Vibrations of a polygonal plate weakened by a circular hole with two rectilinear cuts

We consider free bending vibrations of a finite isotropic plate bounded on the outside by a polygon L2 (e.g., a square, an ellipse, a circle, etc.) and on the inside by the contour L1 formed by the circle of radius r with two rectilinear cuts located symmetrically on the axis Ox. The plate is rigidly clamped along the entire outer contour L2, and the inner contour L1 is free.