Plate flutter problem with mixed boundary conditions

The paper considers the solution of the plate flutter problem with mixed boundary conditions. The mathematical formulation of the problem allows taking into account arbitrary directions of the incoming flow vector. For the numerical solution of the problem, a modern numerical algorithm without saturation is proposed, which allows obtaining the critical flutter speed with sufficient accuracy on a sparse grid. The results of calculations for four materials are presented: titanium, steel, aluminum, duralumin. Based on the calculation results, two analytical dependences for the critical flutter speed are obtained: from the direction of the incoming flow vector, as well as from the dimensionless speed of sound in the plate and the thickness of the plate. The eigenforms $\mathrm{Re}(\varphi)$ corresponding to the critical flutter speed are given.