sand. The flow was incompressible with zero pressure gradient, in the range of 2.3×10³<Uθ/v<1.2×10⁴ and 3.0×10<ku_*/v<2.0×10², where k is the height of roughness element. The velocity defect profiles (U-u)/u_* vs. yu_*/δ_*U for all types of walls were on a single curve within the experimental scatter but the logarithmic line for the rough plate lied slightly above that for the smooth plate. The effect of wire-screen roughness depends only on the pitch to diameter ratio, t/d. Experimental formula for equivalent sand roughness is given as a function of t/d. It is found that the experimental values of wall shearing stress and boundary layer thickness agree well with the present theories.

View full abstract

The author treats here theoretically the secondary flows occurring in the cases of flows with non-uniform velocity profiles passing through an axial compressor or a turbine cascade. He assumes this non-uniformity small and divides the three-dimensional flows into two parts, that is, the two dimensional fundamental potential flow and the perturbation flow. Starting from the equation of motion, he derives the elementary differential equation of the perturbation velocity potential. After solving this equation, he shows the method to determine the circulation about blades satisfying Kutta's condition at the trailing edges. Numerical solutions are obtained on the assumption of semi-actuator disc and are compared with experimental values, and a fairly good agreement is obtained for impulse cascades but not for nozzle blades.

View full abstract

Recently, the Gibson method has been used for flow measuring at hydraulic power plants, but the obtained results have never been compared with volume or weight measurements. Therefore the accuracy of the method is uncertain. Authors made comparative experiments between the weight measurements and the Gibson method by means of a test apparatus of 3 in. diameter pipe line. As a result of the tests, the relative errors of the Gibson method were found to be positive for rapid gate closure, and negative for slow gate closure. The variations of discharge did not affect the discrepancies. The authors proposed such a new treatment of fluid friction coefficient in the Gibson method analysis that the relative errors might become smaller particularly for slow gate closure.

View full abstract

This paper deals with a theoretical investigation on the effect of the dissipative energy on the laminar heat transfer from a disk rotating in uniform forced stream. Under the conditions that the fluid is incompressible and its physical properties are constant, the energy equation is solved exactly for the cases where the variation of the surface temperature is expressed by the general quadratic distribution along the disk radius and the disk surface is thermally insulated.

View full abstract

Temperature distribution and heat transfer rate for the turbulent flow in the thermal entrance region of a circular pipe with a constant surface temperature have been investigated. The universal temperature profiles for turbulent region in the thermal boundary layer were assumed by a polynomial of the third degree in terms of universal velocity, and an energy integral equation was solved. Experimental investigations of the temperature distribution and heat transfer for the air flowing through a pipe were also made.

View full abstract

The experimental study on film boiling was undertaken to clarify how the behavior of bubble formation on the liquid-vapor interface depends upon the degree of subcooling and the size of heating surface, and to determine the influence of the stirring action of bubbles on film boiling heat transfer. The ranges of the experiment are as follows. Heating surface : horizontal platinum-wire of 0.5, 0.7 and 1.0 mm in diameter Test fluid : H₂O, CCl₄ Heat flux : (20∼80)×10⁴ kcal/m²hr for H₂O, (8∼50)×10⁴ kcal/m²hr for CCl₄ Degree of subcooling : 0∼15°C From the experiment performed, the following facts were found : (I) the assumption of smooth liquid-vapor interface, as often adopted in the theoretical analysis, can not be applied for low degree of subcooling ; (II) the behavior of bubble formation is affected by the size of heating surface ; (III) the distance between the bubble formation sites is larger than the critical and dangerous wave length determined by Taylor's instability ; and (IV) the effect of the size of heating surface on heat transfer coefficient can be correlated in a unified law by introducing the concept of equivalent Prandtl number.

View full abstract

An investigation is carried out on the self-excited standing wave which is frequently observed in a boiling channel when subcooled boiling occurs in it. At first, the properties of the self-excited standing wave are made clear experimentally, and then the mechanism of excitation of the standing wave is studied by introducing the effects of collapsing void. As the result, the following facts are found. The self-excited standing wave occurs only in the case of subcooled boiling. It is generated most easily when the heater is located at the loop of the pressure wave. Collapsing voids cause some phase lead in the variation of the exsisting void volume as compared with that in the case of the conservative system. Then the work done to the water column in the channel per cycle of vibration becomes positive and so the vibration grows.

View full abstract

The heat transfer coefficient and the cooling efficiency with transpiration of gaseous coolant were decided experimentally. The conditions selected for the experiments were as follows : Velocity of free stream is 5∼25 m/sec Temperature of free stream is 100∼600°C Coolant flow ratio is 0.5∼5% From these investigations the following results were obtained. (1) The cooling efficiency is proportional to the cooling flow ratio and the proportionality constant increases with Reynolds number of free stream. (2) The heat transfer coefficient invreases with the coolant flow ratio and then begins to decrease. The coolant flow ratio for the maximum value of heat transfer coefficient decreases with an increasing Reynolds number of free stream. (3) The ratio of Nusselt number with and without transpiration of air remains at about unity or slightly larger than unity.

