This paper concerns the fully nonlinear fluid–structure interaction (FSI) of Large-scale floating photovoltaics (LFPV) in waves. The Euler Bernoulli–von Kármán beam models the structure while potential flow represents the fluid. A set of coupled dynamical equations is established. The fully analytic solution is sought with the unified Stokes perturbation method. The characteristic equation is derived up to third order, which has not been reported in literature before. The expressions obtained from the solution are applied to two typical cases of a pontoon LFPV and a membrane LFPV, with physical parameters from literature. The comparison with literature demonstrates our methodology for the membrane-type in waters of arbitrary depth and pontoon-type in relatively deep waters.

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Efficient and affordable solar energy is essential for reducing greenhouse gas emissions and achieving climate neutrality. Large-scale offshore floating photovoltaics (LOFPV) provide creative opportunities for clean and cost-effective renewable energy production close to populated areas. They are composed of solar modules, a membrane platform, ring, moors, anchors, cables, inverters and transformers as a general configuration. The floater ring on the edge and the highly hydroelastic membrane provide a protective environment for solar modules. Besides, the cooling effect of the ocean greatly increases energy production. The result is a highly competitive levelized cost of energy. These advantages make LOFPV ideal for addressing the rapidly increasing demand for renewable energy worldwide and releasing the vast land requirement. In industrial practice, LOFPV is in the prototyping phase at present. The size of installed prototypes is in the magnitude of 100 meters. A further scale-up of size is necessary to bring LOFPV into the massive application. The enlargement increases the nonlinearity in the fluid-structure interaction (FSI) of LOFPV in waves, which is critical but seldom studied. In addition, LOFPV-wave interaction is also a typical FSI problem that can be summarized as a floating sheet in waves. There are two floating sheet applications: ice floe and very large floating structures. Within the topic of floating sheets, the fully nonlinear analysis is rare. Therefore, this dissertation has a twofold objective - to identify and analyze nonlinear properties of LOFPV in waves in particular and to propose analytical approaches for nonlinear FSI problems of floating sheets in general. Analytic solutions are preferable because they offer physical insights qualitatively and fast estimation quantitatively. As a first approximation without waves, the membrane platform of LOFPV is modeled as a clamped circular plate subjected to a non-zero mean oscillating load. Our interest is its nonlinear vibration subjected to a non-zero mean load. A set of coupled Helmholtz-Duffing equations is obtained by decomposing the static and dynamic deflections and employing the Galerkin procedure. The static deflection is parameterized in the linear and quadratic coefficients of the dynamic equations. The effects of the static load on the dynamics, i.e., stiffening, asymmetry, and softening, are identified by means of the numerical solution of the coupled multi-mode system. An analytical solution of the single-mode vibration near primary resonance was derived. The analytical solution provides a theoretical explanation and quick quantification of the influence of the static load on the dynamics. The numerical and analytical results compare well, especially for lower values of the static deflection, confirming the effectiveness of the analytical approach. The semi-nonlinear FSI of LOFPV in free surface waves is presented as an extension of existing FSI literature. The floating structure is modeled as a nonlinear Euler Bernoulli-von Karman (EBVK) beam coupling with water beneath, represented by linear potential theory. By introducing the wave steepness squared as the perturbation, the multi-time-scale perturbation method leads to hierarchic partial differential equations. The analytical solution of the proposed nonlinear FSI model is obtained up to second order. Pontoon structures and LOFPV are studied and compared. The asymptotic solution to the semi-nonlinear FSI model demonstrates that progressive FSI waves remain linear at the primary order and are corrected by the nonlinearity at the second order. Other than in previous literature, it is also theoretically proven also theoretically proves that no resonance occurs in the considered wave propagation problem in such an infinite domain. The fully nonlinear FSI wave on LOFPV is a further extension of our approach. In this fully nonlinear model, the Euler Bernoulli-von Karman beam models the structure while potential flow represents the fluid. A set of coupled dynamical equations is established. A fully analytic solution is sought with the unified Stokes perturbation method. The characteristic equation is derived up to third order, which introduces amplitude-dispersion in the coupled model. It is the first time, to our knowledge, that a third-order nonlinear solution to the floating sheet problem is reported in the literature. The expressions obtained from the solution are applied to two typical cases of a pontoon LOFPV and a membrane LOFPV, with physical parameters from recently published articles. The comparison with literature demonstrates our methodology for the membrane-type LOFPV, which are more flexible, in waters of arbitrary depth and pontoon-type, which is relatively stiffer, in relatively deep waters. This dissertation investigates several nonlinear properties of LOFPV-wave interaction theoretically. The major conclusion is that the nonlinear FSI can be identified and analyzed with our proposed analytical methods. Nevertheless, there are always open topics that deserve academia and industry's attention. The most significant recommendation is to extend our analytical method to three-dimensional from two-dimensional. Industrially, we propose a study on the breaking wave impact onto a reinforced membrane and the structural hydroelastic response for the massive deployment of LOFPV. Methodologically, it is recommended to combine finite-length structure modes and free surface wave propagation, i.e., to couple a local problem with a global problem in the considered domain, for solving wave transmission and scattering problems. @en

The present research analyzes the nonlinear fluid–structure interaction (FSI) of free surface waves with large-scale polymer offshore floating photovoltaics (LPOFPV). The floating structure is modeled as a nonlinear Euler Bernoulli–von Kármán (EBVK) beam coupling with water beneath. The EBVK theory takes the in-plane force into consideration to account for the moderately large deflection slopes in LPOFPV. A multi-time-scale perturbation method leads to hierarchic partial differential equations by introducing the wave steepness squared as the perturbation. The analytical solution of the proposed nonlinear FSI model is obtained up to the second order. Pontoon structures and LPOFPV are studied and compared. The asymptotic solution provides the expressions of the propagating wave through the coupled system and its frequency–amplitude dispersion relation in a closed-form. A property of the solution is that the progressive plane wave through the coupled system remains linear for small dimensionless amplitudes, and features a second order correction for moderately large dimensionless amplitudes. Furthermore, it is also theoretically proven that no resonance occurs in the considered infinite problem. The proposed approach can be extended to the nonlinear coupling between a EBVK beam and Stokes waves.@en

Maritime structures in water always experience a mean hydrostatic pressure. This paper investigates the nonlinear vibration of a clamped circular thin plate subjected to a non-zero mean load. A set of coupled Helmholtz–Duffing equations is obtained by decomposing the static and dynamic deflections and employing a Galerkin procedure. The static deflection is parameterized in the linear and quadratic coefficients of the dynamic equations. The effects of the static load on the dynamics, i.e. stiffening, asymmetry and softening, are investigated by means of the numerical solution of the coupled multi-mode system. An analytical solution of the single-mode vibration near primary resonance is derived. The analytical solution provides a theoretical explanation and quick quantification of the influence of the static load on the dynamics. The numerical and analytical results compare well, especially for lower values of the static deflection, confirming the effectiveness of the analytical approach. The proposed analysis method for plate vibration can be applied to other structures such as beams, membranes and combination forms.

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