Frequency-Domain Identification of Radiation Forces for Floating Wind Turbines by Moment-Matching

The dynamics of a floating structure can be expressed in terms of Cummins’ equation, which is an integro-differential equation of the convolution class. In particular, this convolution operator accounts for radiation forces acting on the structure. Considering that the mere existence of this operator is highly inconvenient due to its excessive computational cost, it is commonly replaced by an approximating parametric model. Recently, the Finite Order Approximation by Moment-Matching (FOAMM) toolbox has been developed within the wave energy literature, allowing for an efficient parameterisation of this radiation force convolution term, in terms of a state-space representation. Unlike other parameterisation strategies, FOAMM is based on an interpolation approach, where the user can select a set of interpolation frequencies where the steady-state response of the obtained parametric representation exactly matches the behaviour of the target system. This paper illustrates the application of FOAMM to a UMaine semi-submersible-like floating structure.

Kernel Function Definition Completion for Time–Domain State–Space Representations of Radiation Forces: Application to the Hankel Singular Value Decomposition

This paper focuses on the formulation of state–space representations of radiation forces for marine structures using Hankel Singular Value Decomposition (HSVD), a method used to obtain a state–space realization from a Hankel matrix, with the classical definition of the kernel function and its new definition given in this paper. The first part shows the influence of a term commonly neglected and the resulting improvement by taking this term into account. The second part will focus on the feedthrough matrix to understand why some models have none and why some others, such as HSVD, have one. An exact definition of the kernel function will be given underlying its discontinuity and its causality. This study also shows the interest of extrapolating hydrodynamic coefficients before approaching radiation forces by a state–space model.

Simultaneous Trapping of Two Types of Particles with Focused Elegant Third-Order Hermite–Gaussian Beams

The focusing properties of elegant third-order Hermite–Gaussian beams (TH3GBs) and the radiation forces exerted on dielectric spherical particles produced by such beams in the Rayleigh scattering regime have been theoretically studied. Numerical results indicate that the elegant TH3GBs can be used to simultaneously trap and manipulate nanosized dielectric spheres with refractive indexes lower than the surrounding medium at the focus and those with refractive indexes larger than the surrounding medium in the focal vicinity. Furthermore, by changing the radius of the beam waist, the transverse trapping range and stiffness at the focal plane can be changed.