A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method. (22nd November 2019)

• Record Type: Journal Article
• Authors: Du, Yuan; Sun, Liping; Miao, Xuhong; Pang, Fuzhen; Li, Haichao; Wang, Siyu
• Other Names: Zappino Enrico Academic Editor.
• Is Part Of: Shock and vibration. Volume 2019(2019)
• Publication Date: 2019-11-22
• Subjects: Shock (Mechanics) -- Periodicals; Vibration -- Periodicals; 534.5
• DOI: 10.1155/2019/7470460
• Languages: English
• ISSNs: 1070-9622

Abstract

Abstract : The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported.