Mathematical Problems Arising in Aircraft Modeling

飞机建模中出现的数学问题

基本信息

  • 批准号:
    0072247
  • 负责人:
  • 金额:
    $ 9.2万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2000
  • 资助国家:
    美国
  • 起止时间:
    2000-09-01 至 2004-08-31
  • 项目状态:
    已结题

项目摘要

0072247ShubovThe primary goal of this proposal is to develop the spectral, asymptotic, and stability analysis for three increasingly more complete and complicated models of an aircraft wing in a surrounding airflow. The first two of these models (1-dimensional and 2-dimensional respectively) have been developed in the Flight Systems Research Center (FSRC) at UCLA in collaboration with NASA Dryden Flight Research Center, Edwards, CA. The designing of the 3-dimensional model is in progress. Among the wing models existing in the extensive modern literature on aeroelasticity, the aforementioned ones are most physically complete. In November 1999, the 1-dimensional model was tested in a series of four flight experiments at Edwards Airforce Base, CA. The experimental results are in excellent agreement with the theoretical predictions of the model at least for low - energy aeroelastic modes. Currently, the collaboration is supported by NSF Grant DMS-9972748 (Interdisciplinary Grants in the Mathematical Sciences). This grant provides the support for a one year visit (Fall 1999 - Spring 2000) of the principal investigator to the Center in order to study in depth the engineering and physical principles of aircraft wing modeling and to continue work on the joint project with the researchers of the Center. During recent years, the investigator's research has been focused on two main directions: (a) spectral and asymptotic analysis of non-self-adjoint operators in a Hilbert space, operators which are the dynamics generators of hyperbolic equations and systems containing damping terms and subject to dissipative boundary conditions; (b) applications of the results of this analysis to the control of distributed parameter systems governed by those equations and systems. The series of results and methods, developed in this research, has now culminated in the work on the aforementioned 1-dimensional model of a vibrating aircraft wing. Substantial progress has been made: the PI was able to obtain first in the literature explicit asymptotic formulas for the high-frequency aeroelastic modes and mode shapes. The objectives of this project include: (a) obtaining space-time domain representations for the solutions of the 1-dimensional model; (b) obtaining spectral asymptotics and representations for the solutions of most recent 2-dimensional model; (c) applying asymptotic and spectral results to the flutter suppression problem; (d) participating in the designing of a 3-dimensional model of a wing and extending the above analysis to this model.The present project can be considered as a theoretical part of the broad wing modeling project conducted by the researchers at the aforementioned Centers. The ultimate goal of the entire project is to give specific practical recommendations to aircraft industry engineers working on flutter suppression in aircraft wings and tails. Flutter is a dynamic instability occurring in an aircraft in flight at a specific speed which is called a flutter speed. Damage inflicted by flutter results in significant cost to the aircraft industry. The objective of this project is to carry out a rigorous mathematical analysis of the aircraft wing model and to apply the results of this analysis to the problem of flutter control. It has been recognized in the engineering community that the results of such an analysis can provide new insights which are not available from experiments or from numerical simulations. In addition to the above technical objectives of the project, the principal investigator is planning to develop a new graduate program on mathematical methods in aircraft engineering for both mathematics and engineering students.
0072247 Shubov本提案的主要目标是为周围气流中飞机机翼的三个日益完整和复杂的模型进行谱分析、渐近分析和稳定性分析。这些模型中的前两个(分别为一维和二维)是由加州大学洛杉矶分校的飞行系统研究中心(FSRC)与加利福尼亚州爱德华兹的NASA德莱登飞行研究中心合作研制的。三维模型的设计正在进行中。在大量的现代气动弹性文献中存在的机翼模型中,上述模型在物理上是最完整的。1999年11月,一维模型在加利福尼亚州爱德华兹空军基地进行了一系列的四次飞行试验。至少对于低能气动弹性模态,实验结果与模型的理论预测非常一致。目前,该合作得到了NSF Grant DMS-9972748(数学科学跨学科赠款)的支持。这笔赠款提供了一个为期一年的访问(1999年秋季至2000年春季)的主要研究员到中心的支持,以深入研究飞机机翼建模的工程和物理原理,并继续与中心的研究人员的联合项目的工作。近年来,研究者的研究主要集中在两个方面:(a)Hilbert空间中非自伴算子的谱分析和渐近分析,这些算子是双曲型方程和含阻尼项的系统的动力生成元,并具有耗散边界条件;(B)将这种分析的结果应用于由这些方程和系统支配的分布参数系统的控制。在这项研究中开发的一系列结果和方法,现在已经在上述振动飞机机翼的一维模型的工作中达到高潮。已经取得了实质性的进展:PI能够在文献中首次获得高频气动弹性模态和模态形状的显式渐近公式。本项目的目标包括:(a)获得一维模型解的时空域表示;(B)获得最新二维模型解的谱渐近性和表示;(c)将渐近和谱结果应用于颤振抑制问题;(d)参与设计一个3-本项目可以被认为是由美国空军进行的宽翼建模项目的一个理论部分上述中心的研究人员。整个项目的最终目标是为从事飞机机翼和尾翼颤振抑制工作的飞机工业工程师提供具体的实用建议。颤振是发生在飞行中的飞机中的动态不稳定性,其以被称为颤振速度的特定速度飞行。由颤振造成的损坏导致航空工业的显著成本。本项目的目的是对飞机机翼模型进行严格的数学分析,并将分析结果应用于颤振控制问题。工程界已经认识到,这种分析的结果可以提供实验或数值模拟所不能提供的新见解。除了该项目的上述技术目标外,主要研究者还计划为数学和工程专业的学生开发一个关于飞机工程数学方法的新研究生课程。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

