I am not that familiar with generators and am, therefore, unable to advise about idealization of the end windings.
Typically, the engineer will simplify the system to something that is idealized as a series of masses and springs. For a single degree of freedom system, this is a single mass and a spring. The spring stiffness is determined depending on the system configuration (for instance, a beam stiffness equivalent would be AE/L where A is the cross-sectional area, E is the modulus, and L is the length of the beam). The fundamental frequency is then calculated as the square root of k/m where k is the stiffness and m is the mass.
More complicated systems are more difficult, but all of this is covered in a basic vibrations course. Virtually any book on vibrations would have to cover this simplification methodology.
Someone more familiar with your particular application may be able to provide more specific examples.