A numerical study of second-order springing of an elastic body using higher-order boundary element method (HOBEM)

Abstract

Second-order springing on an elastic body with forward speed is analyzed by numerical simulations. The boundary-value problem for the velocity potential is solved by means of the direct time-domain higher-order boundary element method (HOBEM). The free-surface boundary condition in the boundary-value problem is approximated on the mean surface up to second order by use of perturbation and Taylor-series expansion methods. The body boundary condition for an elastic body is derived with various quantities which are redefined in the generalized mode. These variables such as mode shape, normal vector, etc. are obtained by using directional derivative and continuum mechanics, and the same mathematical expressions are used to obtain several second-order generalized forces. To validate the numerical results, the second-order hydrodynamic force on the bottom-mounted rigid/elastic cylinders without forward speed is compared with other semi-analytic results. The property of second-order forces on an elastic ship is studied by changing the flexural rigidity and forward speed with elastic response. It is confirmed that the second-order velocity potential is important for a body with forward speed and investigation should be made more on numerical methods for accurate computation of the second-order velocity-potential force with forward speed.