Dynamics and Stability of Stochastic Nonlinear Auto-parametric Systems
随机非线性自参数系统的动力学和稳定性
基本信息
- 批准号:0758569
- 负责人:
- 金额:$ 29万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2008
- 资助国家:美国
- 起止时间:2008-07-15 至 2012-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Auto-parametric systems consist of at least one oscillator that is directly excited and coupled nonlinearly to a subsystem in such a way that the oscillator can vibrate while the subsystem remains stationary. Small amplitude vibration of the single oscillator or of one subsystem may destabilize the entire system. This destabilization is auto-parametric resonance. The purpose of this work is to examine the stationary motion and stability properties of stationary motion of noisy auto-parametric systems. The nonlinear dynamics of such noisy systems are extremely rich and largely unexplored. Auto-parametric resonance has many important engineering applications. For example, in aircraft, vibration of the "suspenders" connecting the engines and the wings occurs due to turbulent air forcing on the wings -- this is stochastic auto-parametric "resonance". Another example is the heave-roll motion of sea vessels produced by agitated waters; in extreme cases the danger of capsizing arises. Shock absorbers are also susceptible to auto-parametric resonance. While the focus of the present study is on the applications above the results of this research will be applicable even to biological problems such as the mathematical modeling of a pool of spiking neurons in the locus coeruleus, a brain nucleus involved in modulating cognitive performance.The approach will be cross-disciplinary, spanning the spectrum from analytical techniques and modeling to numerical and experimental verification. The first challenge is to develop an effective, systematic approach to determine the almost-sure stability of single mode nonlinear solutions. In the presence of a separation of scales, where the noise is asymptotically small, one exploits symmetries to use recent mathematical results concerning stochastic averaging to find a lower-dimensional description of the system. Stochastic numerical simulations will be used to verify the bifurcation behavior obtained through analysis and to provide clues to new phenomena which are global in nature and not detected through the theoretical analysis. The PI will recruit students from underrepresented minority and women groups. The project will directly train both graduate and undergraduate students. The broader impacts of the proposal include a partnership with the Structural Department of the University of L'Aquila, Italy, where experimental validations will be made. Students will work closely with professors from the University of L'Aquila's Nonlinear Dynamics Laboratory. The theoretical component of the proposed research will be tightly coupled to the computational and experimental efforts.
自参数系统由至少一个振荡器组成,该振荡器被直接激励并以这样的方式非线性耦合到子系统,使得振荡器可以在子系统保持静止的情况下振动。单个振荡器或一个子系统的小幅度振动可能会破坏整个系统的稳定。这种失稳是自动参数共振。本工作的目的是研究具有噪声的自参数系统的定常运动及其稳定性。这类噪声系统的非线性动力学非常丰富,而且在很大程度上还没有被探索。自参数共振具有许多重要的工程应用。例如,在飞机中,连接发动机和机翼的“吊杆”由于机翼上的湍流空气压力而发生振动--这是随机的自参数“共振”。另一个例子是搅动水域产生的海船的横摇运动;在极端情况下会出现倾覆的危险。减震器也容易发生自参数共振。虽然本研究的重点是上述应用,但这项研究的结果甚至适用于生物学问题,如对蓝斑中的一组尖峰神经元进行数学建模,蓝斑是参与调节认知行为的大脑核心。该方法将是跨学科的,从分析技术和建模到数值和实验验证。第一个挑战是发展一种有效的、系统的方法来确定单模非线性解的几乎必然稳定性。在存在尺度分离的情况下,其中噪声是渐近小的,人们利用对称性来利用关于随机平均的最新数学结果来找到系统的低维描述。随机数值模拟将被用来验证通过分析获得的分叉行为,并为新的现象提供线索,这些新现象本质上是全球性的,而不是通过理论分析发现的。PI将从代表不足的少数族裔和妇女群体中招收学生。该项目将直接培养研究生和本科生。该提议的更广泛影响包括与意大利L大学结构系的伙伴关系,将在那里进行实验验证。学生们将与L大学非线性动力学实验室的教授们密切合作。拟议研究的理论部分将与计算和实验工作紧密结合。
