Control of Fluid-Elastic Structures and Related Topics

流体弹性结构的控制及相关主题

基本信息

  • 批准号:
    1312952
  • 负责人:
  • 金额:
    $ 17.09万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2013
  • 资助国家:
    美国
  • 起止时间:
    2013-07-01 至 2017-06-30
  • 项目状态:
    已结题

项目摘要

The proposed research is aimed at better understanding the controllability structure of coupled fluid-elastic systems. Specifically, we focus on the situation of a fluid in a three-dimensional domain with a flexible boundary that is described by a plate or membrane equation. We suggest several problems which serve to address our fundamental question: How much control in one or more components of the coupled system is needed to obtain (i) controllability or approximate controllability of the coupled system or (ii) partial controllability (approximate or exact) of one or more components of the system? The proposed research extends the state-of-the-art in several ways. First, the partial controllability problem in the context of a fluid-elastic system has not been addressed for the types of physically-based models we are considering. Secondly, many of the models we propose to analyze have not been studied even for well-posedness. This is a nontrivial step even in the linear case for some of the models (e.g., when considering free boundary conditions). However we also hope to address local controllability for the nonlinear problems associated with the free boundary problem for the Stokes system associated with a moving flexible boundary. Likewise we hope to make some progress in the case of a compressible Navier-Stokes fluid coupled with a plate. Our main analytical tool to attack these problems will be the method of Carleman estimates together with microlocal analysis. Development of Carleman estimates for these types of coupled systems might turn out to be be very useful in a broader context, as it is likely that a similar approach may be useful in the analysis of a variety of other types of coupled systems. We also propose to investigate the closely related inverse problem of determination of plate coefficients through knowledge of the appropriately defined Dirichlet-to-Neumann maps associated with solutions of the coupled plate-fluid system. The fluid-elastic structures we aim to study arise in many practical applications. For example,the problem of minimizing the engine noise in a portion of an aircraft fuselage through controllers placed on and inside the aircraft is closely related to the partial controllability problem (ii) mentioned above. One specific fluid-elastic structure we plan to investigate is the cochlea, which is the auditory organ in the inner ear that translates sound vibrations to electrical impulses transmitted to the brain. A better understanding of the controllability structure of the cochlea could lead to an improved design of cochlear implants and hearing aids.
所提出的研究旨在更好地理解耦合流体弹性系统的可控性结构。具体来说,我们专注于在一个三维域中的流体的情况下,由板或膜方程描述的柔性边界。我们提出了几个问题,用于解决我们的基本问题:有多少控制在一个或多个组件的耦合系统需要获得(一)可控性或近似可控性的耦合系统或(ii)部分可控性(近似或精确)的一个或多个组件的系统?拟议的研究在几个方面扩展了最先进的技术。首先,在流体弹性系统的背景下,部分可控性问题还没有得到解决的类型的物理模型,我们正在考虑。其次,我们提出分析的许多模型甚至没有研究过适定性。这是一个非平凡的步骤,即使在线性情况下的一些模型(例如,当考虑自由边界条件时)。然而,我们也希望解决与移动柔性边界的Stokes系统的自由边界问题相关的非线性问题的局部可控性。同样,我们希望在可压缩Navier-Stokes流体与板耦合的情况下取得一些进展。我们的主要分析工具,以攻击这些问题将是方法的Carleman估计连同微观分析。Carleman估计这些类型的耦合系统的发展可能会在更广泛的背景下是非常有用的,因为它很可能是一个类似的方法可能是有用的,在各种其他类型的耦合系统的分析。我们还建议调查密切相关的反问题的板系数的确定通过适当定义的Dirichlet-诺依曼映射与耦合板流体系统的解决方案的知识。 流体弹性结构,我们的目标是研究出现在许多实际应用中。例如,通过放置在飞机上和飞机内部的控制器使飞机机身的一部分中的发动机噪声最小化的问题与上述部分可控性问题(ii)密切相关。我们计划研究的一个特定的流体弹性结构是耳蜗,它是内耳中的听觉器官,将声音振动转化为传输到大脑的电脉冲。更好地理解耳蜗的可控性结构可以改进耳蜗植入物和助听器的设计。

项目成果

期刊论文数量(0)
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Scott Hansen其他文献

Temporal stability of lake whitefish genetic stocks in Lake Michigan
  • DOI:
    10.1016/j.jglr.2016.01.006
  • 发表时间:
    2016-04-01
  • 期刊:
  • 影响因子:
  • 作者:
    Lucas R. Nathan;Brian L. Sloss;Justin A. VanDeHey;Ryan T. Andvik;Randall M. Claramunt;Scott Hansen;Trent M. Sutton
  • 通讯作者:
    Trent M. Sutton
Heat Transfer Assessment for Tumor Focal Therapy with Rod-Type Probe
使用棒型探针进行肿瘤局部治疗的传热评估
  • DOI:
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Bryan Félix;Ewnet Gebrehiwot;Scott Hansen
  • 通讯作者:
    Scott Hansen
Creation of micro/nano surface structures on silver using collinear double femtosecond laser pulses with different pulse separation
使用具有不同脉冲间隔的共线双飞秒激光脉冲在银上创建微/纳米表面结构
  • DOI:
  • 发表时间:
    2018
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Nicholas Roth;C. Zuhlke;Edwin Peng;Scott Hansen;J. Shield;D. Alexander
  • 通讯作者:
    D. Alexander
Comparison of Cooling and Warming Technologies for Lung Preservation
肺保护冷却和加温技术的比较
  • DOI:
  • 发表时间:
    2019
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Bryan Félix;Ewnet Gebrehiwot;Scott Hansen
  • 通讯作者:
    Scott Hansen
Novel etiology of infantile hemangioma
  • DOI:
    10.1016/j.jamcollsurg.2007.06.162
  • 发表时间:
    2007-09-01
  • 期刊:
  • 影响因子:
  • 作者:
    Chia J. Chung;Susan Fisher;Matthew Gormley;William Hoffman;David M. Young;Scott Hansen
  • 通讯作者:
    Scott Hansen

Scott Hansen的其他文献

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{{ truncateString('Scott Hansen', 18)}}的其他基金

CAREER: Mechanisms controlling spatial patterning of PIP lipids in eukaryotic cell polarity
职业:真核细胞极性中 PIP 脂质空间模式的控制机制
  • 批准号:
    2048060
  • 财政年份:
    2021
  • 资助金额:
    $ 17.09万
  • 项目类别:
    Continuing Grant
Analysis and Control of Layered Media
分层介质的分析与控制
  • 批准号:
    0205148
  • 财政年份:
    2002
  • 资助金额:
    $ 17.09万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Modeling, Analysis and Control Of Multilayer Plates
数学科学:多层板的建模、分析和控制
  • 批准号:
    9623144
  • 财政年份:
    1996
  • 资助金额:
    $ 17.09万
  • 项目类别:
    Standard Grant

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随机进程代数模型的Fluid逼近问题研究
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