【作者】 李伟杰；

【导师】 杨晓东；

【作者基本信息】 沈阳航空工业学院 ， 工程力学， 2010， 硕士

【摘要】 壁板是现代飞行器上一种很重要的结构单元。在高速气流作用下,壁板不仅会发生静态屈曲变形,而且常常会出现颤振现象而导致壁板结构的疲劳寿命降低,甚至产生破坏对航空结构的可靠性造成影响。另外,当高速飞行器机体发生振动时,由于高速气流和壁板支承运动的联合作用,壁板系统会发生包括内共振在内的更为复杂和严重的强迫振动,对结构安全性的危害极大。目前,超音速飞行器的结构设计正向柔性轻型方向发展,这使得壁板的稳定性问题越来越突出。因此,研究各种条件下壁板的稳定性和动力学行为对飞行器设计有很现实的指导意义。基于此,本文将对超音速气流作用下壁板的非线性动力学问题进行研究,具体内容如下:(1)对超音速气流作用下的壁板系统进行力学建模。利用一阶活塞气动理论简化壁板外部受到的气动力,根据Von Karman大变形理论和Hamilton原理建立了超音速气流作用下壁板的横向运动偏微分控制方程。对方程无量纲化和离散化后,得到了常微分方程组。(2)对壁板系统的稳定性和分岔问题进行了研究。利用罗斯-霍维兹判据得到了系统的稳定性区域,发现在某些参数区域内有多个平衡点共存的情况,并通过计算各平衡点处Jacobi矩阵的特征值确定了相应平衡点的稳定性,数值算例验证了理论分析的正确性。(3)利用多元L-P法(MDLP)和增量谐波平衡法(IHB)对超音速气流和支承运动联合作用下壁板系统具有内共振的横向强迫振动进行研究,并对两种方法的结果进行比较分析。讨论了前两阶主共振和组合共振响应情况及内共振与外激励幅值的关系,并分析了各模态的振动情况。研究发现,在系统第2阶固有频率约为第1阶固有频率3倍的情况下,当外激励频率接近前两阶固有频率或其和的一半时,系统将发生内部共振,两个模态相互激励。但某些内共振的发生取决于外激励幅值的大小。更多还原

【Abstract】 The panel is an important structure in modern aerospace vehicles. In the circumstance of high-speed airflow, a static deformation as buckling of the panel can occur, and the flutter may be encountered, which always leads to the fatigue failure of the panel and has harmful influence on the structure reliability. In addition, when the high-speed aircraft vibrates in flight, a complicated and intensive forced-oscillation, including internal resonance, would arise by the combination of high-speed airflow and the support motion, which greatly endangers the flight safety. Now, the structure design of the supersonic aircraft has a flexible and light trend, which makes the panel stability more and more significant. So, the study of the stability and dynamic behavior of the panel under various conditions has practical meanings for the aircraft design. In this dissertation, nonlinear dynamics of the panel in supersonic airflow is investigated. The main contents are as follows:(1) The mechanical system of panels in supersonic airflow is modeled. The aerodynamic load is simplified In terms of the first-order piston theory. Appling the Von Karman deformation strain-displacement relation and Hamilton principle, the partial differential equations of transverse nonlinear vibration for the panels are derived. After nondimensionalization and discretization, a set of ordinary differential equations is obtained.(2) The stability and bifurcations of the panel system are researched. According to the Routh-Hurwitz criterion, the stability regions of the system are obtained. It is found that in some parameter regions, several equilibrium points exist in one region, whose stabilities are determined by calculating the eigenvalues of the corresponding Jacobi matrices. Numerical examples are presented to support the conclusions.(3) Forced vibrations with internal resonance of the panel system are studied through the multiple dimensions Lindstedt-Poincaré(MDLP) method, and the results obtained are compared with those of the incremental harmonic balance (IHB) method. The resonance responses of the first two modes and combination resonance are investigated and the relationship between the internal resonance and excitation amplitude is discussed. The motions of all modes are analyzed. The results show that the internal resonances occur as the excitation frequency is near the first, second natural frequency or half the sum of them under the condition that the second natural frequency is three times the first one, when the first two modes are excited by each other. However some of the internal resonances are decided by the excitation amplitude.更多还原