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65 effective nodes A.K. Chopra Added-Mass Coefficient amplitude Analysis approximate Green function Bessel function body surface boundary condition Circular Cylinder h/a Coefficient for Hemisphere Coefficient for Horizontal Computed by Exact Computer Program cosh Cyclic Loading damping coefficients defined denotes discrete sources Dumbarton Bridge Dynamic E.L. Wilson E.P. Popov Earthquake Response EERC evaluation exact Green function facet Facet Geometry field point finite depth free surface frequency G.H. Powell given Green's Theorem H.B. Seed H.D. McNiven Hemisphere h/a Horizontal Force Coefficient hydrodynamic Hysteretic I.M. Idriss incident wave induced potential integral equation Interaction J.G. Bouwkamp linear Lysmer matrix motion Neumann boundary condition nondimensional numerical procedure NUMERICAL RESULTS 105 oscillation Penzien potential flow R.L. Mayes R.W. Clough radiation condition Reinforced Concrete RESULTS 105 effective Seismic Response Soil Liquefaction solution source point source strength Structures successive approximations triangular element triangular source element V.V. Bertero velocity potential Vertical Circular Cylinder Vertical Force Coefficient water depth