Interdisciplinary Grants in the Mathematical Sciences

这项提议的目的是请求支持对加州大学洛杉矶分校电气工程系飞行系统研究中心进行为期一年的访问。这次访问的目标如下：a)与中心的研究小组合作，深入研究飞机机翼建模的工程和物理原理；b)继续联合项目的工作，包括对中心开发的新的一维飞机机翼模型进行理论、数值和实验研究；c)参与新的二维机翼模型的设计及其理论和数值研究；d)为未来对飞机工程中出现的数学问题的研究创建一个方案；E)以工程和数学专业学生新的特别课程和研讨会主题的形式为研究生课程做出贡献。加州大学洛杉矶分校的中心与NASA Dryden飞行研究中心合作进行的主要研究方向之一是飞机机翼的颤振抑制问题。(颤振是飞机机翼在特定速度下发生的一种特殊类型的不稳定。颤振造成的损害给航空业带来了巨大的成本。)虽然人们已经对颤振现象进行了广泛的实验和数值研究，但新的有效理论模型的设计及其分析研究仍然是一个悬而未决的问题。这些问题的解决对于向飞机工业工程师提供切实可行的建议至关重要。近两年来，国际和平研究所一直与该中心积极合作，致力于一维机翼模型的渐近分析和频谱分析。这项工作是PI近年来在非自伴算子的谱和渐近分析及其在弹性结构控制和稳定中的应用研究的高潮。上述研究得到了五项资助(两项来自NSF，三项来自德克萨斯高级研究计划)，16篇论文发表在档案期刊上，4篇论文被接受，另外3篇论文-提交，18次受邀演讲已在国际会议和其他大学发表。为了成功地继续这项研究，并为开发一种新的二维、物理逼真的飞机机翼模型做出贡献，PI必须花大量时间在该中心获取工程经验并与工程师团队合作。该IGMS项目由重大计划多学科活动办公室(OMA)和数学科学处(DMS)共同支持。

The objective of this proposal is to request support for a one year visit to the Flight Systems Research Center at the Electrical Engineering Department of UCLA. The goals of this visit are the following: a) to study in depth the engineering and physical principles of aircraft wing modelling while working together with the research team of the Center; b) to continue work on the joint project which consists of theoretical, numerical and experimental study of a new one-dimensional aircraft wing model developed at the Center; c) to participatein the designing of a new two-dimensional wing model and its theoretical and numerical investigation; d) to create a program for future research on mathematical problems arising in aircraft engineering; e) to develop a contribution to the graduate program in the form of new special course and seminar topics for both engineering and mathematical students.One of the main directions of research conducted by the Center at UCLA in collaboration with NASA Dryden Flight Research Center is the problem of flutter supression in the aircraft wings. (Flutter is a special type of instability occurring in an aircraft wing at a specific speed. Damage inflicted by flutter results in significant cost to the aircraft industry.) Although an extensive experimental and numerical study of flutter phenome-non has been carried out, the design of new efficient theoretical models and their analytical investigation are still open problems. The solution of those problems is essential for providing practical recommendations to aircraft industry engineers. The PI has been in active collaboration with the Center for almost two years working on the asymptotic and spectral analysis of one-dimensional wing model. This work is the culminating point of the research conducted by the PI in recent years on spectral and asymptotic analysis of nonselfadjoint operators and its applications to control and stabilizaton of elastic structures. The aforementioned research has been supported by five grants ( two from NSF and three - from the Advanced Research Program of Texas), 16 papers have been published in archival journals, 4 papers are accepted and 3 more papers - submitted, 18 invited talks have been presented at International conferences and other universities. To successfully continue this research and to contribute to the development of a new two-dimensional, physically realistic, model of an aircraft wing, it is essential for the PI to spend a significant amount of time at the Center acquiring experience in engineering and collaborating with the team of engineers. This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).