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1

A Nonlinear Oscillator Model in Bluff Body Aerodynamics

Grzędziński J., Nowak M.

Machine Dynamics Problems

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2004

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Vol. 28, No. 1

67-78

EN

The aim of this paper is the construction of a semi-empirical model to provide a phenomenological description of motion of a bluff (non-streamlined) body in a streaming fluid. This case differs significantly from the well known case of an airfoil, when the separation occurs only at high angles of attack. Perhaps the best known difference is the capture of the vortex-shedding frequency by the body frequency over a certain range of reduced velocity. This is usually known as "lock in" phenomenon. Similar synchronization behavior can be also observed among solutions of van der Pol equation, and most of models used in practice are based on equations of this type. The results of calculations of aerodynamic forces based on Navier Stokes equations, for a rotationally oscillating thick plate (with chord to thickness ratio equal to 8), for different amplitudes and a wide range of frequency are presented. It was shown that there exist also "lock in" phenomena for frequencies which are odd multipliers of the body frequency. The known semi-empirical models are able to describe the "lock-in" phenomenon only for the forcing frequency. The "lock-in" phenomenon for higher harmonics may be also described by the van der Pol equation, but until now there are no methods to derive such models.

2

Application of Center Manifold in Mechanical Systems

Grzędziński J.

Machine Dynamics Problems

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2001

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Vol. 25, No. 3/4

79-95

EN

In the paper the method of of center manifold reduction for mechanical systems described by integro-differential equations is briefly presented and applied to the limit cycle calculations of a three-dimensional thin airfoil placed in an incompressible flow. Limit cycle oscillations are caused by a cubic structural restoring force corresponding to theaileron rotation. It is emphasized, that the formal power series expansions used in the method of center manifold reduction may diverge and cause the method not to give satisfactory results for any mechanical system. An example is presented, when the method of center manifold reduction cannot even qualitatively predict the occurrence of a stable limit cycle and the use of other methods is necessary.

3

A comparison of center-manifold reduction of nonlinear integro-differential flutter equation and approximate set of ordinary differential equations

Grzędziński J.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

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1999

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nr 9

7-14

EN

A nonlinear integro-differential flutter equation of a thin airfoil placed in an incompressible flow is solved by two different methods. The first method involves the center-manifold reduction and gives the asymptotic limit cycle amplitude and frequency in terms of power series expansions. The second method replaces the integro-differential equation by an approximate set of first-order ordinary differential equations which are solved by using bifurcation and continuation software package. A comparison of these two methods shows that the domain of a good agreement between them varies significantly depending on the parameters of the problem.

4

A certain approximate solutions of nonlinear flutter equation

Grzędziński J.

Engineering Transactions

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1999

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Vol. 47, iss. 1

39-55

EN

A nonlinear integro-differential flutter equation of a thin airfoil placed in an incompressible flow is solved by two different methods. The first method involves the center-manifold reduction and gives the asymptotic limit cycle amplitude and frequency in terms of power series expansions. The second method replaces the integro-differential equation by an approximate set of first-order ordinary differential equations which are solved by using bifurcation and continuation software package. A comparison of these two methods shows that the domain of a good agreement between them varies significantly depending on the parameters of the problem.