Zoi Stavrothanasi
Ansys Employee
Hello Emre,
It is true that, when massless springs are added to a model, commonly they contribute additional stiffness to the system. This increase in stiffness generally leads to higher natural frequencies. However, it is worth noting, that except friquency, other factors such as changes in mass distribution, boundary conditions, or damping effects can also influence the natural frequencies of the structure. 
You can find more detailed information about spring elements (COMBIN14, COMBIN39, COMBIN40) used in modal analyses in Ansys element librady.

Moreover, in the context of modal analysis, the eigenvalue problem is used to determine the natural frequencies and mode shapes of a vibrating system. For a clearer understanding of the concept, you may find the ”An Eigenvalue Problem — Lesson 3” video from Ansys Learning informative.

Hope these help!