NONLINEAR MATHEMATICAL MODELING OF TRANSONIC FLUTTER BY NONLINEAR DYNAMICS APPROACH

1. 基于Navier-Stokes代码的机翼模型颤振分析对2001年进行的初步分析结果进行了回顾和检验。分析结果表明，尽管极限环振荡（LCO）现象可以用跨声速颤振特征来表示，但由于控制面容纳驱动电机的部分变大导致压力突变，导致分析困难，结果存在一些问题。后续分析将在以后的节目中讨论。基于数值分析的跨声速颤振非线性数学模型的改进对非线性动力学方法导出的非线性数学模型进行了物理检验，引入了两种模态中的非线性项。分岔特性得到了很大的改善，与风洞试验结果相吻合。研究结果在与丹麦合作伙伴（DTU）共同撰写的国际会议上发表。进一步证实了以广义坐标与广义空气动力学非线性关系为中心的数学建模方法的有效性。修复风洞试验模型及跨声速风洞试验结果修复了支撑控制面和连接肋的外板部分的裂纹。在福井大学与日本宇宙航空研究开发机构的合作下，利用机翼模型在日本宇宙航空研究开发机构的跨声速风洞进行了颤振实验。在试验中，以前缘控制面为激振器，对有控制和无控制状态下的机翼模型进行了振动，得到了分岔数据。从而在受控状态下的试验中，先后确定了稳定边界和LCO。这是世界上第一次在开环和闭环颤振之间的动压力下发生LCO。此外，在亚临界动压下的非控制状态下，还观察到一种新的现象，即机翼在LCO中停留一次激振，然后在去除振荡源后停止颤振。少

1. Flutter analysis based on Navier-Stokes code for a wing modelPreliminary analysis results conducted in 2001 has been reviewed and examined. The analytical results show that even though limit cycle oscillation (LCO) phenomena can be expressed specifying transonic flutter features, the results have some problems because an abrupt pressure change due to the enlarged part accommodating driving motors for control surfaces causes analytical difficulties. The follow-on analysis will be treated in the future program.2. Improvement of a nonlinear mathematical model for transonic flutter based on numerical analysisNonlinear terms are introduced in two modes making physical examination to nonlinear mathematical model derived in nonlinear dynamics approach. The bifurcation characteristics have been greatly improved accordingly to fit the wind tunnel test results. The results were presented at an international conference co-authored with a collaborative partner in Denmark (DTU). We discussed and … More confirmed the validity of mathematical modeling approach focusing the nonlinear relationship of generalized coordinates and the generalized aerodynamics.3. Refurbishing a wind tunnel test model and the results of transonic wind tunnel testsCracks at the part of the outer panel supporting a control surface and connecting ribs have been repaired. As the cooperation between the University of Fukui and the Japan Aerospace Exploration Agency, flutter experiment using a wing model at the agency's transonic wind tunnel has been carried out. In the tests bifurcation data have been obtained vibrating the wing model using its leading edge control surface as an exciter for the states with and without control. As a result, stability boundary and LCO have been successively confirmed in the test for controlled state. It is worldwide first time that LCO can happen at the dynamic pressure between the open loop and the closed loop flutter. Furthermore, for uncontrolled state at the subcritical dynamic pressure, a new phenomenon has been observed that the wing excited once staying in LCO then ceased flutter after removing the oscillation source. Less