An analytical method for the solution of earthquake-induced hydrodynamic forces and wave forces on multiple vertical cylinders with arbitrary smooth sections

Analytical methods are developed to investigate the interaction of water with multiple cylinders with arbitrary smooth cross-sections subjected to horizontal ground motion and incident linear waves. Based on the boundary conditions of the seafloor and the water surface, the three-dimensional Laplace equation was transformed into the two-dimensional (2D) Helmholtz equation. Based on the condition that the coefficient function of the cylinder surface can be expanded into a Fourier series, radiation theory and diffraction theory are extended to solve earthquake-induced hydrodynamic forces and wave forces on multiple cylinders. The proposed analytical solution consists of the high-order scattered wave pressures due to diffracted waves. The present method was verified using two double cylinder arrays with elliptical and round-ended cross-sections. Finally, this method was extended to multiple scattering analysis for the interaction of water under earthquake and wave loads.