Frequencies and mode shapes for thick truncated hollow cones

✍ Scribed by G.R. Buchanan; F.T.-I. Wong

• Book ID: 104140154
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 443 KB
• Volume: 43
• Category: Article
• ISSN: 0020-7403
• DOI: 10.1016/s0020-7403(01)00068-6

✦ Synopsis

The ÿnite element method of analysis is employed to study the vibration of truncated thick hollow cones. The three-dimensional strain-displacement equations are used to formulate the ÿnite element in the conical coordinate system. Axial symmetry is assumed and the formulation is reduced to two dimensions while maintaining the three-dimensional character of the analysis. The accuracy of the analysis is established by comparing results for free-free boundary conditions with existing solutions. The e ects of di erent boundary conditions, including ÿxed-free and ÿxed-ÿxed, are studied to determine their e ects on the frequency of vibration. Frequency results are given for an additional boundary condition corresponding to a layer attached to the exterior of a rigid cone. Nondimensional results for an isotropic material with Poisson's ratio of 0.3 are presented in terms of tables, plots of frequency versus cone apex angle and plots of selected mode shapes.