Sho Kusumoto

Exact stationary response solutions of nonlinear dynamic systems

SummaryExact stationary solutions are constructed for nonlinear dynamic systems subjected to stochastic excitation. The results are then applied to both classical and nonclassical stochastic vibration systems.

A new equivalent non-linearization technique

In this paper we propose a new technique for obtaining an approximate probability density for the response of a general non-linear system under Gaussian white noise excitations. In this new technique, the original non-linear system is replaced by another equivalent non-linear system structured by a polynomial formula, for which the exact solution of a stationary probability density function is obtainable. Since the equivalent non-linear system structured in this paper originates directly from certain classes of real non-linear mechanical systems, we will apply this technique to some very challenging non-linear systems in order to show its power and efficiency. The result of the calculations shows that applying the techniques presented here can yield the exact stationary solutions for non-linear oscillators. This is obtained by using an energy-dependent system, and for a non-linearity of a more complex type. A more accurate approximate solution is then available, and is compared with the approximation. Application of the technique is illustrated by examples.

Response of a non-linear system with strong damping to multifrequency excitations

SummaryIn this paper, a new asymptotic calculation method is presented for a class of nonlinear nonautonomous vibration systems with multiple external periodic interferences. Simple calculation formulae of an asymptotic solution for resonance and off-resonance vibration are derived. The paper is concerned with a vibration system representing a class of nonlinear oscillators. Consequently, the calculation of a class of nonlinear oscillators is routinized. Two different Duffing equations are verified which shows that the results are completely in accordance with the solutions of references [3, 4, 6]. The derivation of solutions of Duffing equations becomes easier and simpler. In addition, some errors in reference [6] are pointed out.

An equivalent polynomial approximation technique in nonlinear structural dynamics

SummaryA new technique is proposed to obtain an approximate probability density for the response of a general nonlinear system under Gaussian white noise excitations. In this new technique, the original nonlinear system is replaced by another equivalent nonlinear system, structured by the polynomial formula, for which the exact solution of stationary probability density function is obtainable. Since the equivalent nonlinear system structured in this paper originates directly from certain classes of real nonlinear mechanical systems, the technique is applied to some very challenging nonlinear systems in order to show its power and efficiency. The calculated results show that applying the technique presented here can yield exact stationary solutions for the nonlinear oscillators. This is obtained by using an energy-dependent system, and for a nonlinearity of a more complex type. A more accurate approximate solution is then available, and is compared with the approximation. Application of the technique is illustrated by examples.

Effects of Crystal Orientation on Fracture Toughness and Macrofractography of Single-Crystal Ice.

The effects of crystal orientation on fracture toughness and macrofractography of single-crystal ice specimens were examined by three-point bending test at -10°C. The loading rate KI was about 200kPa√m/s. Four types of single-crystal ice specimens, whose longitudinal directions were normal to the notch planes making respective angles of θ=0°, 45° (I), 45° (II) and 90° from the crystal orientation, were used. These specimens have a sharp edge notch made by pressing the edge of a razor blade on the bottom of the saw-cut slot. A macro replica was made on one side of the fracture surfaces using a dental impression material. The crystal orientation was measured using an etch-pitting method.The specimes of θ=0° and θ=90° exhibited similar fracture toughness values which offered a median value of Kc]50%=110.5kPa√m, and those of θ=45° (I) and θ=45° (II) also yielded similar values which gave Kc]50%=99.2kPa√m. The fracture toughness of columnar grained ice specimens estimated from that of single-crystal ice specimens was higher than the experimental values. Macro replicas clearly showed that the morphology of fracture surface was affected by those crystal orientations and it contained many traces of crack extension along the basal plane {0001} or the prismatic plane {1010}.

Effects of various factors on rime icing. Part II: Effects of stick diameter and water vapor content.

筆者らは屋内で人工的な霧氷を生成し,年間を通して霧氷の観察を可能にすること,ならびに自然環境下では種々の条件にかなりのばらつきがあることを勘案して,低温室内で超音波加湿器により発生させた噴霧の雲粒を用い,雲粒半径および温度のばらつきを最小限に抑えた実験的研究を行っている.第一報では,着氷形状や着氷速度と実験条件(特に温度・風速)との関係について報告した.本報では,雲水量を先報での値より一桁ほど小さく設定し,被着氷物の直径を5種類さらに材質を2種類変化させ,着氷成長の連続観察を行い,着氷の外観形状および雲粒の捕捉率などを調べた.その結果,着氷長さへの被着氷物直径の影響はあまり認められなかった.また,被着氷物直径が4mm以上では着氷幅はその直径程度までしか成長せず,雲粒の捕捉率は時間の依存をほとんど受けない.一方,4mm以下では着氷は風上に向かって末広がりに成長し,雲粒の捕捉率は大きくなった.被着氷物の材質の差は,着氷の初期を除くと着氷長さおよび雲粒の捕捉率への影響はあまり認められない.さらに,雲水量も気温や風速に併せて着氷の成長に対する大きな影響因子の一つであることなどがわかった.

Effects of loading rate on fracture toughness of ice. III. Statistical study on fracture toughness of ice.

A method to express the distribution of the experimental results of fracture toughness of ice was investigated by postulating the Weibull distribution with three parameters. The data were taken from the previous experiments conducted to study the effect of loading rate on the fracture toughness9), 10). Weibull parameters were estimated by several estimation methods11), 12) and the parameters obtained were compared with each other. The effect of loading rate together with that of specimen size on the parameters were discusssd at three loading rate ranges. It was confirmed that the parameters estimated were closely related to the experimental value of fracture toughness.