The need for mesh refinement in a structural analysis module such as Static or Transient is quite clear; if we want the overall results such as displacement and stresses to be more accurate within the elements, then by refining the mesh size we should be able to achieve this. This happens because the mesh refinement improves the quality of the mesh elements and hence the shape functions (of each element) also becomes more accurate and closer to its ideal form, which in turn improves the accuracy of the results within the elements.
But for modal analysis, I couldn't understand the reason that why would inserting more mesh elements within my model would change the natural frequency results? I mean the purpose of modal analysis is not to acquire nodal displacements, neither obtain any elemental strain or stress results; displacements are random and strain/stress results don't exist since there is no force application at all. So why modal fequencies have dependence on the mesh size?
Below shows an example I just did to further elaborate my point.
I mean this is just one body which has a certain mass, and this body has an overall only 6 DOFs, with stiffness in all of these DOFs. Why can't I just idealize this body with a single mass 'm', and with six springs with certain stiffnesses in all 6 directions? Why do I need to associate a mass and stiffness with each separate element and then conduct a modal analysis in FEA?