A semi-analytical method for transverse vibration of sector-like thin plate with simply supported radial edges

In this paper, a semi-analytical method is presented to study the transverse vibration of sector-like thin plate with various boundary conditions. A sector-like plate is generated from a sector plate whose circular edge is replaced by edges of other geometries. The expressions of boundary conditions for arbitrary point on the arc edge are given in a local rectangular coordinate system and transformed into the global polar coordinate system. Fourier expansion is performed on the expressions of the boundary conditions so that the boundary conditions are satisfied on the whole edge. Several examples are presented and the results are calculated numerically and compared with those in literature and obtained by FEM. The good agreement between the results validates the accuracy and applicability of this method for sector-like plates.