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Existence of Optimum Propulsion by Means of Periodic Motions of a Rigid Profile
Author(s) -
Urbach H. P.
Publication year - 1989
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198981293
Subject(s) - inviscid flow , thrust , constraint (computer aided design) , mathematics , compressibility , propulsion , mathematical analysis , suction , classical mechanics , mechanics , physics , geometry , meteorology , thermodynamics
The optimum generation of thrust by means of a rigid profile which performs periodic motions in an inviscid incompressible fluid is discussed. For the description of the flow a linear theory is used. Apart from the demand that a certain mean value of thrust has to be generated, the motions considered have to satisfy an inequality constraint on the contribution of the mean suction force at the leading edge to the total thrust and are furthermore subject to a constraint on their amplitude. This leads to an infinite‐dimensional nonconvex optimization problem. It is proved that for most values of the parameters involved there exists at least one optimum motion.