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1.
In the present paper, based on the precise integration method established in linear dynamic system, an improved precise integration method is presented for nonlinear dynamic system. Firstly, the nonlinear dynamic system is converted into an augmented Lie type dynamic system. Then the precise integration method is improved for solving the above augmented equation and preserving its group structure in the meantime. Finally, two numerical examples are presented to demonstrate the validity and effectiveness of the proposed method. 相似文献
2.
Guoyong Zheng 《Acta Mechanica Sinica》2010,26(3):401-407
Based on the piston theory of supersonic flow and the energy method, a two dimensional wing with a control surface in supersonic flow is theoretically modeled, in which the cubic stiffness in the torsional direction of the control surface is considered. An approximate method of the cha- otic response analysis of the nonlinear aeroelastic system is studied, the main idea of which is that under the condi- tion of stable limit cycle flutter of the aeroelastic system, the vibrations in the plunging and pitching of the wing can approximately be considered to be simple harmonic excita- tion to the control surface. The motion of the control surface can approximately be modeled by a nonlinear oscillation of one-degree-of-freedom. The range of the chaotic response of the aeroelastic system is approximately determined by means of the chaotic response of the nonlinear oscillator. The rich dynamic behaviors of the control surface are represented as bifurcation diagrams, phase-plane portraits and PS diagrams. The theoretical analysis is verified by the numerical results. 相似文献
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The paper develops a reduction scheme based on the identification of continuous time recursive neural networks from input–output data obtained through high fidelity simulations of a nonlinear aerodynamic model at hand. The training of network synaptic weights is accomplished either with standard or automatic differentiation integration techniques. Particular emphasis is given to using such a reduced system in the determination of aeroelastic limit cycles. The related solutions are obtained with the adoption of two different approaches: one trivially producing a limit cycle through time marching simulations, and the other solving a periodic boundary value problem through a direct periodic time collocation with unknown period. The presented formulations are verified for a typical section and the BACT wing. 相似文献
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Regular oscillations or chaos in a fractional order system with any effective dimension 总被引:1,自引:1,他引:0
This paper introduces a fractional order system which can generate regular oscillations or create chaos. It shows that this
system is capable to create regular or nonregular oscillations under suitable conditions. These necessary conditions are achieved
by violation of the no-chaos criteria. The effective dimension of the proposed system can be chosen any order less than three.
Therefore, this system is a good example for limit cycle or chaos generation via fractional-order systems with low orders.
Numerical simulations illustrate behavior of the proposed system in different situations. 相似文献
5.
The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed. 相似文献
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IntroductionTheestablishmentofthetimepreciseintegrationmethodprovidesanewwayforthecomputationofdynamicsystems[1].Theabovemethod ,basedonthesimulationrelationbetweencomputationalstructuralmechanicsandoptimalcontrol,wasdevelopedonthebasisofthesubstructura… 相似文献
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In this paper, an orthogonal function method is presented based on the idea to suppose periodic solution with the method of
harmonic balance. The displacement is expressed in the form of trigonometric functions, a group of simplified eigenequations
are obtained by the use of orthogonarity of trigonumetric functions and linear modes. The method overcomes the difficulty
of a drift term existing ht systems with quadratic nonlinearities. The calculation examples show that the method has the advantages
of high calculation precision, high convergence speed and little calculation work. 相似文献
8.
The nonlinear aeroelastic response of a two-degree-of-freedom airfoil with freeplay and cubic nonlinearities in supersonic flows is investigated. The second-order piston theory is used to analyze a double-wedge airfoil. Then, the fold bifurcation and the amplitude jump phenomenon are detected by the averaging method and the multi-variable Floquet theory. The analytical results are further verified by numerical simulations. Finally, the influence of the freeplay parameters on the aeroelastic response is analyzed in detail. 相似文献
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结构动力方程的更新精细积分方法 总被引:26,自引:3,他引:26
将高斯积分方法与精细积分方法中的指数矩阵运算技巧结合起来,建立了精细积分法的更新形式及计算过程,对该更新精细积分方法的稳定性进行了论证与探讨。在实施精细积分过程中不必进行矩阵求逆,整个积分方法的精度取决于所选高斯积分点的数量。这种方法理论上可实现任意高精度,计算效率较高,其稳定性条件极易满足。数值例题也显示了这种方法的有效性。 相似文献
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非粘滞阻尼系统时程响应分析的精细积分方法 总被引:1,自引:1,他引:1
考虑一个具有非粘滞阻尼特性的多自由度系统响应的时程分析问题.该非粘滞阻尼模型假设阻尼力与质点速度的时间历程相关,数学表达式体现为阻尼力等于质点速度与某一核函数的卷积.在利用状态空间方法将系统运动方程转换成一阶的状态方程的基础上,采用精细积分方法对状态方程进行数值求解,得到一种求解该阻尼系统时程响应的精确、高效的计算方法.通过两个数值算例表明,采用该方法得到几乎精确的数值计算结果,而且计算效率有成数量级的提高. 相似文献
12.
