A unified solution for free vibration of orthotropic circular, annular and sector plates with general boundary conditions

作者：Shi, Dongyan; Liang, Qian; Wang, Qingshan^*; Teng, Xiaoyan

来源：Journal of Vibroengineering, 2016, 18(5): 3138-3152.

DOI：10.21595/jve.2016.17004

• free vibration
• orthotropic annular sector thin plates
• orthotropic annular thin plates
• orthotropic circular sector thin plates
• orthotropic circular thin plates
• general boundary conditions
• Ritz approach

This paper adopts a modified Fourier-Ritz approach to study the free vibration characteristics of orthotropic circular, annular and sector thin plates subjected to general boundary conditions. For the arbitrary plate forms and the boundary conditions, the displacements can be written in the form of a standard Fourier cosine series supplemented with several auxiliary functions. The auxiliary functions, which are closed-form and introduced to remove all the potential discontinuities of the original displacement function and its derivatives in the whole domain, can be usefully employed in improving the convergence of the results. The artificial boundary spring technique and artificial coupling spring technique are adopted to simulate the arbitrary boundary conditions and to ensure appropriate continuity conditions along the radial edges, respectively. Because the displacement field is sufficiently smooth in the whole solution domain, the accurate solution can be obtained by using the Ritz procedure on the basis of the energy functions. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions.

• 出版日期2016-8
• 单位哈尔滨工程大学