Nonlinear dynamical problem of a cyclinder with a slowly changing internal boundary

1975 ◽  
Vol 9 (2) ◽  
pp. 237-242
Author(s):  
U. Tokhtarov ◽  
M. A. Koltunov ◽  
V. I. Morgunov ◽  
I. E. Troyanovskii
Keyword(s):  
Dynamical Problem ◽  
Internal Boundary ◽  
Nonlinear Dynamical ◽  
Nonlinear Dynamical Problem

scholarly journals Approximation theorems of a solution of amperometric enzymatic reactions based on Green’s fixed point normal-S iteration

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Khanitin Muangchoo-in ◽  
Kanokwan Sitthithakerngkiet ◽  
Parinya Sa-Ngiamsunthorn ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Iterative Methods ◽  
Dynamical Problem ◽  
Enzymatic Reactions ◽  
Nonlinear Dynamical ◽  
Numerical Examples ◽  
Approximation Theorems ◽  
Kinetics Of ◽  
Nonlinear Dynamical Problem

AbstractIn this paper, the authors present a strategy based on fixed point iterative methods to solve a nonlinear dynamical problem in a form of Green’s function with boundary value problems. First, the authors construct the sequence named Green’s normal-S iteration to show that the sequence converges strongly to a fixed point, this sequence was constructed based on the kinetics of the amperometric enzyme problem. Finally, the authors show numerical examples to analyze the solution of that problem.

Effects of Non-Linear Eddy-Airfoil Interaction on the Acoustic Radiation of a Thin Wing

2012 ◽  
Author(s):  
A. Manela
Keyword(s):  
Acoustic Radiation ◽  
Dynamical Problem ◽  
Nonlinear Dynamical ◽  
Reynolds Number Flow ◽  
Motion Signal ◽  
Non Linear ◽  
Number Flow ◽  
High Reynolds ◽  
Dynamical Description ◽  
Nonlinear Dynamical Problem

We study the combined effect of boundary animation (small-amplitude heaving) and incoming flow unsteadiness (incident vorticity) on the vibroacoustic signature of a thin rigid airfoil in low-Mach high-Reynolds number flow. The nonlinear dynamical problem for the vortex trajectory is studied using potential flow theory. The dynamical description then serves as an effective source term to evaluate the far-field sound using Powell-Howe’s analogy. The results identify the fluid-airfoil system as a dipole-type source, and demonstrate the significance of non-linear eddy-airfoil interaction on the acoustic radiation. At low heaving frequencies (ωa/U < 1, where ω denotes the heaving frequency, 2a the airfoil chord, and U the mean stream speed), the effect of heaving is minor, and the acoustic field can be approximated by neglecting airfoil motion. However, at ωa/U > 1, heaving becomes dominant, radiating sound through an “airfoil motion” dipole (oriented along the direction of heaving) and airfoil-induced oscillations in the vortex trajectory. In contrast with the periodic “airfoil motion” signal, the non-periodic incident vortex sound has a component along the airfoil chord, which becomes significant when the vortex passes close to the airfoil. The work is suggested as a preliminary tool to examine the acoustic radiation during flapping flight at unsteady flow conditions.

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