Numerical Analysis On The Interaction Between Waves And Hingly Connected Multiple Floating Bodies

A high-order boundary element method is applied for the numerical simulation of interactions between water waves and connected floating3-D bodies in frequency domain by linear potential theory.Many complex marine engineering structures, for example very large floating structure (VLFS), sea pontoon, pelamis wave power device and so on, can be seen as multiple floating-body system consists of N hingly connected rigid floating bodies in the flow field. Assuming that the connection is smooth, and the relative rotation between the floating bodies is permitted. The interaction between waves and multiple floating-body system is a complicated fluid-solid coupling problem. Not only the coupling effect between waves and floating bodies, but all the hydrodynamic effect among the floating bodies need to be calculated. If there are connections among the floating bodies, the effects of the connections must be considered. For a multiple floating-body system, if the number of the bodies is N, the total number of motion modes is6N in the’total modal method’, because the number of motion modes of one body is six. According to the linear potential flow theory, the velocity potential in the flow field can be decomposed into incident velocity potential, diffraction potential and6N radiation potential. For the hydrodynamic between the floating bodies, the radiation and diffraction velocity potentials can be obtained by solving the velocity potential integral equations which satisfied on the body surface, then the added mass, radiation damping and wave exciting force of each floating bodies can be got by the integral of velocity potentials on body surface. For multiple floating bodies which placed on local topography, the local topography will have a significant effect on the wave field and thus affect the hydrodynamic characteristics of multiple floating bodies. For such problems, the local topography will be treated as a fixed structure, and establishde a unified velocity potential integral equation with multiple floating bodies, solving the equation then wave exciting force and hydrodynamic coefficients can be got.For each floating body, six motion response equations can be established. As external force, the connect force and moment are also unknown, so the number of the response equations is not enough. According to the displacement continuous condition on the connection point, additional equations can be added. Then the motion response amplitude of each mode and the connect force and moment can be got by solving these global equilibrium equations. If there are more connections and more floating bodies in the multiple floating-body system, the global equilibrium equations are established by the adoption of constrained matrix for the convenience, which is derived by the principle of minimum potential energy and the method of Lagrange multipliers.In order to verify the established numerical models, the motion responses of free floating bodies, rigid-and hinged-connection floating-body system are calculated respectively. And all have good agreements with published results, which verified the validity and effectiveness of the present method. At the end, the influences of wave incident direction, water depth, hinged position, local topography, and mooring on motion responses are discussed, respectively. The motion responses of hingly connected multiple floating bodies under the irregular waves are also calculated.