Solvability of the Generalized Possio Equation in 2d Subsonic Aeroelasticity
نویسنده
چکیده
We study solvability of the generalized Possio integral equation a tool in analysis of a boundary value problem in 2D subsonic aeroelasticity with the Kutta-Joukowski condition ”zero pressure discontinuity” ψ(x, 0, t) = 0 on the complement of a finite interval in the whole real line R. The corresponding problem with boundary condition on finite intervals adjacent to the ”chord” was considered in [P].
منابع مشابه
Reduction of Boundary Value Problem to Possio Integral Equation in Theoretical Aeroelasticity
The present paper is the first in a series of works devoted to the solvability of the Possio singular integral equation. This equation relates the pressure distribution over a typical section of a slender wing in subsonic compressible air flow to the normal velocity of the points of a wing downwash . In spite of the importance of the Possio equation, the question of the existence of its solutio...
متن کاملOn a Boundary Value Problem in Subsonic Aeroelasticity and the Cofinite Hilbert Transform
We study a boundary value problem in subsonic aeroelasticity and introduce the cofinite Hilbert transform as a tool in solving an auxiliary linear integral equation on the complement of a finite interval on the real line R.
متن کاملA note on unique solvability of the absolute value equation
It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...
متن کاملIterative algorithm for the generalized $(P,Q)$-reflexive solution of a quaternion matrix equation with $j$-conjugate of the unknowns
In the present paper, we propose an iterative algorithm for solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} {underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$. By this iterative algorithm, the solvability of the problem can be determined automatically. When the matrix equation is consistent over...
متن کاملToward a Mathematical Theory of Aeroelasticity
This paper initiates a mathematical theory of aeroelasticity centered on the canonical problem of the flutter boundary an instability endemic to aircraft that limits attainable speed in the subsonic regime. We develop a continuum mathematical model that exhibits the known flutter phenomena and yet is amenable to analysis non-numeric theory. Thus we model the wing as a cantilever beam and limit ...
متن کامل