A discussion regarding reduced-order modelling of inclined elastic and immersed cables under support excitation. (October 2022) - Vernizzi, Guilherme Jorge; Lenci, Stefano; Franzini, Guilherme Rosa
Abstract: This paper investigates the advantages or issues of different reduced-order models (ROMs) for the analysis of elastic cables hanging between two supports at different height. The cable is considered immersed in still fluid and under the action of an imposed boundary motion at the upper support. Nine ROMs are explored, obtained from the combination of three different functions responsible for ensuring the interpolation of the boundary motion with three possible sets of projection functions associated with the degrees of freedom (DOF). For the interpolation functions, the possibilities are: (i) a linear interpolation, (ii) a linear interpolation with a decomposition in axial and transversal directions according to the local angle of each cross-section, or, (iii) a quasi-static approach using the static displacement of the cable due to a unitary displacement applied at the moving boundary. Regarding the number of DOFs, the possible functions sets consists of a single mode of vibration, three modes of vibration, or, a group of five trigonometric functions. The ROMs are then simulated for different conditions and the results are compared to a reference case obtained from Finite Element Method (FEM). Additionally to the numerical analysis, a novel semi-analytical solution is proposed for the single DOF ROMs based on the method of multiple time scales (MMTS). Such solution tackles an issue of using the Morrison damping since it contains an absolute value function in its formulation which makes it unfeasible to compute the integrals that appear in the Galerkin method without knowing the response of the structure. The results show that the choice of the function to interpolate the top motion effects is of top-most importance, since a poor choice of that set of functions leads to low accuracy in the results that cannot be solved by adding more DOFs to the ROM. It is also shown that working with more complex functions instead of simple trigonometric functions leads to a significance enhancement of the computational performance of the simulations. Highlights: To our best knowledge, the present ROM comparison is new in the literature. Poor function choice for top-motion effects causes unsolvable innacuracy in the ROMs. Qualitative analysis towards better projection basis leads to faster accurate ROMs. A semi-analytical MMTS solution is presented to treat sums in the Morrison damping. The ROMs and analytical solution can be automated for a large number of simulations.