A Mathematical Modeling Of Ship Lines Fairing Based On Two Vibration Numbers

This paper studies a mathematical modeling of ship lines fairing, which aims to improve the fairing efficiency and result. In view of the fact that the definition for fairing of the former theorys are unilateralism and inappropriate, we give an new definition by using the first vibration number R related to the concave-convex of curve and the second vibration number S related to swollen-shrivelled of curve. This fairing definition have the quantification standard and is suitable for each kind of spline function and the general function. At last, we designed a fairing method of ship lines based on the new fairing criterias.The contents of this paper are arranged as follow:Chapter 1 gives a brief introduction to the developument situation, present situation of ship lines lofting and some problems in it.Chapter 2 put forward a deinition and some criterias of fairing by using the vibration number R and vibration number S, which are more reasonable and practical.In Chapter 3 we treat the wood spline used in manual lofting to define ship lines as constant section thin girder with concentrated load, and we construct the spline function for mathematical modeling.Chapter 4 ,according to the two vibration numbers of the ship lines, we use the method of resilience and local-linear-interpolation to reduce the vibration R and the method of reduce swollen-shrivelled to reduce the vibration S.Chapter 5 gives some experiment result and analysis, and compare with the other algorithms, draws the conclusion and remarks on future research.