# Free and forced vibration of ring-stiffened conical–cylindrical shells with arbitrary boundary conditions

Free and forced vibration of ring-stiffened conical–cylindrical shells with arbitrary boundary... An analytic method is presented to analyze free and forced vibration characteristics of ring-stiffened combined conical–cylindrical shells with arbitrary boundary conditions, e.g. classical and elastic ones. The combined shell is firstly divided into multiple substructures according to the junctions of shell–shell and shell–plate, and/or the location of driving point. Then, Flügge theory is adopted to describe the motions of the cylindrical and conical segments. Instead of adopting the smeared out method and treating the ring stiffeners as beams, the stiffeners with rectangular cross-section are treated as discrete members and the equations of motion of annular plate are used to describe the motion of stiffeners. Power series, wave functions and Bessel functions are used to express the displacement functions of conical segment, cylindrical segment and annular plate, respectively. Lastly, boundary conditions and continuity conditions between adjacent substructures are used to assemble the final governing equation. Results of present method show good agreement with the results in literature and the results calculated by finite element method (FEM). In addition, the influences of boundary conditions and ring stiffeners on the free vibration are studied. The effects of direction of external force and bulkheads on the forced vibration are also discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ocean Engineering Elsevier

# Free and forced vibration of ring-stiffened conical–cylindrical shells with arbitrary boundary conditions

Ocean Engineering, Volume 108 – Nov 1, 2015
16 pages

/lp/elsevier/free-and-forced-vibration-of-ring-stiffened-conical-cylindrical-shells-EFAXGG9tLl
Publisher
Elsevier
ISSN
0029-8018
eISSN
1873-5258
D.O.I.
10.1016/j.oceaneng.2015.07.065
Publisher site
See Article on Publisher Site

### Abstract

An analytic method is presented to analyze free and forced vibration characteristics of ring-stiffened combined conical–cylindrical shells with arbitrary boundary conditions, e.g. classical and elastic ones. The combined shell is firstly divided into multiple substructures according to the junctions of shell–shell and shell–plate, and/or the location of driving point. Then, Flügge theory is adopted to describe the motions of the cylindrical and conical segments. Instead of adopting the smeared out method and treating the ring stiffeners as beams, the stiffeners with rectangular cross-section are treated as discrete members and the equations of motion of annular plate are used to describe the motion of stiffeners. Power series, wave functions and Bessel functions are used to express the displacement functions of conical segment, cylindrical segment and annular plate, respectively. Lastly, boundary conditions and continuity conditions between adjacent substructures are used to assemble the final governing equation. Results of present method show good agreement with the results in literature and the results calculated by finite element method (FEM). In addition, the influences of boundary conditions and ring stiffeners on the free vibration are studied. The effects of direction of external force and bulkheads on the forced vibration are also discussed.

### Journal

Ocean EngineeringElsevier

Published: Nov 1, 2015

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