基于近似惯性流形的非线性壁板热气动弹性响应降阶方法

摘要

基于近似惯性流形理论提出一种用于高温环境下的二维壁板热气动弹性响应分析的降阶方法。其主要思想是将壁板振动方程的解分解为高低阶模态之和，并利用近似惯性流形理论建立高低阶模态之间的耦合关系，用低阶模态来表示高阶模态的影响。通过与传统的伽辽金法比较，结果表明所提方法可以在不明显损失解的精度的前提下降低系统的自由度，提高计算效率。%A method of reduced order modeling for thermo-aero-elastic response analysis of a nonlinear panel in supersonic flow was presented based on approximate inertial manifolds.Its main idea was that the solution to the panel vibration equation was set as the sum of two groups including lower modes and higher ones.The coupled relations between higher modes and lower ones were established with the theory of the approximate inertial manifolds,lower modes were used to express the effects of higher ones.Compared with the traditional Galerkin method,it was shown that the presented method can reduce DOFs of the system and improve computation efficiency without significant loss of the accuracy of the solution.