A REDUCED ORDER MODEL OF TWO AND THREE-DIMENSIONAL SLACK CABLES

MARIO R. ESCALANTE; MARTA B. ROSALES; RUBENS SAMPAIO; THIAGO RITTO

Ribeirao Preto

Congreso; COBEM 2013 - 22nd International Congress of Mechanical Engineering; 2013

Associação Brasileira de Ciências Mecânicas ABCM

Cables and other flexible pipes are found in many applications of Civil, Aerospace, and Mechanical Engineering. Many offshore problems involve slender rods or cables (pipelines, risers and mooring lines). To design efficient structures, usually non-linear unidimensional theories are used to predict their dynamic response. Here, two models are analyzed, two-dimensional and three-dimensional representations of a slack cable, respectively. Since an economical and efficient model is desired to perform parametric studies, a Proper Orthogonal Decomposition (POD) and a Galerkin projection are performed to obtain a Reduced Order Model (ROM) for each case. The plane cable case ROM is constructed using a basis derived from the dynamics of an inextensible chain (a similar and simpler problem). The three-dimensional cable is modeled considering also the bending and torsional rigidities. A POD is performed on an accurate dynamic model previously solved by a finite element discretization. Different dynamic actions are evaluated in both cases and verifications with complete models are shown. The response of the cables to prescribed, low and high speed, dynamic displacements at one of the ends is evaluated and in the tridimensional case, an end angular motion is added. The necessary number of Proper Orthogonal Modes is assessed.