Higher-order derivatives of the Green function in hyper-singular integral equations

Abstract Hyper-singular integral equations are often applied in the frequency-domain wave diffraction/radiation analyses of marine structures with thin plates or shell sub-structures. Their numerical solutions require higher-order derivatives free-surface Green function featuring hyper-singularity, and hence corresponding evaluation is very challenging. To circumvent associated difficulties, this paper will propose alternative formulations for both Rankine-source parts function. For term G F , analytically expressed by a combination itself its first-order horizontal radial derivative. Further, we derive an asymptotic representation, enabling us to deal exactly removable singularity representation. The superiority proposed formulation demonstrated comparing conventional direct differentiation. term, analytical expressions velocities induced uniform dipole distribution over flat panel (involving second Rankine source term) presented, which directly relevant implementation based on constant methods. As illustrative examples, linear hydrodynamic coefficients submerged circular impermeable perforated calculated verification purposes. formulas simple easy implement hyper-singular equations.