Study on Havelock form translating-pulsating source Green's function distributing on horizontal line segments and its applications

摘要

Calculation of free surface Green's function is the fundamental element in numerically solving and analyzing hydrodynamic performance of ships or floating structures. Three dimensional translating and pulsating (3DTP) frequency domain Green's function in Havelock form is of explicit physical meaning, while it is difficult to be evaluated for its integrand has infinity multipliers k and high-frequency oscillatory behavior. To extend it to ship hydrodynamic problems, integration of 3DTP along line segment is outlined and analytically performed in advance. A theta-type integral of Havelock form Green's function distributing on a horizontal line segment is obtained. The integrals of both 3DTP source Green's function distributing on a horizontal line segment and partial derivatives are derived, as a result, both the order of infinity multiplier and the amplitude of oscillation function decrease, and the term with infinity number vanishes as well. It avoids the difficulties and also provides a new robust approach to obtain integral of Green's function over a panel accurately and stably.