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

• Published in: Applied Mathematical Modelling 2018-08, Vol.60, p.48-63
• Main Authors: Guan, Xianlei, Tang, Jinyuan, Shi, Dongyan, shuai, Cijun, Wang, Qingshan
• Format: Article
• Language: English
• Subjects: Boundary conditions; Different boundary shapes; Finite element analysis; Finite element method; Fourier expansion; Fourier transforms; Geometry; Sector-like plate; Thin plates; Transverse oscillation; Transverse vibration; Vibration analysis
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.03.007

•The concept of sector-like plate is proposed due to the lack of researches on these kinds of structures.•A semi-analytical method is used to analyze the vibration of sector-like plates.•The method converges quickly and the results are accurate by comparing the results with the reference results.•The method is applicable for the vibration problems of sector-like plates. 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.