Hydroelastic and elastoacoustic analysis of partially and fully submerged shells in infinitely deep water

When designing a ship or offshore structure, factors such as initial cost, security, safety and performance must be considered by naval engineers. To determine the characteristics of a ship via model experiments can't preferred in all circumstances not only because of the high cost but also because of the unfavorable consequences caused by misinterpretation of experiment results. For these reasons, semi-empirical formulas and computational methods are frequently used in problems related to shipbuilding and offshore engineering . As a structural component, plates and shells are commonly used in many engineering fields such as aviation, marine engineering, nuclear power plants, production of space vehicles and petrochemical industry. In shipbuilding and offshore industry, plates and shells are commonly used as a side plating of the hull, tank bulkheads and for splitting compartments of the superstructure. Offshore petrol platforms, low speed conventional ships and mono or multi hull high speed crafts operates under the environmental dynamic loads such as wind and waves. In particular, the impact of wave loads on the structural integrity and dynamic characteristics of ships and marine structures might be very strong. In order to be able to accurately determine the effects of wave loads on marine structures, computational methods are often used in which principles of hydrodynamics and structural mechanics are approached together. Hydroelasticity is an engineering discipline which examines the behaviour of the elastic structures in fluid medium. When the theory of hydroelasticity is approached in terms of ships and offshore structures, it is possible to determine the resulting stress distributions, rotations and deformations as a result of motions of the fluid. To determine the dynamic behaviour of structures in contact with fluid is of high importance in vibration analysis of marine structures. For freely vibrating structure, the influence of the interaction forces on the dynamic characteristics of the structure is weak when the surrounding fluid is low in denstiy, such as air. However, in the case when the surrounding fluid is relatively high in density, such as water, the effect of the fluid on the dynamic characteristics of the structure, such as mode shapes and natural frequencies, is important with regard to in-vacuo conditions. Under these conditions, motions of the structure and fluid are strongly coupled, thus, structural and fluid equations of motions must be solved simultaneously. In this thesis, it is assumed that fluid actions and related pressure distribution over the structure only occur due to modal vibrations of the structure; in other words, it is assumed that both elastic structure and surrounding fluid has no forward speed. The linear hydroelasticity theory is adopted in order to determine the wet dynamic characteristics of the structure under the fluid-structure interaction forces. In the linear hydroelasticity theory, it is assumed that fluid is non-viscous and incompressible; the rotational motions of the fluid is neglected. It is also assumed that fluid forces directly corresponds to inertial effects of the structure, thus, displacements of the elastic structure due to modal vibrations are in same phase with the acceleration of the fluid particles. Analysis of the fluid-structure interaction system by the linear hydroelasticity theory can be divided into two parts. In first part of the analysis, in-vacuo analysis in brief, dynamic analysis of the structure in vacuo conditions and in the absence of external forces is carried out by solving equation of motion with neglecting the structural damping effects. In second part of the analysis, wet analysis in brief, it is assumed that structure conserves its in-vacuo mode shapes, the in-vacuo displacements of the structure constitutes of the boundary condition of the potential flow problem. In wet part analysis, similar with in-vacuo analysis, the damping effects in the equation of motion are not included in the mathematical by assuming that the resulting velocity field across the surrounding fluid medium is negligible. The wet part of linear hydroelasticity theory involves the determination of the fluid forces acting on the structure by calculating the fluid pressure field generated by the modal vibrations of the elastic structure. In this study, fluid-structure interaction forces were obtained by means of boundary element based potential flow analysis along the fluid-structure interaction surface, which was performed by distributing constant strength point sources placed on to geometric centre of each boundary element. By means of this theory it is possible to determine the dynamic characteristics of marine vessels or offshore structures moving around the free surface, as well as structures within the infinite fluid environment partially submerged into and/or partially filled with liquid. In this study, the dynamic characteristics of structure partially in contact with fluid where the free surface effects are introduced into the problem, as well as the structures totally immersed into the unbounded fluid medium in which the free surface effects is not been taken into account, are investigated. In the dynamic fluid-structure interaction problem, it is assumed that the structure vibrates at relatively high frequencies, thus, it is possible to neglect the effect of the free surface waves occurred due to the dynamic motions of the fluid-filled and/or submerged structure in the suggested mathematical model. The linearized free surface condition is introduced into the mathematical model by the image method. For this purpose, submerged part of the structure is mirrored outwards as the free surface becomes mirror line. Application of image method involves mirroring the boundary conditions constituted by modal displacements through the wetted surface, also named by kinematic boundary conditions, with opposite sign as free surface becomes mirror line. By this way, the linearized free surface condition is reduced to classical Neumann problem. In the absence of axial flow, generalized hydrodynamic damping coefficients considered to be zero. Therefore, interaction between the structure and fluid takes place only through the added mass matrix which is made up of added mass coefficients that represents the increment of the kinetic energy of the fluid. The added mass matrix is formed by boundary element based potential flow analysis that each coefficient of the matrix is calculated by integrating velocity potentials obtained by using the fundamental solution of the Laplace problem along the entire surface of the structure in contact with the fluid. After forming the added mass matrix, it is possible to obtain each wet natural frequencies and corresponding mode shapes by solving the eigenvalue problem representing the motion of the structure in the fluid environment. The validity of the mathematical model where the structure is in the infinite fluid environment is investigated for the spherical and cylindrical shells by the analytical solutions. In the case where the structure is in the infinite fluid environment and the free surface effects are neglected, it is observed that the interaction between the natural modes is weak because of the non-diagonal added mass terms being very close to zero. From here, the result is that there is no energy transfer between the natural modes when the structure is infinitely immersed in the fluid and the free surface effects are absent, and therefore mode shapes of the structure under the wet state and vacuum conditions are in same geometric configuration. In the case where the cylindrical shell partially in contact with the fluid in the horizontal position, the results obtained by including free surface effects are compared very well with those obtained by the experimental and numerical studies in the literature. Due to presence of the free surface it has been observed that some of the non-diagonal terms of the added mass matrix are considerably larger than the others so that the interaction between some natural modes of the structure is strong due to presence of the free surface. It is also observed that due to strong interaction between some particular modes, there is a significant difference between the wet and in vacuo mode shapes.