On a numerical method of the bending vibrations problem for thin elastic plave

The problem of small bending vibrations occurring in a thin elastic plate of variable thickness with a bending moment and a shearing force applied to the plate contour is considered. A difference method is proposed. It is based on reduction of initial partial differential equation to a system of equations with first-order time derivatives. A two-level implicit scheme is considered for solving this system. Stability of the difference scheme is proved. The system of difference equations was solved by splitting with respect to spatial variables into two subsystems.