Analytical method for determining eigenvalues in the problem of vibrations of a plate moving in gas

An analytical method for determining eigenvalues for differential equations using special functions is presented. As an example, vibrations of an infinite-width cantilever plate moving with the supersonic velocity in a gas are described. For a two-dimensional problem, the analytical dependence between the plate eigenvibration characteristics and velocity was obtained, which allows us to make conclusions about motion stability. The developed technique can be applied to study many problems whose solution is associated with finding of eigenvalues. In contrast to similar techniques, the described method yields sufficiently accurate analytical expressions for eigenvalues, which allows one to use them in specific calculations.