6. Mass matrix

Obviously, this matrix only intervenes in dynamic problems. The pulley cable element is only used in the Code_Aster for quasistatic cable laying problems [§7].

Note:

However, [bib2] shows the example of a dynamic problem involving a cable-pulley.

The mass matrix of the element \({N}_{1}\) \({N}_{2}\) \({N}_{3}\) is obtained by assembling the « coherent » mass matrices of the two-node cable elements \({N}_{3}\) \({N}_{1}\) and \({N}_{3}\) \({N}_{2}\) [bib6] and adding the pulley’s point mass.

Note that during dynamic analysis, this mass matrix needs to be updated because the lengths \({l}_{1}\) and \({l}_{2}\) vary.