The total energy, which is the sum of strain and kinetic energy, of a string with time-varying length is discussed. It is well known that the total energy is conserved in a string with constant length and no dissipation. The total energy of a string with time-varying length, however, is not conserved because the energy is transferred through the moving boundary. This non-conservation of energy is discussed and shown with examples using exact solution of a string with time-varying length for free and forced vibration.

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1．はじめに

白色雑音を利用した電子回路特性の計測は，周波数可変の発振器を必要としない簡易な計測法であることは広く知られている．通常の計測では，熱雑音は邪魔な存在であり，熱雑音より大きな信

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Required bracing stiffness to give the specified effective length factor of columns in symmetrical braced frames is calculated by using the buckling slope-deflection method. Formulas to evaluate required bracing stiffness are shown in the following cases: 1) to take the effective length factor which is equivalent to the one when the sidesway is prevented, 2) to take any effective length factor and 3) to take the effective length factor as unity.

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A method is proposed to analyze dynamic response of a string with time-varying length. In this paper, we derived a finite element model of the string on the assumption that the tension of the string is constant and the length varies at constant speed. The finite element model consist of many constant elements and a telescopic element. The constant element is an ordinary finite element string model and the telescopic element is a finite element of which length varys with time. The equations of motion with time-varying coefficients are derived and solved by direct method such as the Wilson θ method to calculate the dynamic response of a string. Numerical results are compared with exact solutions and the validity of this method is verified.

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With ramie, Manila hemp and Japanese hemp cords immersed in water, the amount of absorbed water and the change in length and diameter were studied by the method stated in the previous paper, and the following results were obtained: (1) When the cord in water is not loaded, the amount of water, absorbed per unit mass of the cord till the end of t hours' immersion, q, is given by
q=Q₀(1-e^-a₀t)+Q₁(1-e^-a₁t)+Q₂(1-e-^a₂t),
where the constants α₀, α₁, α₂ and the ratio of the constants, Q₀:Q₁:Q₂, chiefly depend on the kind of fibre. (2) Whether the cord in water, is loaded or not the value of Q₀+Q₁+Q₂ or Q depends mainly upon the apparent specific volume of the cord and partly on the kind of fibre and the twisting of cord. (3) Whether the cord of ramie fibre, ramie yarn or Manila hemp fibre is immersed in water or exposed in air, the change in length, Δl, and that in radius, Δr, resulted by 24 hours' loading follow the formula,
Δl=-BΔr,
where the value of B almost coincides with the calculated value of 4π²(N-n)²a²r₀/l₀, where N and n are the number of the upper and the lower twists of cord respectively, r₀ and l₀ the radius and the length of cord respectively, and a is a costant (1/2 in this case). The value of B of the loaded cord of Japanese hemp fibre is different in water and in air, suggesting that certain change in the fibre takes place when the cord is immersed in water.

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Elastic buckling strength of columns in steel moment resisting frames had been studied for uniform vertical loads by many researchers. But in Japan where seismic loads are significant, the axial forces corresponding to overturning moment due to seismic loads should be considered in design. In such load conditions, the column that suffers larger compressive force can be laterally supported by other columns which sustain moderate or tensile axial forces. This paper proposes a method to estimate elastic buckling strength of columns in moment resisting frames under anti-symmetric vertical loads on beam-to-column nodes. The accuracy of estimation is confirmed by comparing to the results obtained by geometrical non-linear analyses or eigenvalue analyses for portal frames.

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The high precision gears are strongly required for advanced motion and power transmission. And the improved evaluation technology for the precision gears is becoming indispensable. Moreover, the reliability of the measured value became important when the accuracy of the gear becomes high, and the establishment of the traceability system has been needed. For the establishment of the traceability system, the higher precision gear measuring machine (GMM) with lower uncertainty is expected to improve gear calibration uncertainty. For the purpose, we proposed a new concept of the high precision GMM from analyzing the problems of the conventional GMM, and we have developed a prototype of the high precision GMM using the direct drive mechanism. Then, the high measurement capability of the developed GMM was verified by the evaluation method using the gear artifacts such as involute, helix and pitch artifact. On the other hand, some new methods conducting GMM accuracy evaluation using simple shapes such as sphere and plane have been proposed as standards. Therefore, we tried a new evaluation method for tooth profile measurement using a sphere artifact whose sphere was treated as the tooth flank, and the high measurement capability of the developed GMM was verified by a new evaluation method. This paper describes about the evaluation results of the developed GMM for tooth profile measurement using sphere artifacts and discusses the effectiveness of the sphere artifact as a new artifact.

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The buckling-restrained brace is a brace whose core plate is covered with a restraining part to prevent buckling. In this study, two types of buckling-restrained braces are tested and evaluated. Welding a pair of mortal-filled steel channels forms the restraining part of one type. The restraining part of the other type consists of steel channels and flat steel plates with high-strength bolts. The restraining parts are designed to have an equal geometrical moment of inertia that is used as a variable in imposing buckling restraint. Then, the hysteresis characteristics, final fracture shape and cumulative absorbed energy are investigated.

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This study is to propose a useful simple method in the case of initial design for analyzing beam — like anisotropy structures with rotation and/or extension. The anisotropic beam like structure with rotation and extension is modeled as following simplified structures; the mass-less beam which can only change length over time, and the rigid disk which can only change weight according to the length of beam. Using this model, the equation of motion is formulated to consider bending, extension and rotation. In this formulation, the follower force by inertia during extension is also considered. The stable region and the equation of motion are given which describe the dynamic behavior of beam's tip. To evaluate the validity of the numerical simulation results, the experimental apparatus is developed, which can change the length of anisotropic beams during rotation, and the displacement of beam's tip motion are measured. By the comparison of the displacement of beam's tip from rotation center, the analytical results become bigger than the experimental ones just after the extension. That displacement difference just after extension depends on the quantification of the eccentricity, which value changes correspond to the length. But considering about the internal damping, the simulation results get the qualitative tendency of the dynamic behavior of during extension and after extension.

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In this paper, first, elastic buckling behavior of the plane frames subjected to horizontal loads is discussed in detail using a numerical analysis. Then, it is shown that, story drift angle smaller than 1/200 by horizontal loads have no influence on column buckling length. Following conclusions come out from above and past knowledge. When we design with the Japanese first level designing seismic load, the buckling length of column in plane frames can be shorter than member length. And we propose the calculation method for the buckling length of column in plane frames. It is a method for the buckling mode without member angle.

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Since ECKER (1875) noted three finger formulae, II>IV, II=IV and II<IV, by the extent of projection of the index and ring fingers, various studies have been reported.

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A brief description is given of an interferometric method for the direct evaluation of line standards in terms of wave-length of light, and its application to the practical measuring instrument for precision scales up to one meter.
In order to transfer the interval of the lines to be measured to the mechanical displacement of a reflecting mirror of interferometer by the application of Eppenstein's method, a photo-electric microscope is tested experimentally and the Eppenstein's principle is analysed theoretically. The characteristic of interferometers which have the right angle prisms or corner-cube prisms, is examined analytically in order to estimate the measuring accuracy of the mechanical displacement by the method of fringe counting.
The accuracy of the practical instrument is 0.05μ in the length of 1 meter.

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This paper is a study of the buckling length of columns for the case of subjecting the axial forces corresponding to the overturning moment to the frames whose nodes horizontal displacement is not constrained. In this case, it is shown that taking a column length to the buckling length becomes safe side evaluation, unless the rotational resistance of both sides of columns is low. Moreover, about the buckling length in that case, it is shown that axial deformation of columns may influence to it, and more exact consideration can be performed by considering axial deformation of columns.

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