Influence of non-linear forces on beam behaviour in flutter conditions

Tizzi, S.

doi:10.1016/s0022-460x(03)00177-9

Cited by 4 publications

(13 citation statements)

References 8 publications

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“…A vibrating beam exposed to a high supersonic flow along the x axis, previously analyzed with the linear aerodynamic model [Tizzi 1994;2003], is considered and drawn in Figure 1. Figure 1.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…As in [Tizzi 2003], the aerodynamic expressions of an infinite plate along the third, not considered y axis are applied, together with the structural constitutive relations of a beam; this hypothesis can be accepted if the beam width b w is much greater than L.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Three different schemes have been exploited for the flutter computational work, as in the case of the beam flutter analysis with linearized and idealized piston theory [Tizzi 1994;2003]. First a numerical procedure [Tizzi 1994;1996;2003] which arises from the Rayleigh-Ritz method [Kantorovich and Krylov 1964, pp.…”

Section: Introductionmentioning

confidence: 99%

“…First a numerical procedure [Tizzi 1994;1996;2003] which arises from the Rayleigh-Ritz method [Kantorovich and Krylov 1964, pp. 258-303;Mikhlin 1964, pp.…”

Section: Introductionmentioning

confidence: 99%

“…Then the Galerkin method [Kantorovich and Krylov 1964;Mikhlin 1964;Tizzi 1994;2003] was employed in the case of a simply supported beam, as in Dowell's model [1966;1967], to validate the results of Ritz and FEM procedures.…”

Section: Introductionmentioning

confidence: 99%

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Influence of the nonlinear aerodynamic force components on a vibrating beam, simply supported or clamped at both ends, exposed to a high supersonic airflow along its axial direction

Tizzi

2009

J. Mech. Mater. Struct.

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In this work we analyze the case of a vibrating beam, simply supported or clamped at both ends, under the effect of a high supersonic airflow along its axial direction. A complete aerodynamic model of the piston theory, which also takes into account the nonlinear components of the distributed aerodynamic transversal force, is used. The postcritical flutter behavior and its influence on the vibration state solutions of a fluttering beam without aerodynamic damping have been studied. This paper focuses particularly on the effects of these nonlinear aerodynamic forces on three frequencies, which are useful in characterizing the postcritical flutter solution set of the undamped beam in the whole frequency range: the minimum frequency, the frequency where the change of the modal shape with lower amplitude occurs, and the frequency corresponding to the solution with minimum amplitude of the vibration mode. Special attention has been given to the influence on the solution of the vibrating undamped beam with minimum modal amplitude, whose frequency is the most important among the three mentioned above; in fact, in the neighborhood of this particular solution, there exists the flutter state of the vibrating damped beam in limit cycle conditions. Three different schemes, two of them semianalytical (based on the classical and well known RayleighRitz and Galerkin methods) and one of them numerical (based on the finite element method), have been herein exploited, as in the author's previous papers, where beam flutter models with linear aerodynamic analysis were used. The good agreement between the results obtained by the three methods corroborates their effectiveness.More sophisticated models have been herein set up, considering that a more accurate analysis is necessary than in previous cases, where the aerodynamic numerical model was limited to within the framework of the quasisteady linearized piston theory, both for the coupling component between odd and even order vibrating modes, and for the aerodynamic damping component.The results obtained enable us to assess quantitatively the influence of these nonlinear aerodynamic forces on the postcritical beam flutter behavior, and particularly on the undamped beam solution with minimum amplitude of the vibration mode.

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…First a numerical procedure [Tizzi 1994;1996;2003] which arises from the Rayleigh-Ritz method [Kantorovich and Krylov 1964, pp. 258-303;Mikhlin 1964, pp.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Influence of the nonlinear aerodynamic force components on a vibrating beam, simply supported or clamped at both ends, exposed to a high supersonic airflow along its axial direction

Tizzi

2009

J. Mech. Mater. Struct.

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Aeroelastic flutter analysis for 2D Kirchhoff and Mindlin panels with different boundary conditions in supersonic airflow

Song

2014

Acta Mech

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Stability Analysis of a Flutter Panel with Axial Excitations

Peng

DeSmidt

2016

Advances in Acoustics and Vibration

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This paper investigates the parametric instability of a panel (beam) under high speed air flows and axial excitations. The idea is to affect out-of-plane vibrations and aerodynamic loads by in-plane excitations. The periodic axial excitation introduces time-varying items into the panel system. The numerical method based on Floquet theory and the perturbation method are utilized to solve the Mathieu-Hill equations. The system stability with respect to air/panel density ratio, dynamic pressure ratio, and excitation frequency are explored. The results indicate that panel flutter can be suppressed by the axial excitations with proper parameter combinations.

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Influence of non-linear forces on beam behaviour in flutter conditions

Cited by 4 publications

References 8 publications

Influence of the nonlinear aerodynamic force components on a vibrating beam, simply supported or clamped at both ends, exposed to a high supersonic airflow along its axial direction

Influence of the nonlinear aerodynamic force components on a vibrating beam, simply supported or clamped at both ends, exposed to a high supersonic airflow along its axial direction

Aeroelastic flutter analysis for 2D Kirchhoff and Mindlin panels with different boundary conditions in supersonic airflow

Stability Analysis of a Flutter Panel with Axial Excitations

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