Among the nonlinear panel flutter, chaos is the most complicated motion, which is significant for the fatigue failure prediction. The present study constructed the aeroelastic equations for the panel in supersonic flow based on von Karman large deflection theory and first-order piston theory. A reduced order model (ROM) using the proper orthogonal decomposition (POD) method was constructed to analyze the chaotic motion and compare with the traditional Rayleigh-Ritz and Galerkin methods. A cantilever and simply-supported plate with thermal effects were investigated regarding the complex dynamic responses, and the chaotic motion were identified effectively using the Poincare map and Largest Lyapunov Exponent (LLE). Numerical examples turn out that the POD/ROM can get the accurate chaotic solutions, using fewer modes and less computational efforts. In addition, the POD method works better to identify the periodic motion with a long chaotic transient.%当马赫数较高时,气动加热产生的面内热应力,使得壁板的抗弯刚度减弱,导致壁板出现复杂的动力学响应,对疲劳破坏预测意义重大.本文将基于特征正交分解法(POD)建立降阶模型(ROM)用于超音速气流中受热壁板的非线性颤振分析.考虑均匀受热的简支板,采用von Karman大变形理论,一阶活塞理论及准定常热应力理论建立壁板的热气动弹性方程.基于Galerkin混沌响应解作为快照数据提取最优POD模态,建立POD降阶模型.分别采用时程图,相平面图,庞加莱映射,分岔图及最大李亚普诺夫指数(LLE)判断混沌等复杂响应.结果表明,POD方法以更少的模态,更短的计算耗时得到与Galerkin方法吻合较好的稳定性边界及复杂响应解.另外,发现壁板颤振系统存在长时间的瞬态混沌现象,而POD方法比Galerkin方法能够更快地收敛到稳态的周期运动.
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