The method we use is currently only applicable to simple-simple boundary conditions, therefore changing the BCs on the buckling tab will not affect the natural frequency results. The boundary conditions specified on this tab are applicable to panel buckling only.
The method we use is a standard plate based modal analysis with simple-simple BCs. Unfortunately we have no formal documentation for this method yet.
The method we are using is based on the following:
Whitney, J., Structural Analysis of Laminate Anisotropic Plates, Technomic Publishing Company, 1987.
The method is described in Section 7.7 (pp. 197-203)
Formal documentation of this method should be coming sometime soon.