A unified solution for vibration analysis of functionally graded circular, annular and sector plates with general boundary conditions

• Published in: Composites. Part B, Engineering Engineering, 2016-03, Vol.88, p.264-294
• Main Authors: Wang, Qingshan, Shi, Dongyan, Liang, Qian, Shi, Xianjie
• Format: Article
• Language: English
• Subjects: Annular; B. Vibration; Boundary conditions; C. Numerical analysis; Circularity; Fourier series; Functionally graded plate; Functionally gradient materials; Mathematical analysis; Mathematical models; Plates
• ISSN: 1359-8368; 1879-1069
• DOI: 10.1016/j.compositesb.2015.10.043

The vibrations of functionally graded circular plates, annular plates, and annular, circular sectorial plates have been traditionally treated as different boundary value problems, which results in numerous specific solution algorithms and procedures. It is the problem itself that has been an overwhelming task for a new researcher or application engineer to comprehend. Furthermore each type of plate usually needs treating separately when different boundary conditions are involved. In this paper, a unified method is presented for the vibration analysis of the plates mentioned above with general boundary conditions based on the first-order shear deformation theory and Ritz procedure. The material properties are assumed to vary continuously through the thickness according to the general four-parameter power-law distribution. Regardless of the shapes of the plates and the types of boundary conditions, the displacements of the plates are described as an improved Fourier series expansion which is composed of a double Fourier cosine series and several auxiliary functions. As an innovative point of this work, the auxiliary functions are introduced to eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries and to accelerate the convergence of series representations. The accuracy, reliability and versatility of the current solution are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions. Some new results of functionally graded circular, annular and sector plates with various boundary conditions are presented, which may serve as datum solutions for future computational methods. In addition, the influence of boundary conditions, the material and geometric parameters on the vibration characteristics of the plates are also reported.