非线性流固耦合动力学分析的时域频域混合法研究

项目名称： 非线性流固耦合动力学分析的时域频域混合法研究

项目编号： No.11272361

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 刘济科

作者单位： 中山大学

项目金额： 86万元

中文摘要： 本项目拟研究一种时域频域混合计算方法，用于非线性流固耦合动力学中一类问题的求解。这类问题是指描述结构振动的常微分方程和描述流体运动的偏微分方程组成的非线性流固耦合系统。本项目的主要思路是，在谐波平衡法的基础上结合最小值求解技术和增量过程，用频域法求解常微分方程，而偏微分方程则采用时域法求解。结合循环法和最小二乘法实现频域解和时域解的相互转换，用于处理耦合部分。在频域内构造迭代算法，获得半数值半解析解。将所提方法重点用于研究机翼非线性颤振，并在此基础上进一步研究大型旋转机械的油膜振荡和超声作用下的微泡振动等流固耦合问题，分析极限环振动、分岔、混沌等复杂非线性动力学特性。本项目有望为非线性流固耦合动力学问题的研究提供一种高效、高保真的计算方法，不仅具有重要的理论意义和学术价值，而且在航空航天、大型旋转机械、生物医学工程等相关领域的流固耦合动力学分析和设计中具有广阔的应用前景。

中文关键词： 流固耦合；非线性颤振；时域分析；频域分析；混合法

英文摘要： This project is to investigate a new kind of methods to analyze one category of nonlinear fluid-structure interaction problems such as nonlinear airfoil flutter, oil whipping of a rotor-bearing system and bubble oscillations in an ultrasonic field. The equations modelling stuctural oscillations are solved by frequency domain methods, for instance, by combining the harmonic blancing with minimization techniques and incremental process. The governing equations of fluid dynamics are solved by time domain methods using as little assumptions as possible. The cyclic method and the least squares method are employed to realize the effective and accurate transformations between time domain and frequency domain solutions. Semi-analytical frequency domain solutions can be obtained by constructing iterative algorithms in the frequency domain. This new technique is then employed to investigate other fluid-structure interaction problems. The noninear dynamical behaviors such as limit cycle oscillations, bifurcations and roots-to-chaos are to be investigated by employing the proposed method. It is expected from this study to provide one kind of effective methods with high fedelity for nonlinear dynamical systems modelling fluid-structure interactions. These methods can be widely applied to the aeroelastic analysis of aircraft,

英文关键词： fluid-structure interaction；nonlinear flutter；time-domain analysis；frequency-domain analysis；hybrid method