数据更新时间:{{ journalArticles.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ monograph.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ sciAawards.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ conferencePapers.updateTime }}

{{ item.title }}
  • 作者:
    {{ item.author }}

数据更新时间:{{ patent.updateTime }}

Marianna Shubov其他文献

Marianna Shubov的其他文献

{{ item.title }}
{{ item.translation_title }}
  • DOI:
    {{ item.doi }}
  • 发表时间:
    {{ item.publish_year }}
  • 期刊:
  • 影响因子:
    {{ item.factor }}
  • 作者:
    {{ item.authors }}
  • 通讯作者:
    {{ item.author }}

{{ truncateString('Marianna Shubov', 18)}}的其他基金

Asymptotic and Spectral Analysis and Control Problems for Aeroelastic Energy Harvester Models
气动弹性能量收集器模型的渐近谱分析与控制问题
  • 批准号:
    1810826
  • 财政年份:
    2018
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant
Flutter Analysis and Control for Elastic Structure in Axial Air Flow: Applications to Palatal Flutter and Energy Harvesting
轴向气流中弹性结构的颤振分析与控制:在腭颤和能量收集中的应用
  • 批准号:
    1211156
  • 财政年份:
    2012
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant
Control and Stabilization Problems for Aircraft Wing Models in Subsonic Air Flow
亚音速气流中飞机机翼模型的控制与稳定问题
  • 批准号:
    0604842
  • 财政年份:
    2006
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant
Mathematical Analysis of Aircraft Wing Models and Application to Flutter Control
飞机机翼模型的数学分析及其在颤振控制中的应用
  • 批准号:
    0514977
  • 财政年份:
    2004
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant
Mathematical Analysis of Aircraft Wing Models and Application to Flutter Control
飞机机翼模型的数学分析及其在颤振控制中的应用
  • 批准号:
    0080441
  • 财政年份:
    2000
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant
Interdisciplinary Grants in the Mathematical Sciences
数学科学跨学科资助
  • 批准号:
    9972748
  • 财政年份:
    1999
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Spectral Operators Generated by Damped Hyperbolic Equations
数学科学:由阻尼双曲方程生成的谱算子
  • 批准号:
    9706882
  • 财政年份:
    1997
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Resonances in Coulomb-Like Quantum Systems with External Field
数学科学:类库仑量子系统与外场的共振
  • 批准号:
    9212037
  • 财政年份:
    1992
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Standard Grant

相似海外基金

Mathematical inverse problems arising in acoustic imaging
声学成像中出现的数学反问题
  • 批准号:
    RGPIN-2022-04547
  • 财政年份:
    2022
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
Study on free boundary problems arising in mathematical ecology and related nonlinear diffusion equations
数学生态学中自由边界问题及相关非线性扩散方程的研究
  • 批准号:
    19K03573
  • 财政年份:
    2019
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Mathematical programming techniques for the solution of hard combinatorial optimization problems arising in transportation
用于解决运输中出现的硬组合优化问题的数学编程技术
  • 批准号:
    435824-2013
  • 财政年份:
    2018
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
The Mathematical Modelling of Various Problems arising in the Biomedical Sciences
生物医学科学中出现的各种问题的数学建模
  • 批准号:
    RGPIN-2014-04772
  • 财政年份:
    2018
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
The Mathematical Modelling of Various Problems arising in the Biomedical Sciences
生物医学科学中出现的各种问题的数学建模
  • 批准号:
    RGPIN-2014-04772
  • 财政年份:
    2017
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical programming techniques for the solution of hard combinatorial optimization problems arising in transportation
用于解决运输中出现的硬组合优化问题的数学编程技术
  • 批准号:
    435824-2013
  • 财政年份:
    2017
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
The Mathematical Modelling of Various Problems arising in the Biomedical Sciences
生物医学科学中出现的各种问题的数学建模
  • 批准号:
    RGPIN-2014-04772
  • 财政年份:
    2016
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
Study on free boundary problems and reaction-diffusion equations arising in mathematical ecology
数学生态学中的自由边界问题和反应扩散方程研究
  • 批准号:
    16K05244
  • 财政年份:
    2016
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Mathematical programming techniques for the solution of hard combinatorial optimization problems arising in transportation
用于解决运输中出现的硬组合优化问题的数学编程技术
  • 批准号:
    435824-2013
  • 财政年份:
    2016
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Discovery Grants Program - Individual
Mathematical and computational analysis of moving boundary problems arising in snow and ice phenomena
冰雪现象中移动边界问题的数学和计算分析
  • 批准号:
    16H03953
  • 财政年份:
    2016
  • 资助金额:
    $ 9.2万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了