项目成果
期刊论文数量(0)
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专利数量(0)
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N. Sri Namachchivaya其他文献
Random Perturbations of Aeroelastic and Mechanical Systems
- DOI:
10.1016/j.proeng.2016.05.100 - 发表时间:
2016-01-01 - 期刊:
- 影响因子:
- 作者:
Nishanth Lingala;N. Sri Namachchivaya;Prince Singha;Hoong Chieh Yeong - 通讯作者:
Hoong Chieh Yeong
Optimal nudging in particle filters
- DOI:
10.1016/j.probengmech.2013.08.007 - 发表时间:
2014-07-01 - 期刊:
- 影响因子:
- 作者:
N. Lingala;N. Perkowski;H.C. Yeong;N. Sri Namachchivaya;Z. Rapti - 通讯作者:
Z. Rapti
Stability of noisy nonlinear auto-parametric systems
- DOI:
10.1007/s11071-006-9063-7 - 发表时间:
2006-12-21 - 期刊:
- 影响因子:6.000
- 作者:
N. Sri Namachchivaya;David Kok;S. T. Ariaratnam - 通讯作者:
S. T. Ariaratnam
Reduced normal forms for nonlinear control of underactuated hoisting systems
欠驱动提升系统非线性控制的简化范式
- DOI:
10.1007/s00419-011-0557-5 - 发表时间:
2011 - 期刊:
- 影响因子:2.8
- 作者:
C. Rapp;E. Kreuzer;N. Sri Namachchivaya - 通讯作者:
N. Sri Namachchivaya
Rigorous Stochastic Averaging at a Center with Additive Noise
在带有加性噪声的中心进行严格的随机平均
- DOI:
10.1023/a:1019614613583 - 发表时间:
2002 - 期刊:
- 影响因子:2.7
- 作者:
N. Sri Namachchivaya;R. Sowers - 通讯作者:
R. Sowers
N. Sri Namachchivaya的其他文献
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{{ truncateString('N. Sri Namachchivaya', 18)}}的其他基金
BECS: Decadal Climate Prediction Based on Coupled Ocean-Atmosphere Models and Networks of Aerial and Oceanic Sensors
BECS:基于海洋-大气耦合模型以及空中和海洋传感器网络的十年气候预测
- 批准号:
1024772 - 财政年份:2010
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
DynSyst_Special_Topics: Multiscale Dynamics and Information in Data Collection and Assimilation for Complex Systems
DynSyst_Special_Topics:复杂系统数据收集和同化中的多尺度动力学和信息
- 批准号:
1030144 - 财政年份:2010
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
Stability and Nonlinear Dynamics of Variable Speed Milling
变速铣削的稳定性和非线性动力学
- 批准号:
0504581 - 财政年份:2005
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
International Workshop on Applied Dynamical Systems
应用动力系统国际研讨会
- 批准号:
0544619 - 财政年份:2005
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
Workshop on Bifurcation Theory and Spatio-Temporal Pattern Formation; Decembe 11-13, 2003; Toronto, Canada
分岔理论与时空格局形成研讨会;
- 批准号:
0344525 - 财政年份:2003
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
Dynamics of Noisy Nonlinear Mechanical Systems
噪声非线性机械系统的动力学
- 批准号:
0301412 - 财政年份:2003
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
International Symposium on Nonlinear Stochastic Dynamics
非线性随机动力学国际研讨会
- 批准号:
0129587 - 财政年份:2001
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
Parametrically Excited Nonlinear Gyroscopic Systems
参数激励非线性陀螺仪系统
- 批准号:
0084944 - 财政年份:2000
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
Nonlinear Dynamics of Flexible Spinning Discs
柔性旋转盘的非线性动力学
- 批准号:
9610456 - 财政年份:1997
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
Experimental Studies in Mechanical Systems Under Harmonic and Stochastic Excitations
谐波和随机激励下机械系统的实验研究
- 批准号:
9212959 - 财政年份:1992
- 资助金额:
$ 29万 - 项目类别:
Standard Grant
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