The diffraction of second-order bichromatic Stokes waves by a semi-immersed horizontal rectangular cylinder is investigated theoretically. The problem is assumed two-dimensional and the fluid domain is divided into three regions: fore, beneath and aft of the structure. Analytical expressions for the velocity potentials in each region at both first- and second-order are obtained by an eigenfunction expansion approach. The solutions in each fluid region are linked through matching conditions on the imaginary fluid interfaces between them. Semi-analytical expressions are derived for the sum- and difference-frequency hydrodynamic loads to second-order. Numerical results are presented which illustrate the influence of the different wave and structural parameters on these quantities at both first- and second-order.
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