View full abstract

If there occurs a rapid temperature change in the gas while constant frequency sound waves are passing through the gas, the waves undergo frequency change after passing through the gas. That is, the receiver receives the sound waves with a frequency different from that of the sound source. Here, the mathematical relations between the frequency change of the sound waves and the temperature change dT/dt (T : absolute temperature of gas, t ; time) of the gas are derived and by integrating these relations the relations between the frequency change of the sound waves and the gas temperature T are obtained. From these relations, using the obtained data of the frequency change of the sound waves, it is possible to measure the temperature T and the temperature change dT/dt of the gas. The experiments are successfully done with the polytropically compressed air in a rapid compression machine equipped with sound source and receiver using ultrasonic waves. The measured temperature based on this principle is coincident with the temperature calculated from measured pressure volume relations assuming polytropic change of the air in the machine. The maximum temperature change attained in the measurement is about several tens of thousands degrees centrigrade/second. From this fact it is surely expected that this method will be applicable for the measurement of instantaneous gas temperatures in reciprocating engines.

View full abstract

The effect of static electricity on the disintegration of a liquid jet and on the droplet size of a distilled water is investigated by using an injection syringe. The following results are obtained : (1) Static electricity increases the rate of atomization and creates peculiar phenomena such as sinuous, zigzag, winding and wavy flows. (2) At the jet stream velocity of about 1 m/sec, the effect of static electricity on atomization is the most remarkable. (3) In the regions of sinuous and wavy flow, droplets descend in a circular spiral motion. (4) In the regions of zigzag and winding flow, the droplets descend in an elliptic spiral motion. The local mean droplet diameter measured along the major axis is greater than the one along the minor axis. (5) The local mean droplet diameter becomes smaller as the distance from the center becomes greater.

View full abstract

To apply a small gas turbine to the vehicles as the power plant, it is necessary to have the effect of the engine braking. Recently, the small gas turbine which has this characteristic by varying the nozzle angle of the axial power turbine has appeared. In present experiments the radial inflow turbine which has variable nozzles is applied and its performances are measured in the braking condition produced by varying the nozzle angle widely, as well as in the normal condition, and the results are compared with each other. From these experiments and comparisons, it is shown clearly that the radial inflow turbine has the satisfactory performances for both the normal and braking conditions. For example in braking condition, the change of absorbing power is proportional to revolutional speed, moreover, the deviation of mass flow from the normal condition is small.

View full abstract

High capacity magnetic storage drums are obtained by means of small constant clearances between head cores and drum surface. An air floating head mechanism is a kind of head supporting methods and is of an application of self-acting air bearing. In this report, the following characteristics of the mechanism in vibration of the drum surface are described. By solving Reynolds equation and linearized equation of motion of the slider, the relative vibration of the trailing edge of the slider to that of drum surface, and conditions inducing the best following action and resonance with drum vibration were obtained. Numerical solutions of the nonlinear equation show that higher order vibrations appear as amplitude of the drum vibration increases. Theoretical results agree well with available experimental ones.

View full abstract

In order to investigate the generating mechanism of gear noise, a power circulating type gear testing machine was installed in an anechoic room. From some preliminary measurements, the effects of operating conditions, accuracies, blank thickness and lubrication on gear noise were studied. The more detailed experiments were successively performed about the generating mechanism, with the test gear which had much involute errors. The largest source is considered to be the load fluctuations in the direction of line of action. Sound intensity is proportional to fluctuating load and square of fluctuating frequency. Tooth profile errors have much effects upon gear noise, especially under the light loads. If separation occurs at a certain speed, noise suddenly increases, and a strange noise of subharmonic frequency is occasionally built up.

View full abstract

The results of mathematical analyses or experiments of punch-stretching and deep drawing have been examined to obtain a systematic understanding of lubrication effects on the press forming limits of sheet metals. For this purpose, the relations of lubrication effects to size and shape effects in press forming have mainly been investigated. The limiting stretching depth depends strongly upon workhardenability of sheet metal, but the correlation between them is weakened by the presence of friction in the round-bottomed punch-stretching rather than in the flat-bottomed one. In non-axisymmetric punch-stretching, there is the accumulation effect which is caused by the combination of whole and local geometries of a pressed part and is also affected by lubrication. In deep drawing, the lubrication effect on the limiting drawing ratio is complicated and is generally stronger in non-axisymmetric drawing than in axisymmetric one.

View full abstract

In blanking, many factors influence tool wear. In this report, the authors investigated how the wear on cutting edges of blanking tool increased with the number of parts blanked, and discussed how the wear influenced the blanking force, energy, dimensional accuracy, burr height, etc. (1) On the face of punch and die, crater wear occurred and changed gradually into crater-slope wear with the increasing number of parts blanked, but punch flank wear and die opening wear were slope wear and increased uniformly. (2) Die face wear was greater than punch face wear, but at the sharp corners punch face wear and punch flank wear were remarkable. (3) The blanking force scarcely increased with the number of parts blanked, but the blanking energy increased considerably. (4) Dimensions, burr height and dishing increased and the sheared surface became worse with the number of parts blanked.

View full abstract

The tool tip temperature of a face-milling tool in machining a medium carbon steel was investigated by the tool-work thermocouple method, and the effect of the cutting condition, particularly the cutting fluid, the cutter diameter, and the work width on the temperature cycle was studied. For every rotation of the tool, the tool tip temperature builds up abruptly at the start of cut, retains a high level during the cut and is cooled during the non-cutting period. The tool-chip interface temperature during a cut depends mainly on the carbide grade, the cutting speed and the feed. The temperature at the start of the succeeding cut after cooling is also affected by those three factors as well as by the cutting fluids, the cutter diameter and the work width. The tool life date in the past investigations show that the starting temperature affects the tool life of the carbide face-milling tool.

View full abstract