Free transverse vibration analysis of general polygonal plate with elastically restrained inclined edges

•A semi-analytical solution for the transverse vibration of polygonal plate with arbitrary shape and elastically restrained edges is obtained.•The proposed method simplifies the complex surface integral over irregular plate area into a summation of plate boundary points and offers a unified procedure to deal with the vibration of polygonal plate with various shapes.•The elastically restrained boundary conditions of all edges including inclined edges are considered.