Firstly, the cubic spline interpolation is adopted for modeling the flexible cable elements and the virtual 1powers of tensile strain, inertia and gravity forces on the cable are formulated.
A party line is formulated and chosen.
Then a continuum model of the central span (deck, cables, and hangers) is formulated.
An elastic continuous monodimensional model for damaged cables, including geometric nonlinearities, is formulated for the purpose.
A three-node curved isoparametric finite element is formulated for dynamic analysis of bridge stay cables by regarding the cable as a combination of an "ideal cable element" and a fictitious curved beam element in the variational sense.
A finite element model with multiple degrees-of-freedom is formulated for the hybrid system of a sagged stay cable incorporated with MR dampers.
Since the element is formulated within the framework of large curvature assumption, cables with large sag, as encountered in long-span cable-stayed bridges and suspension bridges, can be modeled accurately.
A parametric section model is formulated to synthetically describe the geometrically nonlinear dynamics of cable-stayed and suspended bridges through a planar elastic multi-body system.
Next, the proposed DPC method is formulated.
Free vibrations of the passively controlled cable system have then been formulated analytically through complex modal analysis.
