A unified solution for free vibration of orthotropic annular sector thin plates with general boundary conditions, internal radial line and circumferential arc supports

In this paper, a modified Fourier-Ritz approach is adopted to analyze the free vibration of orthotropic annular sector thin plates with general boundary conditions, internal radial line and circumferential arc supports. In the present method, regardless of boundary conditions, the displacements of the sector plates are invariantly expressed as a standard Fourier cosine series and several auxiliary closed-form functions. These auxiliary functions are introduced to eliminate any potential discontinuities of the original displacement function and its derivatives throughout the whole domain including its edges, and then to effectively enhance the convergence of the results. Since the displacement field is constructed to be adequately smooth in the whole solution domain, an accurate solution can be obtained by using Ritz procedure based on the energy functions of the sector plates. The excellent accuracy and reliability of the current solutions are compared with the results found in the literature, and numerous new results for annular sector plates with various boundary conditions are presented. New results are obtained for annular sector plates subjected to elastic boundary restraints and arbitrary internal radial line and circumferential arc supports in both directions, and they may be served as benchmark solutions for future researches.