共查询到19条相似文献,搜索用时 109 毫秒
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不可压气流中二元机翼颤振的分岔点研究 总被引:5,自引:0,他引:5
对不可压气流中二元机翼颤振系统的分岔点进行了研究,应用中心流形理论将四维系统降低了二维系统,用后继函数判别法对分岔点的真假中心及稳定性问题进行了分析。 相似文献
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研究两个自由度的机翼在不可压缩流作用下颤振的分支问题.运用罗司-霍维茨判据确定系统的分叉点,应用中心流形理论将四维系统降为二维系统,用直接求周期解方法对分叉点的真假中心及稳定性问题进行了分析,并研究了系统的极限环颤振.结果表明,本文研究的分叉点不是中心,而是稳定或不稳定焦点.在两个分叉点处,系统发生了超临界和亚临界Hopf分叉,产生稳定或不稳定极限环. 相似文献
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碰撞振动系统的一类余维二分岔及T2环面分岔 总被引:9,自引:0,他引:9
建立了三自由度碰撞振动系统的动力学模型及其周期运动的Poincaré映射,当Jacobi矩阵存在两对共轭复特征值同时在单位圆上时,通过中心流形-范式方法将六维映射转变为四维范式映射.理论分析了这种余维二分岔问题,给出了局部动力学行为的两参数开折.证明系统在一定的参数组合下,存在稳定的Hopf分岔和T2环面分岔.数值计算验证了理论结果. 相似文献
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以r_{sl}, r_{f}以及x_{c}为分岔参数,对具有串补电容的单
机无穷大电力系统的失稳振荡问题,运用动态分岔理论进行了研究. 对系统同时出现有3对
纯虚根特征值的一类多参数高余维分岔情况,运用中心流行方法降维后得到约化方程,对此
强非线性约化方程的求解难点,运用多参数稳定性理论、谐波平衡法、归一化技术和Normal
Form方法,得到了系统的解析解. 由分析得知,系统会出现3种Hopf分岔情况、二维环面
情况,以及三维环面分岔解,甚至会出现四维环面,或者更高维的环面分岔. 详细讨论
了系统各种分岔解的稳定性条件和稳定区域,并作了详细的数值分析加以验证. 相似文献
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本文应用空间滤波方法:FST(Filter-space technique)方法,研究二维Rayleigh-Bénard(RB)湍流热对流系统中湍动能、热能和拟涡能的能量输运.研究中Rayleigh数(Ra)选取为1x10^8、1x10^9和1x10^10,Prandtl数(Pr)固定为4.38.我们展示了的结果表明,在二维RB系统中,三个Ra数下全场的平均湍动能和平均拟涡能在不同滤波尺度下的能量输运与Kraichnan在1967年预测的二维湍流中的级串理论有所偏差,而中心区域的能量都是向小尺度输运的.结果还揭示了瞬时能量输运的一些局部特性,包括它们在小尺度上不对称的分布. 相似文献
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自冯康先生创立Hamilton系统辛几何算法以来,诸如辛结构和能量守恒等守恒律逐渐成为动力学系统数值分析方法有效性的检验标准之一。然而,诸如阻尼耗散、外部激励与控制和变参数等对称破缺因素是实际力学系统本质特征,影响着系统的对称性与守恒量。因此,本文在辛体系下讨论含有对称破缺因素的动力学系统的近似守恒律。针对有限维随机激励Hamilton系统,讨论其辛结构;针对无限维非保守动力学系统、无限维变参数动力学系统、Hamilton函数时空依赖的无限维动力学系统和无限维随机激励动力学系统,重点讨论了对称破缺因素对系统局部动量耗散的影响。上述结果为含有对称破缺因素的动力学系统的辛分析方法奠定数学基础。 相似文献
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综述近年来非线性动力系统降维理论与方法的研究现状.主要介绍非线性动力系统现有降维方法的基本思想、特点与局限性;这些方法包括: 基于中心流形理论的降维方法, Lyapunov-Schmidt (L-S)方法, 非线性Galerkin方法和本征正交分解技术(proper orthogonaldecomposition, POD)方法;并简单介绍了基于规范形理论和快慢流形动力系统的降维方法.最后提出关于高维非线性动力系统降维的一些新设想,并讨论了今后研究工作的方向. 相似文献
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Based on the piston theory of supersonic flow and the energy method, the flutter motion equations of a two-dimensional wing with cubic stiffness in the pitching direction are established. The aeroelastic system contains both structural and aerodynamic nonlinearities. Hopf bifurcation theory is used to analyze the flutter speed of the system. The effects of system parameters on the flutter speed are studied. The 4th order Runge-Kutta method is used to calculate the stable limit cycle responses and chaotic motions of the aeroelastic system. Results show that the number and the stability of equilibrium points of the system vary with the increase of flow speed. Besides the simple limit cycle response of period 1, there are also period-doubling responses and chaotic motions in the flutter system. The route leading to chaos in the aeroelastic model used here is the period-doubling bifurcation. The chaotic motions in the system occur only when the flow speed is higher than the linear divergent speed and the initial condition is very small. Moreover, the flow speed regions in which the system behaves chaos axe very narrow. 相似文献
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The post-Hopf-bifurcation response of an airfoil in incompressible two-dimensional flow 总被引:2,自引:0,他引:2
A bifurcation analysis of a two-dimensional airfoil with a structural nonlinearity in the pitch direction and subject to incompressible flow is presented. The nonlinearity is an analytical third-order rational curve fitted to a structural freeplay. The aeroelastic equations-of-motion are reformulated into a system of eight first-order ordinary differential equations. An eigenvalue analysis of the linearized equations is used to give the linear flutter speed. The nonlinear equations of motion are either integrated numerically using a fourth-order Runge-Kutta method or analyzed using the AUTO software package. Fixed points of the system are found analytically and regions of limit