钟万勰院士于1991年首先提出计算矩阵指数的精细积分方法,其要点是2N类算法和增量存储。精细积分方法可给出矩阵指数在计算机意义上的精确解,为常微分方程的数值计算提供了高精度、高稳定性的算法,现已成功应用于结构动力响应、随机振动、热传导以及最优控制等众多领域。本文首先介绍矩阵指数精细积分方法的提出、基本思想和发展;然后依次介绍在时不变/时变线性微分方程、非线性微分方程以及大规模问题求解中发展起来的各种精细积分方法,分析了其优缺点和适用范围;最后介绍了精细积分方法的基本思想在两点边值问题、椭圆函数和病态代数方程等问题的扩展应用,进一步展示了该思想的特色。 相似文献
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精细积分法在电报方程求解中的应用 总被引:1,自引:0,他引:1
将精细积分法应用到了二维的电报方程的数值计算之中。实例计算表明,该方法具有简单、计算精度高、无条件稳定、不需要进行复杂、费时的频域一时域转换及卷积积分,直接时域分析,处理非零初始值容易等优点。与传统的FFT法及NILT法相比,其效率更高,功能更强。 相似文献
16.
精细积分方法的评估与改进 总被引:9,自引:1,他引:8
详细分析了结构动力分析的精细积分方法的稳定性、计算精度,在此基础上提出了对现有精细积分方法的改进策略。算例证实了本文对精细积分方法改进的科学性与可行性。 相似文献
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Nonlinear oscillations with parametric excitation solved by homotopy analysis method 总被引:1,自引:0,他引:1
An analytical technique, namely the homotopy analysis method (HAM), is used to solve problems of nonlinear oscillations with parametric excitation. Unlike perturbation methods, HAM is not dependent on any small physical parameters at all, and thus valid for both weakly and strongly nonlinear problems. In addition, HAM is different from all other analytic techniques in providing a simple way to adjust and control convergence region of the series solution by means of an auxiliary parameter h. In the present paper, a periodic analytic approximations for nonlinear oscillations with parametric excitation are obtained by using HAM, and the results are validated by numerical simulations. 相似文献
18.
This paper presents an improved precise integration algorithm for transient analysis of heat transfer and some other problems.
The original precise integration method is improved by means of the inverse accuracy analysis so that the parameterN, which has been taken as a constant and an independent parameter without consideration of the problems in the original method,
can be generated automatically by the algorithm itself. Thus, the improved algorithm is adaptive and the accuracy of the algorithm
is not dependent on the length of the time step in the integration process. It is shown that the numerical results obtained
by the method proposed are more accurate than those obtained by the conventional time integration methods such as the difference
method and others. Four examples are given to demonstrate the validity, accuracy and efficiency of the new method.
Project supported by the National Natural Science Foundation of China (No. 19872016, 19872017), the National Key Basic Research
Special Foundation (G1999032805) and the Foundation for University Key Teachers by the Ministry of Education of China. 相似文献
19.
Duhamel项的精细积分方法在非线性微分方程数值求解中的应用 总被引:2,自引:0,他引:2
基于Duhamel项的精细积分方法,构造了几种求解非线性微分方程的数值算法。首先将非线性微分方程在形式上划分为线性部分和非线性部分,对非线性部分进行多项式近似,利用Duhamel积分矩阵,导出了非线性方程求解的一般格式。然后结合传统的数值积分技术,例如Adams线性多步法等,构造了基于精细积分方法的相应算法。本文算法利用了精细积分方法对线性部分求解高度精确的优点,大大提高了传统算法的数值精度和稳定性,尤其是对于刚性问题。本文构造的算法不需要对线性系统矩阵求逆,可以方便的考察不同的线性系统矩阵对算法性能的影响。数值算例验证了本文算法的有效性,并表明非线性系统的线性化矩阵作为线性部分是比较合理的选择。 相似文献