Low tension cables: the analytical solution and power series approach

CARLOS P. FILIPICH; MARTA B. ROSALES; PRISCILLA ALMEIDA

Brasilia, Brasil

Congreso; COBEM 2007 19th International Congress of Mechanical Engineering; 2007

As is known, low tension cables (or chains) adopt a catenary curve when subjected to self weight. The dynamic problem governing equations are derived in which the static problem of the slack cable is included.  The cable is fixed at one end (A) while the other end (B), not fixed, is at a different level. The slope at the fixed end is assumed arbitrary. When this type of cable or chain is employed as a mooring device, it is necessary to know the forces for each geometric configuration specially at end B. First, the analytical solution is stated and from it values of the horizontal and vertical forces at end B may be found for different values of static displacements (q, horizontal and h, vertical) at that end. On the other hand, being this the main goal, a power series approach was employed to obtain explicit expansions of the horizontal and vertical forces in terms of q and h. The availability of these expansions allows us to introduce these forces in a quasi-static analysis of the general problem of a floating platform. The series may be introduced in the dynamic differential equations that govern the strongly non-linear motion of the platform.