The Nonlinear Analysis And Computation On Horizontal Catenary Under Concentrating Force

After years of practice and demonstration,the technical route of China's deep-sea mining is the use of hydraulic mining,the deep-sea mining system is mainly composed of a water platform,underwater lifting system and the crawler type collector is composed of three parts.The spatial shape of the hose in the lifting pipeline has a crucial influence on the safety and stability of the system,the autonomous walking of the ore collecting operation vehicle and the effective control of the trajectory.In this paper,catenary theory is used to analyze the force of flexible pipeline,which provides the basis for the design and analysis of deep sea mining system.With the method of theoretical analysis and program design of C,This research is based on the catenary theory,making nonlinear analysis and calculation about the catenary under concentrated force and providing the reference for the hose configuration design of the deep-sea mining system.The main research contents and conclusions are as follows:1.Use both of the arc length constraint equation and the boundary condition constraint equation of catenary to obtain the transcendental equation of catenary horizontal tension.With the dimensionless treatment for the transcendental equation acquired,the simplest parametric dependence of the horizontal tension is obtained and an optimized algorithm for solving the transcendental equation is also acquired.2.Discuss the intrinsic meaning of generalized dip angle ? and ?.Classify three categories of catenary,deduce the critical parameters of classification and at the meantime acquire the explicit function relation between the critical horizontal tension and catenary length and the vertical distance.3.Reveal the functional relationship between the constraint force and the tangential tension of the catenary which is at the upper and lower boundaries and the radius of curvature r or the geometric parameters s,c and l.This simple function relation do great help to solve mathematic problem and the inverse problem of catenary relaxation constraints.4.Acquire the balance equation that is permanently available when both the coverage force and the concentrated force put on the catenary and reveale the dependent function relationship between the segmental catenary and the concentrated force.5.Calculate the complex mechanical responses of catenary with different horizontal forces which is under different concentrated forces by non dimensional processing.The asymmetric and nonlinear behaviors of the maximum vertical distance difference worth extra attention.6.Derive the theoretical calculation formula which is available when any concentrated force is put on the catenary and the trace of horizontal catenary when a extremely concentrated force put on an exact or different point of it with various weight and from different directions.