Second-order sum-frequency hydroelastic analysis of a flexible structure in bichromatic waves

Due to the complexity of the second-order boundary value problem (BVP) considered in the generalized mode, the second-order hydroelasticity analysis is still challenging. Based on the beam-connected-discrete-modules (BCDM) method, this study proposes a second-order hydroelastic method for floating structures in the frequency domain. In this method, the second-order BVP for flexible structures is replaced by multi-rigid-body hydrodynamics which has been extensively studied. The first-order hydroelastic responses of a hemisphere and the second-order sum-frequency forces using the proposed method are verified against the results obtained by general commercial software and published data. Then, the effect of flexural rigidity on the second-order hydrodynamic forces and responses is investigated. The results show that the second-order forces are dominated by the first-order springing, especially for the quadratic product force component. Additionally, due to the discrete property of the BCDM method for hydrodynamics, the present method can be directly extended to inhomogeneous wave conditions.