Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Application of Modal Expansion Method to Very Flexible Floating Structures (VFFSs)
Min Zhang, Sebastian Schreier
Delft University of Technology, Delft, Zuid-Holland, The Netherlands.

Solar@Sea I & II (2020).
Structures with square kilometers in horizontal size and a few meters invertical dimension have been widely studied in Very Large Floating
Structures (VLFSs) which were mainly designed to serve as floatingairport, floating bridge, floating storage base, floating power plants,
floating islands, and even floating cities (Watanabe et al., 2004; Wangand Tay, 2011; Lamas-Pardo, Iglesias and Carral, 2015). For suchhorizontally large and vertically thin structures, the elastic motion will
be dominant rather than the rigid body one. Hydroelastic analysis is ofkey importance when interacting with waves.
Hydroelastic problem can be generally addressed by boundary element
method (BEM) (e.g. Wu et al., 1996; Kashiwagi, 1997; Hermans, 2000;
Andrianov, 2005; Montiel, 2012), finite element method (FEM) (e.g.
Meylan and Squire, 1994; Ohkusu and Nanba, 1996; Karperaki et al.,2015) and hybrid BEM-FEM method (e.g. Utsunomiya et al., 1995;
Wang and Meylan, 2004; Shirkol and Nasar, 2018). Among them, BEM
has the advantage of computational efficiency due to the reduction ofspatial dimensions of the problem by one, leading to a smaller system ofequations in the computation procedure. Modal expansion method (Wuet al., 1995; Wu et al., 1996) as a typical BEM solution has beencommonly used in the hydroelastic study of VLFSs. In this method, thestructure deformation is approximated by the summation of the productof modal functions and their complex amplitudes. The wave field isexpressed by potential theory and solved by boundary integral equation
using Green’s functions. The coupling is achieved by evaluating thehydrodynamic forces on the wet structure surface for unit amplitude
motions of each mode.
In the open literature, modal expansion method gained a degree of
popularity as it gives explicit solutions and accurate predictions for thehydroelastic analysis of VLFSs with amplitude of motions usually in theorder of the structure thickness. However, VFFSs have a characteristicof being able to follow the wave elevation and the vertical displacement
could reach a few times the structure thickness (Schreier and Jacobi,2021). There are currently no engineering tools available for such
structures interacting with waves. Therefore, the purpose of this work is
to apply the modal expansion method to a VFFS and discuss theapplicability of the solution. In this paper, the hydroelastic response ofthe VFFS under regular waves is analyzed by modal expansion method.
The motion of the structure is estimated by classic thin plate theory. The
wave field is represented by linear potential theory and solved byboundary integral method. The verification of the present scheme isABSTRACTThis paper presents an application of modal expansion method to wavestructure interaction problem of Very Flexible Floating Structures(VFFSs), like Offshore Floating Photovoltaics (OFPV) membranestructures. In literature, the modal expansion method was applied towave-structure interaction of Very Large Floating Structures (VLFSs),
where wave amplitude and structure deformation amplitude were of theorder of structure height. For VFFSs, wave and structure deformation
amplitude could be of the order of ten times the structures thickness. In
this study, we explore the applicability of the modal expansion method
to this new field. The wave field is addressed by boundary integral
equation using free surface Green’s function method and the structure
deformation is approximated by structure vibration modes. Assuming
small-amplitude wave and small structure motion, the coupling isachieved by solving the governing equilibrium equation based on theclassic thin plate theory. The verification of the present method withrespect to panel resolution and mode truncation is discussed. Structure
displacements of numerical analysis are compared with experimentalresults. The comparison shows that the solution provides acceptableprediction for longer waves (wavelength is one-fifth of the structure
length), whereas for shorter waves (wavelength is one-tenth of thestructure length), obvious discrepancies occur, especially at the aftregion of the structure.

KEY WORDS: Hydroelastic analysis; modal expansion method; Very
Flexible Floating Structure

INTRODUCTIONVery Flexible Floating Structures (VFFSs) have been foreseen as
promising support structures for the development of Offshore Floating
PV (OFPV) due to physical and economic advantages. The inherent
flexibility allows the system to easily deform with wave motions, thus
leading to low wave forces acting on the structure and the moorings.
Trapani et al. (2013) firstly reported the concept of a flexible floating
system based on a thin floating polymer layer with length of 600 m andwidth of 200 m. More recently, pre-stretched membranes of several
millimeters thin are used for mounting rigid PV panels in the project ofOcean Sun (2018). The potential of floating, non-rigid thin-film PV
modules for large-scale offshore PV installations has been tested by3063