Nonlinear loading of a two-dimensional heaving box. (January 2016)

• Record Type: Journal Article
• Authors: Rodriguez, Marcos; Spinneken, Johannes; Swan, Chris
• Is Part Of: Journal of fluids and structures. Volume 60(2016:Jan.)
• Page Start: 80
• Page End: 96
• Publication Date: 2016-01
• Subjects: Floating structure -- Nonlinear diffraction -- Nonlinear radiation -- Potential flow -- Boundary element method -- Rectangular box; Fluid-structure interaction -- Periodicals; Fluid mechanics -- Periodicals; Structural dynamics -- Periodicals; Structural analysis (Engineering) -- Periodicals; 620.106
• DOI: 10.1016/j.jfluidstructs.2015.11.001
• Languages: English
• ISSNs: 0889-9746

Abstract

Abstract: A numerical investigation is presented addressing the nonlinear heave response of a rectangular box. The work specifically concerns the importance of the relative body dimensions, expressed through the product of the half-beam b and the wavenumber k . When subjected to moderately steep incident waves, the second-harmonic content of the heave motion is found to be as large as 25% of the first-harmonic content. In considering the extent of this second-harmonic motion, three regimes may be defined: (i) the long wave regime, where kb ≤ 0.4, (ii) the intermediate regime, where 0.4 < kb < 1.0 and (iii) the diffraction or short wave regime, where kb ≥ 1.0 . Expressed in terms of the wavelength λ = 2 π / k, these regimes correspond to (i) b ≤ 0.06 λ, (ii) 0.06 λ < b < 0.16 λ and (iii) b ≥ 0.16 λ . The second-harmonic motion content is found to be particularly pronounced in regimes (i) and (iii). Perhaps surprisingly, this second-harmonic content is also found to be practically non-existent for some intermediate cases lying within regime (ii). Three sources of nonlinearity are shown to be particularly important. First, the interaction between the first-order incident waves and the first-order scattered waves is key to the nonlinear loading in regime (iii). Second, the generation of freely propagating second-harmonic radiated waves due to the body motion is important in (i). Third, the local standing wave field associated with the radiation problem is found to contribute to the loading in regime (iii). In addition, the location of the body resonance also plays a critical role in defining the extent of the second-harmonic motion content. The focus of the present work lies on a clear physical interpretation of the sources of these nonlinear loads, coupled with an analysis of the body dynamics. Abstract : Highlights: The excitation, radiation and floating problem of a heaving box are considered. Comparisons to a fully nonlinear potential flow method are provided. Key sources of nonlinear forcing are identified and explained. Significant harmonic motion content is observed in more than one wave regime. The importance of both nonlinear forcing and dynamic response is considered.