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对于线性或非线性系统振动方程,可采用自由度减缩降低其规模,再运用Newmark方法或Newmark-Newton-Raphson方法求解其动态响应,关键在于如何挑选合适的减缩基矢量,并了解减缩的影响。对于一般线性减缩变换,本文通过比较变换前后分别得到的位移响应,给出了误差表达式。 相似文献
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提出一种求解非线性动力系统多重周期解的新的思路和方法(伪不动点追踪法),这一方法由寻找非线性动力系统同时存在的各个周期解间的联系入手,引入一个反映系统全局瞬态信息的标量函数,将非线性动力系统求各个周期解的问题转化为此标量函数的寻优问题.文中以布鲁塞尔振子及轴承转子系统为例,顺序求得了T,
2T, 4T,…周期解,从而得到了一些新的现象和结论. 相似文献
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大部分工程实际问题可以用多自由度非线性系统来描述,这些系统的数学模型是许多个耦合的两阶常微分方程.一般地,要精确求解这些方程非常困难,因此可以考虑它们的解析近似解.同伦分析方法是解非线性系统响应的有用工具,本文将它应用于多自由度非线性系统的求解中.利用求两自由度耦合van del Pol振子周期解的实例,展示了同伦分析方法的有效性和巨大潜力.同时,把得到的解析近似解与系统的Runge-Kutta数值解作了比较,结果表明同伦分析方法是求解多自由度非线性系统的有效方法. 相似文献
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齿轮—转子—滑动轴承系统时变非线性动力特性研究 总被引:4,自引:0,他引:4
本文应用求周期解的数值计算方法-打靶法和判定周期解稳定性的Floquet乘子研究了齿轮-转子-滑动轴承系统中齿轮啮合时变刚度,滑动轴承非线性特性对转子系统不平衡响应和失稳的影响,并比较了平衡位置失稳和不平均响应周期解失稳,以及按双轴计算与单轴计算结果的差别,为工程设计理论计算提供基础。 相似文献
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本文利用切比雪夫多项式的若干良好性质,对非自治强非线性动力系统进行分析。将状态矢量在主周期上先展开谐波级数的形式,再将各谐波展开为切比雪夫多项式的形式,从而将求周期解的问题转变为非线性代数方程组的求解问题,得出一种可以方便、迅速地获得近似周期解的解析方法。此方法不依赖于小参数假设,可以用于分析强非线性问题和高维问题,而且对参数激励系统同样有效。以Duffing系统周期解的计算为例,通过与标准谐波平衡方法和四阶Runge-Kutta数值积分结果比较,说明此方法的有效性。 相似文献
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基于可观测状态的轴承-转子系统周期解计算及稳定性分析 总被引:2,自引:0,他引:2
分析了轴承-转子系统的稳定性和分岔,基于系统可观测状态信息给出1种求解系统周期解及识别周期解稳定性的方法,同时将该方法与Floquet理论相结合分析系统周期解的稳定性及失稳分岔形式,将转速作为分岔参数分析系统响应的周期、拟周期、多解共存和跳跃现象.结果表明,采用该方法计算系统周期解及稳定性时,利用系统可观测稳态和瞬态信息,即可求解出系统Jacobian矩阵而无需实时求解轴承非线性油膜力的Jacobian矩阵.与传统PNF方法相比,该方法不仅具有很高的精度而且可以节约计算量,同时可以预测追踪随控制参数变化的系统周期解及其稳定性,可用于指导轴承-转子系统的非线性动力学设计. 相似文献
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强非线性振动系统周期解的能量迭代法 总被引:4,自引:1,他引:4
对于完全强非线性系统:x^.. g(x) f(x,x^.)x^.=0,提出求周期近似解析解以及这些解的稳定性的新方法。式中,g(x)、f(x,x^.)x^.分别是x,x、x^.的非线性函数。方法是基于能量原理,求出其一次近似解析解,然后引进牛顿迭代思想,得到周期系统数微分方程,最后根据谐波平衡原理及最小二乘法求其高次近似解,高次近似解的表达式由计算机辅助推导。计算参考文献[2]和[3]中的例题,令其中ε=1,研究该完全强非线性系统的周期解及其稳定性,本文方法与龙格-库塔数值法算得的结果对照如图1-3所示,它们表明本文方法不仅有效而且精度较高。 相似文献
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具有裂纹-碰摩耦合故障转子-轴承系统的动力学研究 总被引:9,自引:0,他引:9
以非线性动力学和转子动力学理论为基础,分析了带有碰摩和裂纹耦合故障的弹性转子系统的复杂运动,在考虑轴承油膜力的同时构造了含有裂纹和碰摩故障转子系统的动力学模型。针对短轴承油膜力和碰摩-裂纹转子系统的强非线性特点,采用Runge-Kutta法对该系统由碰摩和裂纹耦合故障导致的非线性动力学行为进行了数值仿真研究,发现该类碰摩转子系统在运行过程中存在周期运动、拟周期运动和混沌运动等丰富的非线性现象,该研究结果为转子-轴承系统故障诊断、动态设计和安全运行提供理论参考。 相似文献
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非线性系统周期强迫不平衡响应的稳定性分析 总被引:4,自引:0,他引:4
多自由度强非线性系统是工程实际中经常遇见的一类模型,利用非线性动力学分析中的打靶法求解该类系统的周期解,并对Flopuet主导特征值判断周期解的失稳方式,利用该方法对旋转机械中的一个具体模型;双盘县臂柔性转子-非同心型挤压油膜阻尼器(SFD)系统周期强迫不平衡响应的稳定性和分岔行为进行了分析,分析表明,在该系统中存在着第二Hopf分岔、倍周期分岔、鞍-结分岔三种分岔形式。 相似文献
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In this paper, a nonlinear dynamic model of a quarter vehicle with nonlinear spring and damping is established. The dynamic characteristics of the vehicle system with external periodic excitation are theoretically investigated by the incremental harmonic balance method and Newmark method, and the accuracy of the incremental harmonic balance method is verified by comparing with the result of Newmark method. The influences of the damping coefficient, excitation amplitude and excitation frequency on the dynamic responses are analyzed. The results show that the vibration behaviors of the vehicle system can be control by adjusting appropriately system parameters with the damping coefficient, excitation amplitude and excitation frequency. The multi-valued properties, spur-harmonic response and hardening type nonlinear behavior are revealed in the presented amplitude-frequency curves. With the changing parameters, the transformation of chaotic motion, quasi-periodic motion and periodic motion is also observed. The conclusions can provide some available evidences for the design and improvement of the vehicle system. 相似文献