cycle oscillations are detected for velocities well below the divergent flutter boundary. Bifurcation diagrams showing both stable and unstable periodic solutions are calculated, and the types of bifurcations are assessed by evaluating the Floquet multipliers. In cases where the structural preload is small, regions of chaotic motion are obtained, as demonstrated by bifurcation diagrams, power spectral densities, phase-plane plots and Poincaré sections of the airfoil motion; the existence of chaos is also confirmed via calculation of the Lyapunov exponents. The general behaviour of the system is explained by the effectiveness of the freeplay part of the nonlinearity in a complete cycle of oscillation. Results obtained using this reformulated set of equations and the analytical nonlinearity are in good agreement with previously obtained finite difference results for a freeplay nonlinearity. 相似文献
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In this paper the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil is studied. The aerodynamic moment on the two-dimensional rigid airfoil with nonlinear torsional stiffness is computed using the ONERA dynamic stall model. The pitch natural frequency, a cubic structural nonlinearity parameter, and the structural equilibrium angle are assumed to be uncertain. The effect on the amplitude of the response, the bifurcation of the probability distribution, and the flutter boundary is considered. It is demonstrated that the system parametric uncertainty results already in 5% probability of pitching stall flutter at a 12.5% earlier position than the point where a deterministic analysis would predict unstable behavior. Probabilistic collocation is found to be more efficient than the Galerkin polynomial chaos method and Monte Carlo simulation for modeling uncertainty in the post-bifurcation domain. 相似文献
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The Hopf bifurcations of an airfoil flutter system with a cubic nonlinearity are investigated, with the flow speed as the bifurcation parameter. The center manifold theory and complex normal form method are Used to obtain the bifurcation equation. Interestingly, for a certain linear pitching stiffness the Hopf bifurcation is both supercritical and subcritical. It is found, mathematically, this is caused by the fact that one coefficient in the bifurcation equation does not contain the first power of the bifurcation parameter. The solutions of the bifurcation equation are validated by the equivalent linearization method and incremental harmonic balance method. 相似文献
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《Journal of Fluids and Structures》1999,13(1):75-101
In this paper, the effect of a cubic structural restoring force on the flutter characteristics of a two-dimensional airfoil placed in an incompressible flow is investigated. The aeroelastic equations of motion are written as a system of eight first-order ordinary differential equations. Given the initial values of plunge and pitch displacements and their velocities, the system of equations is integrated numerically using a fourth order Runge-Kutta scheme. Results for soft and hard springs are presented for a pitch degree-of-freedom nonlinearity. The study shows the dependence of the divergence flutter boundary on initial conditions for a soft spring. For a hard spring, the nonlinear flutter boundary is independent of initial conditions for the spring constants considered. The flutter speed is identical to that for a linear spring. Divergent flutter is not encountered, but instead limit-cycle oscillation occurs for velocities greater than the flutter speed. The behaviour of the airfoil is also analysed using analytical techniques developed for nonlinear dynamical systems. The Hopf bifurcation point is determined analytically and the amplitude of the limit-cycle oscillation in post-Hopf bifurcation for a hard spring is predicted using an asymptotic theory. The frequency of the limit-cycle oscillation is estimated from an approximate method. Comparisons with numerical simulations are carried out and the accuracy of the approximate method is discussed. The analysis can readily be extended to study limit-cycle oscillation of airfoils with nonlinear polynomial spring forces in both plunge and pitch degrees of freedom. 相似文献
