Instability of Axial Flow Over a Plate Hinged at Its Leading Edge
This paper describes a study of the flow instability over a plate hinged at its leading edge by the pseudospectral numerical method for fluid loading and the Galerkin method for the eigen-value problem. The mechanism of modal coupling for the plate flutte
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Abstract This paper describes a study of the flow instability over a plate hinged at its leading edge by the pseudospectral numerical method for fluid loading and the Galerkin method for the eigen-value problem. The mechanism of modal coupling for the plate flutter is illustrated. It is found that flutter arises from the coupling between the first and second in-vacuo modes, with flow-to-structure energy transfer. The fluid loading on the second in-vacuo mode is found to be the dominant source of instability. Compared with a cantilever plate with the same material property, the plate with a simply supported leading edge has similar threshold of flutter velocity, which suggests that the bending stiffness of the plate is crucial for the stability instead of the structural boundary condition at the leading edge. This conclusion is also validated by the analytical study for a simplified model in which the flexible plate is replaced by two rigid plates connected by a hinge. Keywords Flutter
Simply supported plate Modal analysis
1 Introduction The stability of cantilever plate in axial flow is of great importance in engineering. Many methods for this theoretical model have been applied. The first study was given by Kornecki et al. (1979) with Theodorsen’s thin airfoil theory and Kutta condition. Watanabe et al. (2002) adopted the Navier–Stokes equation, and also gave a good collection of the comparison between various experiments and theories on the flutter of a cantilever plate. His summary showed that the theoretical C. Zhang (&) N. Liu L. Huang Laboratory of Aerodynamics and Acoustics, Zhejiang Institute of Research and Innovation, Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China e-mail: [email protected]
Y. Zhou et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, DOI: 10.1007/978-3-642-40371-2_48, Ó Springer-Verlag Berlin Heidelberg 2014
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results by various methods were consistent, but typical measured flutter speed was about twice as much as the theoretical predictions. The precise reason for such significant discrepancy remains to be identified and it is beyond the scope of the current study. In this paper, we investigate the effect of the structural boundary condition at the leading edge of the flexible plate on the flutter occurrence. We extend our numerical method originally written for a cantilever plate to simulate the flutter of plate with a simply supported leading edge, and conduct the modal analysis for the new configuration. The analysis first focuses on the flutter mechanism. The flutter properties for simply supported and cantilever configurations are compared in order to illustrate the dominant control parameter for the instability. A simplified model with two rigid plates is proposed to further clarify the effects of the structural boundary condition and the bending stiffness of the plate.
2 Numerical Method The fundamental model is shown in Fig. 1. A rectangular flexible plate, whi
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