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Significance Statement
Over the past few decades the studies of forced and free mechanical oscillations of bluff bodies in a stationary viscous fluid have attracted increasing attention of scientists and engineers. The reason of a such interest is a wide range of practical applications including robotics, sensors and drives of heads on micromechanical generators, cooling devices, the stability of oil platforms and the measurements of damping properties of material. The last mentioned application has initiated this work.
The paper focused on the calculation of the aerodynamic forces acting on a cantilever plates vibrating in the surrounding air to distinguish the aerodynamic component of damping. It is assumed that the aerodynamic interaction can be reduced to inertial effect of added mass and a hydrodynamic damping. The inertial effect leads to the reduction of the resonance frequencies of the structure. Aerodynamic damping increases the decrement of vibrations of the plate compared with it in vacuum. The range of vibration amplitudes realized in the present laboratory experiments lies mostly in the intermediate zone, where the viscous and inertial effects are comparable. Unfortunately previous experimental, numerical and theoretical researches of the aerodynamic forces acting on a plate poorly investigated this region.
However, the intermediate range of vibration amplitudes is characterized by relatively low Reynolds numbers, acceptable for the direct numerical simulation of the flow around the plate. To construct a computational model we assume that the length of the plate is much greater than the other two its characteristic dimensions and the length of the vibration wave of the basic structural mode considerably exceeds its displacements. Therefore, the plate can be considered locally planar.
The direct numerical simulation of the viscous flow around the plate was carried out on the base of the open source software package OpenFOAM. All calculations were performed in the range of parameters typical for damped flexural vibrations of test specimens. According to the results of calculations we construct the approximating equation for the aerodynamic damping in terms of dimensionless parameters of the process considered. Its relative error in the entire range of the observed parameters of does not exceed 8%.
The reported study was supported by RSCF, research project No. 14-19-00667.
Journal Reference
Mechanics of Composite Materials, July 2014, Volume 50, Issue 3, pp 267-278.
G. Egorov, A. M. Kamalutdinov, A. N. Nuriev, V. N. Paimushin.
- Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga region) Federal University, Kazan, Russia and
- Institute of Aviation, Land Transport, and Energy, Kazan National Research Technological University, Kazan, Russia.
Abstract
The aerodynamic component of damping of a vibrating plate in the range of parameters characteristic of damped flexural vibrations of test specimens is investigated. On the basis of a large series of numerical simulations in the dynamics of two-dimensional flow of gas around a plate, we managed to suggest a unified approximating equation for the damping constant in terms of dimensionless parameters of the process considered.
