10711

9894

كارشناسي ارشد

رياضي محض ﴿آناليز تابعي﴾

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1394

هفت، 80ص.

به فارسي و انگليسي

1396/10/05

كتابنامه

علوم رياضي

رياضي

ID9894

Solution of Cauchy Type of Singular Integral Equations of Airfoil Seyed Abolghasem Shaddel shaddel 11@yahoo com September 05 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Farid Bahrami fbahrami@cc iut ac ir Advisor Dr Mohammadreza Raoo Raoo @cc iut ac ir 2010 MSC 65R20 42E05 Keywords Singular Integral Equations Cauchy Chebyshev of Polynomials Airfoil AbstractThis thesis is a generalization of the works done by Abdulkawi Eshkuvatov and Nik Long 1 Weintroduce solution of cauchy type singular integral equations of airfoil During the last three decades the singular integral equation methods have been studied One of the important reason is applicationof this area at the sevral basic elds such as elasticity plasticity fracture mechanics electromagnetisof antenna hydrodynamics and aerodynamics Hence its intersting the rst step introduce at rst step inner production Hilbert space and then integral equation and Chebyshev polynomials properties suchas zero extrema orthogonality and recurence relation Then we make mathemathics modeling of air foils For make mathemathics model of airfoil we need to be de nd vorticity circulation and streamlinethat introuce in chapter three Also for convinence we assume the airfoil is thin and ow is inviscidand uncompressible This assumption caused to we can use from Laplase equation and combined simplebasic ow for making complex ow After this we obtain singular integral equation rst kind with acauchy type singular kernel over a nite interval ie 1 1 t 1 x 1 dt K x t t dt f x 1 t x 1 If consider kernel K x t 0 zero then its so called airfoil equation as below

فريد بهرامي

محمدرضا رئوفي

مهدي نعمتي، محمود منجگاني