液体を部分的に封入した中空回転体の自励振動解析（浅水長波近似による非線形解析）

摘要

An axially symmetric cylinder, mounted on an elastic support system and partially filled with liquid is assumed to undergo a whirling motion parallel to the axis. Rotor unbalance, gravity, and gyroscopic terms are considered negligible and liquid motion is taken as being axially uniform. In the analysis, shallow-water theory is applied assuming that a liquid layer is thin, and nonlinear effects that exist in the surface wave of a liquid in a rotor are considered to predict the finite amplitude of whirl motions. The modal coupling equations including the nonlinear effects of the wave motion are presented by applying Galerkin's method. Periodical solutions are determined by applying the harmonic balance method to the modal coupling equations. Whirl amplitudes predicted by the analysis are compared with the experimental results in the previous works. The time series analysis on the modal coupling equations shows periodic and aperiodic amplitude modulations at a particular rotating speed region.%液体を部分的に封入した中空回転軸系では，軸の危 険速度を超えたある回転数域で液体の波動により自励 振動が発生することが知られており，これまで多くの 研究が行われてきた．最初は，微小じょう乱を仮定し た線形の不安定問題として振動が発生する回転数域が 検討された．その後，定常応答を求めるため，流 体波動の非線形性を考慮した検討が行われてきた．