Finite element analysis of the panel flutter of stiffened shallow shells

• Published in: Continuum mechanics and thermodynamics 2023-07, Vol.35 (4), p.1275-1290
• Main Authors: Bochkarev, Sergey A., Lekomtsev, Sergey V., Matveenko, Valery P.
• Format: Article
• Language: English
• Subjects: Aeroelastic stability; Analysis; Boundary conditions; Classical and Continuum Physics; Curved panels; Cylindrical shells; Eigenvalues; Engineering Thermodynamics; External pressure; Finite element method; Flat plates; Flow control; Gas flow; Heat and Mass Transfer; Original Article; Panel flutter; Physics; Physics and Astronomy; Shallow shells; Shell stability; Stability analysis; Stringers; Structural Materials; Superposition (mathematics); Theoretical and Applied Mechanics; Vibration
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-022-01123-6

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.