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P.K. Kankar S.P. Harsha Pradeep Kumar Satish C. Sharma 《European Journal of Mechanics - A/Solids》2009,28(4):841-857
Dynamic analysis of a high-speed rotor bearing systems is challenged by their highly nonlinear and complex properties. Hence, an approximate response surface method (RSM) is utilized to analyze the effects of design and operating parameters on the vibration signature of a rotor-bearing system. This paper focuses on accurate performance prediction, which is essential to the design of high performance rotor bearing system. It considers distributed defects such as internal radial clearance and surface waviness of the bearing components. In the mathematical formulation the contacts between the rolling elements and the races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The governing differential equations of motion are obtained by using Lagrange's equations. In terms of the feature that the nonlinear bearing forces act on the system, a reduction method and corresponding integration technique is used to increase the numerical stability and decrease computer time for system analysis. Parameters effects are analyzed together and its influence considered with DOE and Surface Response Methodology are used to predict dynamic response of a rotor-bearing system. 相似文献
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《Journal of Fluids and Structures》2006,22(1):59-75
The application of the finite element corotational theory to model geometric nonlinear structures within a fluid–structure interaction procedure is proposed. A dynamic corotational approximately-energy-conserving algorithm is used to solve the nonlinear structural response and it is shown that this algorithm's application with a four-node flat finite element is more stable than the nonlinear implicit Newmark method. This structural dynamic algorithm is coupled with the unsteady vortex-ring method using a staggered technique. These procedures were used to obtain aeroelastic results of a nonlinear plate-type wing subjected to low speed airflow. It is shown that stable and accurate numerical solutions are obtained using the proposed fluid–structure interaction algorithm. Furthermore, it is illustrated that geometric nonlinearities lead to limit cycle oscillations. 相似文献
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This work reports a numerical study undertaken to investigate the dynamic response of a rotor supported by two turbulent flow
model journal bearings with nonlinear suspension and lubricated with couple stress fluid under quadratic damping. This may
be the first time that analysis of rotor-bearing system considered the quadratic damping effect. The dynamic response of the
rotor center and bearing center are studied. The analysis methods employed in this study are inclusive of the dynamic trajectories
of the rotor center and bearing center, power spectra, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent
analysis is also used to identify the onset of chaotic motion. The modeling results provide some useful insights into the
design and development of rotor-bearing system for rotating machinery that operates at highly rotational speed and highly
nonlinear regimes. 相似文献