Asymptotic Analysis On The Hydroelastic Response Of A Floating Thin Plate Due To A Moving Load

The concept of Very Large Floating Structures (VLFS) emerged as exploiting ofthe ocean resources had been paid much attention. In recent years, the research on theVLFS is of stirring interest among the community in ocean engineering. The purposeof this thesis is to study analytically the hydroelastic response of pontoon-type VLFSdue to a moving load. We assume that the fuid is inviscid and incompressible, andthe fow is irrotational. The VLFS is modeled a thin elastic plate with small defectionas the horizontal scale of VLFS is much larger than the vertical one. The interactionbetween moving line and point loads with pontoon-type VLFS is considered with theassumption of small-amplitude waves. In the framework of the linear potential theory,the Fourier integral transform method is used to deal with the governing equation andboundary conditions. Then some asymptotic analytical solutions are deduced with theaid of the stationary-phase method and the residue theorem. The line load of infnitelength in the three dimensions is simplifed as a point load in the two dimensions.The main works and results of the thesis are outlined as follows:1) In the model of a thin elastic plate foating on an infnitely deep fuid, we considera uniformly moving line load as the starting point. A steady-state solution ofthe wave resistance is obtained with the residue theorem. It is found that whenthe velocity of the moving load is greater than the critical velocity (namely theminimal phase speed of the fexural–gravity waves), the wave resistance frstincreases to a peak then decreases as the moving velocity increases. The steady-state solution of the plate defections are deduced by the residue theorem and themethod of artifcial viscous parameter. It is found that the defections are similarto that due to a static load when the moving speed is less than the minimal phasespeed, and there is no fexural–gravity wave propagation. When the velocity ofmoving load is greater than the minimal phase speed, the fexural and gravitywaves are generated in the leading and trailing regions, respectively. A qualitativecomparison with experimental results is presented. 2) For the two-dimensional model, a suddenly started line load is studied. Asymp-totic behaviors of transient fexural–gravity wave resistance and wave profles areanalyzed for diferent moving speeds in large time domain. To avoid the difcultyarising from the singularity of integrand, we diferentiate the integral solutionswith respect to time frstly, then calculate the integral using the stationary-phasemethod, and fnally integrate with time. Some important conclusions are drawn.There exist fexural–gravity waves even when the velocity of moving load is lessthan the minimal phase speed. The transient wave resistance and wave proflesdecay diferent increasing or decreasing rates. When the moving speed equal tothe minimal phase speed, the transient wave and wave resistance decreases as thetime increases. When the moving speed equals to the minimal phase speed, tran-sient wave resistance and wave profles increase with1/2as the time increases, asteady state could not be achieved.3) In the model of a thin elastic plate foating on a fuid of fnite depth, a uniformmoving point load is considered. It is found that when the velocity of moving loadis less than the critical velocity, there is no wave resistance. When the velocity ofthe moving load is greater than the critical velocity, the wave resistance decreasesas the velocity of moving load increases, which is diferent from the phenomenonin the two-dimensional case. A two-step method is used to deal with the doubleintegral which has a singular point in the steady wave. The frst step is to usethe residue theorem for one of the two integration variables, and then use thestationary-phase method for the other. The analytical expressions for the platedefection in various situations are presented, and the wave crest patterns areshown. There are a caustic and cusps as the moving speed of load changes.4) For the three-dimensional model, a suddenly started point load is considered.Asymptotic behaviors of the transient fexural–gravity wave resistance and waveprofles are studied in large time domain. It is also found that there exist waveresistance even when the velocity of point load is less than the minimal phasespeed. The transient wave resistance and wave profles have the decay rates with respect to the when the moving speed is less than the minimal group speed. Whenthe moving speed equal to and above the maximal group speed, transient wavedecreases with time in diferent rates between the leading and trailing regions ofthe point load. When the moving speed equals to the minimal phase speed, thetransient wave increases logarithmically as time increases, a steady state couldnot be achieved. This singular phenomenon may be due to the limitation of thelinear theory.The hydroelastic responses of a thin elastic plate due to uniformly moving andsuddenly started concentrated loads are systematically studied by means of analyticalmethods. A qualitative study is performed for the relation between the fexural–gravitywave motion and the moving velocities of the load, which provides a basis for the furtherinvestigation on the hydroelastic response caused by complex loads.