Abstract—

A mathematical formulation and an algorithm for its numerical implementation are presented, intended to study the aeroelastic stability of cylindrical shells of arbitrary cross-section. The problem is solved in a three-dimensional formulation using the finite element method. The reliability of the results obtained is confirmed by comparison with the known solutions for circular shells. The dependences of the static pressure in an undisturbed gas flow, at which the loss of stability occurs, obtained for different ratios of the ellipse semiaxes and variants of the kinematic boundary conditions are analyzed. The possibility of increasing the boundaries of the aeroelastic stability of a cylindrical shell with an elliptical cross-section in comparison with a circular configuration in the case of cantilever fastening is demonstrated.

中文翻译：

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椭圆形截面圆柱壳的气动弹性稳定性

摘要-

提出了数学公式及其数值实现的算法，旨在研究任意截面的圆柱壳的气动弹性稳定性。使用有限元方法以三维公式解决了该问题。通过与已知的圆形外壳解决方案进行比较，可以确定所获得结果的可靠性。分析了椭圆半轴的不同比例和运动边界条件的变化所获得的，在未扰动气流中产生静力损失的静压力的相关性。在悬臂固定的情况下，与圆形构造相比，具有增大椭圆形横截面的圆柱形壳体的空气弹性稳定性的边界的可能性被证明。