Blending Functions for Vibration Analysis of a Cylindrical Shell with an Oblique End

The free vibration problem of a cylindrical shell with an oblique end is considered. A theoretical solution based on the Sanders–Budiansky linear shell theory, and the differential quadrature method, is presented. The surface of the shell is first developed onto a plane, and the resulting irregular domain is then mapped, using blending functions, onto a square parent domain. The analysis is finally carried out in the parent domain. Two solutions are derived, using either trigonometric or polynomial trial functions in the circumferential direction of the domain. Convergence, validation and parametric studies are carried out. Results from the two solutions are compared with each other and with finite element results. The paper ends with an appropriate set of conclusions.