Free and forced vibration of submerged ring-stiffened conical shells with arbitrary boundary conditions

• Vibration analysis of submerged ring-stiffened conical shells via an analytic method.
• The method is applicable to classical and elastic boundary conditions.
• Treating stiffeners as discrete members can be used to study non-uniform stiffeners.
• The present results agree well with those in literature and calculated by FEM.
• The method can be easily extended to study step-wise submerged conical shell.

An analytic approach is presented to analyze free and forced vibration of submerged ring-stiffened conical shell with arbitrary boundary conditions at low frequencies. According to the junctions of shell-stiffener, the shell is firstly divided into multiple substructures, e.g. conical segments and stiffeners. To take into account fluid loading, conical segments are divided into more narrow strips and those strips are approximately considered as local cylindrical shells. Then, Flügge theory is used to describe the motion of conical strips and displacement functions are expressed as power series. Instead of utilizing smeared out method, ring stiffeners are treated as discrete members and the equations of motion of annular plate, rather than curve beam, are adopted to describe the motion of stiffeners with rectangular cross-section. Lastly, boundary conditions and continuity conditions of adjacent substructures are used to assemble the final governing equation. Comparisons of free and forced vibration results of present method and those in literature and/or calculated by finite element method show the validity of present method. The effects of boundary conditions, ring stiffeners and fluid loading on free vibration are studied. The effects of external point force and fluid loading on forced vibration are also discussed.