Application of the 3D time-domain Green's function for finite water depth in hydroelastic mechanics. (1st October 2019)

• Record Type: Journal Article
• Authors: Yang, Peng; Li, Jingru; Gu, Xuekang; Wu, Dongwei
• Is Part Of: Ocean engineering. Volume 189(2019)
• Publication Date: 2019-10-01
• Subjects: Time-domain -- Green's function -- Finite water depth -- Hydro-elastic -- Fluid-structure interaction; Ocean engineering -- Periodicals; Ocean engineering; Periodicals; 620.4162
• DOI: 10.1016/j.oceaneng.2019.106386
• Languages: English
• ISSNs: 0029-8018

Abstract

Abstract: Based on the boundary element method and the superposition principle of structural elastic modes, the three-dimensional time-domain Green's function in finite water depth is applied to hydroelasticity, and the theoretical basis of three-dimensional time-domain hydroelasticity is established. To address the difficulty and divergence of the three-dimensional time-domain Green's function in finite water depth, a numerical solution method that has high accuracy and good stability is developed using series expansion, asymptotic methods and fourth-order differential equations. Taking a large bulk carrier as an example, the corresponding predictions of resonance frequency, motion, wave load and hydroelastic response with speed in finite water depth are carried out. The numerical results are compared with the results of the three-dimensional frequency domain method and the time-domain method of inner and outer region matching and are verified by the towing model test. The three-dimensional time-domain hydroelastic theory and numerical method established in this paper are of great significance for fluid coupling analysis, structural dynamic response research and wave load prediction of complex floating bodies with speed. Highlights: The three-dimensional hydroelastic method has been more and more widely used. At the same time, more and more complex problems need to be solved by time-domain method. Based on the boundary element method and the superposition principle of structural elastic modes, the three-dimensional time-domain Green's function in finite water depth is applied to hydroelasticity, and the theoretical basis of three-dimensional time-domain hydroelasticity is established. Aiming at the difficulty and divergence of three-dimensional time-domain Green's function, a numerical solution method of three-dimensional time-domain Green's function in finite water depth with high accuracy and good stability is proposed by using series expansion, asymptotic method and fourth-order differential equation. Taking a large bulk carrier as an example, the numerical results are compared with the results of three-dimensional frequency domain method and time domain method of inner and outer region matching method, and are verified by towing model test. Some important conclusions are as follows. (1) The numerical analysis shows that the time interval of the fourth-order differential equation is 0.001, and the fourth-order Runge-Kutta method could obtain stable and high-precision numerical results. (2) F − F ∞ and its derivatives with X are more intense and oscillatory attenuation, while F − F ∞ and its derivatives with V are more gentle. The larger the horizontal scale of the floating body, the longer the time axis of Green's function needs to be calculated, and the more time elapses. But the time axis of Green's function and the calculation time-consuming have little change when the vertical scale of the floating body increases. (3) The convergence rate of the integral of Green's function, incident potential and diffraction boundary condition in finite water depth could be accelerated by adding and subtracting an appropriate asymptotical function. (4) The impulse response function approaches zero when the non-dimensional time is larger than 3.0 for the bulk carrier with forward speed 14.8 kn. The time-domain method provides the results with good agreement to experiment data. At the ratio of wave length to ship length is about 1.0, the predictions of TDGF and IORM and the experimental results for the vertical bending moment all drop down, while the prediction of the frequency domain method does not.