Numerical study on the second-order hydrodynamic force and response of an elastic body - In bichromatic waves

The second-order hydrodynamic force and response of an elastic body in bichromatic waves are studied by using higher-order boundary element method (HOBEM). To solve the boundary value problem, the free-surface wave Green function is adopted in the boundary integral equation and the discretization is conducted by quadratic shape function. In the boundary condition, the normal vector variation on the body surface is re-defined to consider both rigid and elastic body motions. It is invoked especially for the derivation of second-order body boundary condition and several generalized forces in zero forward speed condition. In the second-order quantities, the second-order velocity potential force is obtained by using indirect formulation in the generalized mode and the contribution of each component is investigated. The validation for the second-order forces is first conducted by comparing with published data. The excitation force on the rigid body motion of a hemisphere is calculated and showed a good agreement with other semi-analytic and numerical results. Using simplified structural model, several vertical bending modes of an elastic hemisphere are considered as a numerical test. Second-order hydrodynamic force and response for the two-node vertical bending are obtained and properties of second-order quantities are confirmed.