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The dynamics of a structurally non-linear two-dimensional airfoil in turbulent flow is investigated numerically using a Monte
Carlo approach. Both the longitudinal and vertical components of turbulence, corresponding to parametric (multiplicative)
and external (additive) excitation, respectively, are modelled. The properties of the airfoil are chosen such that the underlying
non-excited, deterministic system exhibits binary flutter; the loss of stability of the equilibrium point due to flutter then
leads to a limit cycle oscillation (LCO) via a supercritical Hopf bifurcation. For the random system, the results are examined
in terms of the probability structure of the response and the largest Lyapunov exponent. The airfoil response is interpreted
from the point of view of the concepts of D- and P-bifurcations, as defined in random bifurcation theory. It is found that
the bifurcation is characterized by a change in shape of the response probability structure, while no discontinuity in the
variation of the largest Lyapunov exponent with airspeed is observed. In this sense, the trivial bifurcation obtained for
the deterministic airfoil, where the D- and P-bifurcations coincide, appears only as a P-bifurcation for the random case.
At low levels of turbulence intensity, the Gaussian-like bell-shaped bi-dimensional PDF bifurcates into a crater shape; this
is interpreted as a random fixed point bifurcating into a random LCO. At higher levels of turbulence intensity, the post-bifurcation
PDF loses its underlying deterministic LCO structure. The crater is transformed into a two-peaked shape, with a saddle at
the origin. From a more universal point of view, the robustness of the random bifurcation scenario is critiqued in light of
the relative importance of the two components of turbulent excitation. 相似文献
18.
This paper shows the mechanism of instability and chaos in a cantilevered pipe conveying steady fluid. The pipe under consideration
has added mass or a nozzle at the free end. The Galerkin method is used to transform the original system into a set of ordinary
differential equations and the standard methods of analysis of the discrete system are introduced to deal with the instability.
With either the nozzle parameter or the flow velocity increasing, a route to chaos can be observed very clearly: the pipe
undergoing buckling (pitchfork bifurcation), flutter (Hopf bifurcation), doubling periodic motion (pitchfork bifurcation)
and chaotic motion occurring finally.
The project supported by the National Key Projects of China under grant No. PD9521907 and Science Foundation of Tongji University
under grant No. 1300104010. 相似文献
19.
Yahya Modarres-Sadeghi Michael P. Pa?¨doussis Christian Semler 《International Journal of Non》2008,43(1):18-25
The aim of the study described in this paper is to investigate the two-dimensional (2-D) and three-dimensional (3-D) flutter of cantilevered pipes conveying fluid. Specifically, by means of a complete set of non-linear equations of motion, two questions are addressed: (i) whether for a system losing stability by either 2-D or 3-D flutter the motion remains of the same type as the flow velocity is increased substantially beyond the Hopf bifurcation precipitating the flutter; (ii) whether the bifurcational behaviour of a horizontal system and a vertical one (sufficiently long for gravity to have an important effect on the dynamics) are substantially similar. Stability maps and tables are used to delineate areas in a flow velocity versus mass parameter plane where 2-D or 3-D motions occur, and limit-cycle motions are illustrated by phase-plane plots, PSDs and cross-sectional diagrams showing whether the motion is circular (3-D) or planar (2-D). 相似文献