An Analytical Study Of The Vibration And Acoustic Radiation Of Submerged Ring-stiffened Conical Shell

The stern of a submarine structure can be modeled by a ring-stiffened conical shell. It has significant scientific and engineering significance on researching the vibration and acoustic of conical shell and controlling the noise of submarine. The paper presents an analytical approach for the free and forced vibration of submerged ring-stiffened conical shell with elastic boundary conditions at low frequencies and analyzes its vibro-acoustic characteristics.Firstly, the ring-stiffened conical shell is divided into multiple substructures according to the junctions of shell-stiffener. The Flügge theory is used to describe the motion of conical segments and the displacement functions are expressed as a power series. The fluid loading is taken into account by dividing the divided conical segments into more narrow strips and they are considered to be local cylindrical shells. The ring stiffeners are treated as discrete members and the equations motion of annular plate are adopted to describe the motion of stiffeners. Then, boundary conditions and continuity conditions of adjacent substructures are used to assemble the final governing equation. The far-field pressure of a conical shell is solved by using the Element Radiation Superposition Method(ERSM). Comparisons of the results of the present method and the results in literature or calculated by finite element method(FEM) show the validity and accuracy of the present method.Secondly, the present method is used to research the free vibration of submerged ring-stiffened conical shell. The effects of fluid loading, semi- vertex angle, boundary conditions, length, thickness and stiffeners are studied as conical shell is under classical boundary conditions. Then the fundamental frequency and the beam frequency of conical shell are well considered with four kinds of elastic boundary conditionsFinally, on the basis of research on the free vibration characteristics, the vibration response and sound radiation of conical shell are analyzed. The effects of vertical excitation, longitudinal excitation, symmetric/asymmetric excitation, and dipole source excitation, as well as the fluid loading and structure parameters, are discussed. Comparisons between cylinder shell and conical shell are presented.Overall, the present method of dealing ring stiffeners has higher accuracy. It can be used to deal with arbitrary distributed stiffeners. Most literatures focus on researching vibration of shells with classical boundaries, but present paper has analyzed vibration of conical shell with elastic boundary conditions. Comparisons between conical shell and cylinder shell, as well as dipole source and force excitation, are well discussed. The conclusions can be used to provide theoretical guidance on structural acoustics design of the stern of a submarine.