Modal Analysis with Cable Member/Members, Unstable Structure

In the case of models with membranes / cable members, an initial prestress allows for the convergence of the calculation. In RFEM 6, there are two options for considering the initial prestress: an initial state or a minimum change in length. In addition to numerical convergence, it is even more important to consider that the natural frequencies of a cable depend on the initial tension: it is necessary to have a tensile load, and its magnitude influences the results.

For a simply supported cable with only self-weight, a modal analysis without an initial state is defined:

1 Single-Span System | Member Type: Cable Member | FAQ 005668

The result is the error message “10060 - The stiffness matrix is singular | The structure is unstable”:

2 Modal Analysis Without Initial Condition

The first solution is to select a load case with tensile force as an initial state. In this case, considering the nonlinearities (third-order analysis) of a cable element, a horizontal reaction results from a pure vertical load. The horizontal reaction corresponds to a tensile force. It's important to emphasize that the load cases or load combinations of the "Mass Source" option have no influence on the stiffness matrix. Therefore, two selections are necessary.

3 Modal Analysis with Initial State

The second option is to define an initial deformation in the modal case setting.

4 Modal Analysis with Initial Prestress

It is recommended to evaluate the influence of the initial values (initial state or minimum change in length) on the vibration modes. Relatively small variations of these values may lead to significant changes in the natural frequencies.