A Semi-analytical Study On The Structural Response And Acoustic Radiation Of Combined Conical-Cylindrical Shell

Cylindrical shell and truncated conical shell are modeled to simulate the middle part and the stern of a submarine structure in the research of its structural vibration and sound radiation. This paper focuses on the cylindrical shell, conical shell and cylindrical-conical combined shell and analyzes their vibration and radiation in vacuo and in fluid, respectively.Firstly, the low frequency dynamic response of a submerged cylindrical shell is presented. General analytical harmonic solutions for the cylindrical shell displacements are given in the form of wave propagation. The structural wavenumber is solved by numerical "searching method", as one key work for this part. Axi-symmetric and asymmetric excitations are considered to simulate excitations from the propulsion system. They are axi-symmetric axial excitation at the end, asymmetric radial excitation and axial excitation at the end, as well as radial excitation at the middle of the shell. The contribution from the individual circumferential modes, in particular, the breathing and bending modes, on the hull structural responses are studied. The effects of end plates, external fluid loading on the cylindrical shell and stiffeners and bulkheads are discussed for different cases. Stiffeners on the cylindrical shell are modeled by smeared approach.Secondly, the free vibration of a conical shell is solved. The solution for the conical shell displacements are presented in the form of a power series. The conical shell is divided into narrow strips to reflect the variation of the vibration as the radius changes along the length of the cone. Regarding to submerged conical shell, fluid loading is taken into account by considering the conical narrow strips as locally cylindrical shell, whose fluid loading can be solved by the approach mentioned in the previous part. The effects of parameters of the conical shell, such as boundary conditions, semi-vertex angle, thickness, length, stiffeners, as well as fluid loading, on structural responses and radiated pressure the conical shell are analyzed for different cases. Stiffeners on the conical shell are also solved by smeared approach. Thirdly, after the discussion of the solution for the free vibration of conical shell, the solution of structural responses and acoustic radiation of a conical shell are presented. Three cases of excitations at different points in various directions are considered, which are the excitations on the smaller end along its generator and normal to its surface, as well as the excitation on the middle point of the shell normal to its surface. The Element Radiation Superposition Method (ERSM) is introduced to solve the far-field pressure of a conical shell. The total acoustic pressure of conical shell is assumed to be the superposition of the radiated pressure of all divided elements, which is approximated using the analytical solution of the radiated pressure from a piston with a cylindrical baffle. The effects of the influence factors, such as excitations, stiffeners and fluid loading on the structural responses and acoustic radiation are discussed.Fourthly, based on the solutions of cylindrical and conical shell, the structural responses and acoustic radiation of the cylindrical-conical combined shell is solved by building the discontinuity conditions between cylinder and cone, using triangle transform between cylindrical coordinate system and conical system. Four excitations in different directions are considered, which are set at the end of the conical shell, the coupled point of the hull and the middle of the cylindrical shell, respectively. The ERSM is also used to solve the far-field radiated pressure of the combined shell. The contribution of the circumferential modes and the effects of external fluid loading, stiffeners and bulkheads are discussed for different cases to analyze the characteristic of the structural responses and acoustic radiation of the combined shell.Lastly, conical-cylindrical-conical shell is considered as the simplified submarine model to solve its structural responses and far-field pressure. Axi-symmetric and asymmetric excitations are included. The effects of conical ends, fluid loading and stiffeners are discussed, which is compared with those for the model of cylindrical shell with endplates in Chapter2.The semi-analytical methods mentioned in this paper are validated by the numerical results gained from the software using FEM/BEM method. The conclusions of the paper can provide a useful reference to comprehend the vibration characteristic of typical underwater stern structure in the future.