SECOND-ORDER THEORY OF OSCILLATING CYLINDERS,

Two-dimensional cylinders of arbitrary shape undergo small-amplitude forced sinusoidal motion in sway, heave and roll in or near the free surface of an infinitely deep ideal fluid. Equations for the theoretical fluid response to second-order are derived and their solution formulated in terms of Fredholm integral equations. A numerical procedure is developed and applied to three surface-piercing cylinder sections. Graphs of added mass, damping coefficient, pressure distribution, force and asymptotic wave amplitude as functions of non-dimensional wave number k are presented for the pure motions and for combined sway and heave, sway and roll, and heave and roll. The results indicate the significance of second-order coupling forces which result in the later motion cases. Additionally, second-order response coefficients are shown to be important in the higher frequency range. Author