Vol. 11, No. 1 (1955)
1955, 27 (1): 19-27. doi: 10.7498/aps.11.19
The problem of bending of orthotropic rectangular plates with clamped edges on elastic foundation may be reduced to the following differential equation and boundary conditions (?4w)/(?x4)+2λ(?4w)/(?x2?y2)+(?4w)/(?y4)+kw=q/D. w=0, (?w)/(?x)=0 at x=±a, w=0, (?w)/(?y)=0, at y=±b. In the case of isotropic plates, λ = 1. In this paper a perturbation method is proposed for the solution of this problem fay expanding w in power series of λ: w=w0+w1λ+w2λ2+……. It is proved that this series is convergent when -1 ≤λ≤1.
1955, 27 (1): 37-54. doi: 10.7498/aps.11.37
The buckling problem of various beams of variable cross sections has been fully considered by many authors, and the eigenfunctions and eigenvalues of the buckling problem of those beams are available in books and papers on this subject. Firstly, this paper shows that the deflection of these beams under the combined action of lateral load and axial tensile force can be expanded in a series of buckling eigenfunctions and that the coefficients in such an expansion can be simply expressed in terms of the known eigenfunctions, eigenvalues, the axial tensile force and the lateral load. Furthermore making use of the eigenfunction expansion, an approximation method is given to determine the axial tensile force acted on the supports of a beam of fixed span.
1955, 27 (1): 73-89. doi: 10.7498/aps.11.73
The object of the present work is to investigate the characteristics of piezo-electric resonantors which are cut from the natural coloured quartz, and compare the results with those obtained from those plates cut from the ordinary clear quartz in order to see if coloured quartz might be used as piezo-electric material in practice. In this work four points were stressed, they are: (1) the frequency constants of piezo-electric oscillation, (2) its stability, (3) its selectivity and activity and (4) its frequency-temperature coefficient curves. Further more a comparison of the characteristics of oscillations before and after the heat-treatment of the material was made. By the results of these experiments it concludes that the natural coloured quartz plates can be excited into piezo-electric oscillation and serve as piezo-electric resonantors. The frequency constant of a Y-cut plate from coloured quartz is about 2% lower than that of same type cut plate from clear quartz, while the frequency constants of the X-cut plate and the AT-cut plate from the coloured and clear quartz are practically the same. The heat-treatment to the three types cut plates of both kinds of quartz has a definite influence on their frequency. This effect is more pronounced to the coloured quartz plates. Likewise, heat-treatment improves, from the point-view of statistics, the selectivity and activity of oscillation of both kinds of quartz. Finally, the values of some coefficients of stiffness of the coloured and clear quartz were discussed.
1955, 27 (1): 91-106. doi: 10.7498/aps.11.91
It is well-known that blue brittleness and temper brittleness of steel are related to diffusion and precipitation in steel. An attempt was made in the present research to investigate this problem by means of internal friction measurements. Experiments show that the diffusion of carbon in α-iron is not affected by carbon concentration, alloying elements and the stage of precipitation in iron. The diffusion of nitrogen in α-iron is, however, hindered by the addition of alloying elements, and is enhanced during the initial stage of precipitation.The internal friction peak (around 250℃ for a frequency of vibration of 1 cycle per second) associated with the precipitation of carbon or nitrogen in a cold worked a-iron specimen previously observed was further studied. It is found that in specimens of sufficiently high carbon or nitrogen content, the internal stress resulting from the quenching of the specimens from high temperatures also gives rise to this internal friction peak. Further experiments show; (1) this internal friction peak is associated with the phenomenon of strain aging or quench aging, and it occurs under conditions corresponding to the appearance of blue brittleness in steel; (2) the carbon or nitrogen associated with this internal friction peak is in a dispersed atomic form. This correlation suggests that the blue brittleness of steel is a process of strain aging or quench aging and it is directly associated with the separation of carbon or nitrogen atoms from solid solution into stress regions or defects in steel.A tentative suggestion concerning the mechanism of temper brittleness in steel has been made that temper brittleness is associated with the process of precipitation of nitrides instead of carbides in steel.