Interdisciplinary Grants in the Mathematical Sciences

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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).