Influence of Initial Deflection Imperfections on Critical Flutter Aerodynamic Pressures of Shallow Cylindrical Shells
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摘要: 为研究初始挠度缺陷对圆柱形扁壳气动弹性系统颤振临界动压的影响，将初始挠度引入圆柱形扁壳气动弹性方程，采用微分求积法进行离散，运用特征值方法分析了线性系统在超声速轴向流中的颤振临界动压.研究结果表明，初始挠度缺陷会显著影响颤振临界动压.在本文计算参数下，当初始挠度周向半波数等于1时，颤振临界动压参数与初始挠度缺陷因子成比例关系；当周向半波数小于4时，随着初始挠度缺陷因子的增加，系统颤振临界动压大都呈现减小趋势；对于小曲率情况，当周向半波数大于4时，初始挠度缺陷因子的增加带来的颤振临界动压变化并不显著；对于大曲率情况，当周向半波数大于4时，随着初始挠度缺陷因子的增加系统颤振临界动压显著减小；初始挠度的形式会影响产生耦合模态颤振的周向半波数.Abstract: To study the effect of initial deflection imperfection on the flutter critical dynamic pressure of a cylindrical shallow shell aeroelastic system, an initial deflection was introduced into the aeroelastic equation of cylindrical shallow shells. The differential quadrature method was used to discretize the system, and the flutter critical dynamic pressure of a linear system in supersonic axial flow was analysed using the eigenvalue method. The results showed that the initial deflection imperfection can significantly affect the flutter critical dynamic pressure. Herein, when the circumferential half wave number of the initial deflection equals 1, the critical dynamic pressure parameter of flutter is proportional to the initial deflection imperfection factor. When the circumferential half wave number is less than 4, with the increase in the initial deflection imperfection factor, the critical dynamic pressure of the system tends to decrease. For the small curvature condition, when the circumferential half wave number is greater than 4, the flutter critical dynamic pressure change caused by the increase in the initial deflection imperfection factor is not significant. For the large curvature condition, when the circumferential half wave number is greater than 4, the flutter critical dynamic pressure decreases significantly with the increase in the initial deflection imperfection factor. It was also found that the geometric form of the initial deflection affected the circumferential half wave number of the flutter coupling modes.
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Key words:
- initial deflection /
- shells /
- flutter /
- critical aerodynamic pressure /
- differential quadrature method /
- piston theory
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图 1 小曲率α=20、θ0=0.05时, 初始挠度缺陷因子对颤振临界动压的影响
Figure 1. Effect of initial deflection imperfection factor on the flutter critical aerodynamic parameter at small curvature wherein α=20, θ0=0.05
图 2 n0=1时, 颤振临界动压参数随初始缺陷因子的变化
Figure 2. Flutter critical aerodynamic parameter vs initial deflection imperfection factor at n0=1
图 3 n0=2时, 无量纲特征值虚部随动压变化
Figure 3. Imaginary parts of non-dimensional eigenvalues vs aerodynamic pressure at n0=2
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