Research On Configuration Characteristics And Mechanical Properties Of Catenary Under Vertical Load

The catenary theory has become increasingly mature and widely used in engineering fields such as bridge suspension cables,anchor cables and electric cable erection.In terms of marine technology,catenary theory can also be used to study the deep-sea mining flexible cable.The good working configuration and stress condition of flexible cable are related to the efficiency of mining transportation and the safety of the whole mining system.Therefore,starting from catenary theory,this paper studies the configuration characteristics and mechanical characteristics of catenary under vertical load.This study can provide guidance for the design and development of flexible cable.At the same time,it can also provide some reference value for the analysis of pliable chains and ropes in engineering.The main research contents and conclusions are as follows:(1)Based on the classical catenary solution of the suspension structure,the nonlinear transcendental equation for calculating the horizontal tension of the catenary is derived by introducing the assumption of the catenary’s non extensibility and full flexibility.At the same time,a more simple calculation expression of the tangential tension and the vertical tension component at ends of the catenary is proposed.Based on the theory of catenary under uniform load,The nonlinear equations is established to calculate the geometry configuration and tension of catenary under vertical concentrated force.The equations consist of two unknowns which is the curvature diameter of catenary and the ordinate of the equilibrium position of the point of concentrated force.(2)Asynchronous solution is adopted in the calculation of equations.The equation system is transformed into a quadratic equation of one variable with the square of curvature diameter.Through the analysis of the coefficients of the equation,the equation has the special solution,the implicit solution,the multiple root and the general solution,while the general solution has two kinds of expressions of big one and small one.The special solution,the implicit solution and the multiple root of the equation are analyzed respectively,and the calculation expression corresponding to the curvature diameter is obtained.Meanwhile,the application of large solution and small solution of the equation is divided into different zones according to the value of vertical concentrated force,the position and the range of the balance position of the point of action of concentrated force.Through the analysis of the example,the errorbetween the calculation result of the algorithm in this paper and that of the algorithm in the literature is small.And,the stress configuration of catenary is basically consistent.(3)In view of the two vertical concentrated forces acting on the catenary,the nonlinear equations are established by introducing the transcendental equation,the force balance equation and the geometric configuration constraint equation of the catenary.Newton iterative method is used to solve the unknown number synchronously,and then the geometric configuration and tension of catenary are determined.(4)According to the positive and negative values of the generalized dip angle? of the left end point,the catenary is divided into three kinds of catenary with different geometric configuration features and mechanical characteristics.In the theory that catenary is only affected by uniform load,different geometric configuration conditions and tension conditions of catenary are taken as known quantities,and the geometric configuration and tension conditions of catenary are determined reversely.(5)The test is carried out by the flexible cable configuration and tension testing device.The comparison between the test results and the theoretical calculation results shows that the two results are in good agreement,which verifies the correctness of the theoretical derivation.