【作者】 范晨光；

【导师】 杨翊仁；

【作者基本信息】 西南交通大学 ， 固体力学， 2010， 博士

【摘要】 为研究高速飞行薄壳的气动弹性非线性颤振响应,本文基于超音速气动力活塞理论和大变形几何非线性理论,建立了薄壳大挠度气动弹性颤振方程。采用微分求积法(DQM)对气动弹性方程进行离散,将DQM与模态缩减方法(NMs)相结合对系统进行降维,数值模拟了薄壳的非线性气动弹性响应情况。主要内容包括：(1)薄壳在蒙皮设计中存在多种形式,对各类结构形式分别进行气动颤振研究是非常繁琐的工作。选取圆柱形扁壳和完全截锥壳作为两类基本研究模型,将薄壳的气动弹性颤振问题归结为对这两类模型的气动弹性颤振问题的研究,建立了两类模型的大挠度气动弹性振动方程。(2)将微分求积法(DQM)引入到薄壳大挠度气动弹性颤振方程的离散化过程中。建立了几何非线性圆柱形扁壳气动弹性颤振方程的二维DQM离散格式及几何非线性完全截锥壳气动弹性颤振方程的一维DQM离散格式。(3)圆柱形扁壳气动弹性颤振问题,包括线性分析和非线性响应分析。在线性分析中,用特征值方法分析了结构系统的固有频率及气动弹性系统的颤振临界动压；讨论了不同网点数对计算精度的影响；讨论了不同曲率、不同长宽比、初应力对系统的颤振临界动压的影响。在非线性分析中,采用模态缩减方法对系统进行降维,通过数值积分着重研究了系统的模态截断问题及各类非线性响应现象与模态截断的联系。结果表明,极限环响应、概周期响应和混沌运动是圆柱形扁壳非线性响应的三种基本类型。讨论了不同曲率参数下产生极限环颤振的形态,讨论了曲率、初应力等参数对极限环颤振幅值的影响。研究了一类小周角、小曲率扁壳的气动叉式分岔行为；研究了特定动压下,以初应力为参数的分岔过程及通向混沌的途径。(4)完全截锥壳气动弹性颤振问题,包括线性分析和非线性响应分析。在线性分析中,用特征值方法分析了不同周向波数对应的系统固有频率及1-2阶模态耦合颤振临界动压；讨论了网点取值对计算精度的影响；讨论了不同顶角、径厚比及长径比时,系统的最小临界动压及对应周向波数；讨论了旋转角速度、初应力等参数对系统固有频率及颤振临界动压的影响。在非线性分析中,基于驻波颤振假设,结合线性模态缩减手段,研究了极限环颤振的幅值随动压的变化情况；研究了几何参数、初应力及旋转角速度对极限环幅值的影响。(5)完全圆柱壳和完全锥壳气动弹性颤振问题。作为截锥壳方程的特例,其气动弹性性质与完全截锥壳的非常类似。对完全圆柱壳气动弹性问题的研究,主要集中在边界条件、内压、轴压对颤振临界动压的影响以及极限环幅值的预测。由于完全锥壳在顶点的奇异性,采用近似方法求解了不同边界条件下的颤振临界动压,预测了驻波颤振极限环的幅值。更多还原

【Abstract】 Based on the Piston Theory of supersonic aerodynamics and the theory of thin shell with geometric nonlinearity, the aeroelasticity flutter equations of the thin shell in axial supersonic airflow are established in order to analyze the nonlinear flutter responses of the aeroelastic system. The differential quadrature method (DQM) is introduced to discritize the governing differential equations of aeroelastic system. The higher-dimensions nonlinearity flutter equations can be reduced to the lower-dimensions one by the method of nature mode reduction of freedom degrees, the critical aerodynamic pressure of which is obtained with the method of eigenvalue analysis. The numerical integral method is used to calculate the nonlinear response of the aeroelasticity system. The major parts of this thesis can be specified as follows.(1) Thin shells have many kinds of forms in the skin stressed design of flight vehicle. It is difficult to investigate the aeroelastic flutter characteristics of all kinds of thin shell respectively. By means of choosing two types of basic model of thin shell, a shallow cylindrical shell model and a circular truncated conical shell model, as researching objects, the aeroelastic flutter problems of all kinds of thin shell can be reduced to the flutter analysis of these two basic models. The governing equations are established by the large-amplitude shell theory.(2) Differential quadrature method (DQM) is introduced to discretize the governing equations of the thin shell with geometric nonlinearity. The discret forms for the shallow cylindrical shells based on two-dimensional DQM and the discret forms for circular truncated conical shells based on one-dimensional DQM are found.(3) The aeroelastic flutter problems of a shallow cylindrical shell model, including linear analysis and nonlinear response analysis, are studied. In linear analysis part, the nature frequencies and linear critical flutter dynamic pressures are investigated by the eigenvalue method. The number of sampling points is discussed to get accurate results, and the effects of different curvatures, length-width ratios, initial stress, on the critical flutter aerodynamic pressure, are discussed. In the nonlinear analysis part, a nature mode reduction method is used to reduce the freedom degrees of the aeroelastic system, the nonlinear responses of which are compared with the ones of the primary system to get correct cut number of nature modes. It is found that the limite cycle oscillations (LCO), quasi-periodic responses and chaos are three typical nonlinear phenomena of the thin shell aeroelastic system with geometric nonlinearity. The curvature of the shell is emphasized to investigate the vibrating shape of LCO, and the effects of different curvatures and initial stress on the LCO amplitudes are discussed. When the circumferential angel is relatively small, a pitchfork bifurcation is found with different initial values of numerical integral at a certain aerodynamic domain. Taking initial stress as bifurcation parameter, the bifurcation process of the aeroelastic system and the routing to chaos are studied.(4) The aeroelastic flutter of a circular truncated conical shell model, including linear flutter and nonlinear flutter, is studied. In linear analysis part, the nature frequencies of the shell structure and 1-2 flutter critical aerodynamic pressures with different circumferential wave numbers are discussed with the eigenvalue analysis method. The effects of sampling point on calculating accuracy are discussed. Semi-cone angle, radius-thickness ratio, length-radius ratio, these parameters are emphasized on the influence to the minimal critical flutter aerodynamic pressures and the circurmferential wave. The angular velocity and initial stress parameters are also introduced to the nature frequency analysis and flutter analysis. In nonlinear analysis part, based on the assumption of standing-wave flutter and the nature modes reduction, the amplitude of LCO is investigated numerically. The effects of the geometric parameters, initial stress and angular velocity, on the LCO amplitude, are also studied.(5) The aeroelastic flutter of the circular cylindrical shell model and the circular conical shell model is studied. These two shell models can be taken as the special cases of a circular truncate conical shell model, the aeroelastic characteristics of which are similar to those of the circular truncate conical shell model. The research is focused on the influence of boundary conditions, inner pressure and axial press, on the critical flutter aerodynamic pressure and LCO amplitude of the circular cylindrical shell model. Because of the singularity of aeroelastic equations of the conical shell model at the vertex point of the conical shell, an approximate solution of LCO of standing-wave flutter is obtained by numerical approach.更多还原