DYNAMIC STABILITY OF NONLINEAR SDOF SYSTEMS FOCUSING ON THE MOVEMENT OF OSCILLATION CENTER AXIS

本研究では, 復元力低下領域における構造物の動的応答特性の基本的な理解に向けて, 振動中心軸の移動(ドリフト)を伴う非線形一自由度系の動的安定性に関する理論的および解析的検討を行った. 具体的には, 外力振動数に対するドリフト量の応答倍率を導出し, 数値解析によりその妥当性を検証した. この結果, 応答倍率から算出される理論値を, 解析により再現することができた. また, 応答倍率から導かれるドリフト量-外力振動数関係上の特異点において, 応答が急激に片側に発散する傾向が確認された. それにより, 応答倍率における特異点のドリフト量が, 構造物の動的安定性を考える上で重要な指標となり得る可能性が示された.In this study, the dynamic stability of nonlinear single-degree-of-freedom systems with the movement of oscillation center axis (drift) is theoretically and analytically investigated to understand basic dynamic response characteristics of structures in the region of reduced restoring force. Specifically, The response magnification factor of the drift to forced frequency is derived and validated by numerical analysis. As a result, the theoretical value calculated from the response magnification factor was reproduced by the analysis. In addition, it was confirmed that the response diverges to one side rapidly at the singularity on the drift-frequency relation derived from the response magnification factor. Thereby it was suggested that the amount of drift on the singularity may be an important indicator for the dynamic stability of structure systems