The aeroelastic stability of flat plates and shallow cylindrical shells stiffened with stringers is investigated. In the case of a curved panel, the supersonic gas flow is parallel to its generatrix. A mathematical formulation of the dynamics problem is based on the variational principle of virtual displacements taking into account the work done by the inertial forces and aerodynamic pressure of the external supersonic gas flow determined according to the quasi-static aerodynamic theory. The solution is found by the finite element method in a three-dimensional formulation using the mode-superposition technique. The estimation of the shell stability is based on the analysis of complex eigenvalues of the system of equations calculated under gradually increasing aerodynamic pressure. The validity of the obtained results is confirmed by comparing them with the known solutions to a number of relevant problems. Numerical examples are used to analyze in detail the influence of the curvature ratio, the boundary conditions specified at the edges of the shallow shell, and the number of stringers on the boundary of stability loss. It is demonstrated that with an optimal arrangement of reinforcing elements, it is possible to achieve a significant increase in the critical parameters of the flutter.

研究了用纵梁加强的平板和浅圆柱壳的气动弹性稳定性。在曲面面板的情况下，超音速气流平行于其母线。动力学问题的数学公式是基于虚拟位移的变分原理，同时考虑了根据准静态气动理论确定的外部超音速气流的惯性力和气动压力所做的功。解决方案是通过有限元方法使用模式叠加技术在三维公式中找到的。壳体稳定性的估计是基于对逐渐增加的空气动力压力下计算的方程组的复特征值的分析。通过将所得结果与许多相关问题的已知解决方案进行比较来确认所得结果的有效性。通过数值算例详细分析了曲率比、浅壳边缘规定的边界条件、稳定损失边界上纵梁数量的影响。结果表明，通过增强元件的优化布置，可以显着提高颤振的关键参数。